A New and Improved Spin-Dependent Dark Matter Exclusion Limit Using the PICASSO Experiment

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1 A New and Improved Spin-Dependent Dark Matter Exclusion Limit Using the PICASSO Experiment by Kenneth John Clark A thesis submitted to the Department of Physics, Engineering Physics and Astronomy in conformity with the requirements for the degree of Doctor of Philosophy Queen s University Kingston, Ontario, Canada July 28 Copyright c Kenneth John Clark, 28

2 ABSTRACT The PICASSO project is a direct dark matter search experiment located 27 metres underground in SNOLAB. Superheated droplets of Freon (C 4 F ) are used as the active mass, providing a target for the incoming neutralinos. Recoiling nuclei deposit energy in the superheated Freon droplets, triggering a phase transition, the pressure waves of which can be detected using piezo-electric sensors. Previously published limits using an exposure of.98±.9 kg day obtained a peak spin-dependent cross section exclusion limit for neutralino-proton interactions of.3 pb at a neutralino mass of 29 GeV/c 2 at a 9% confidence level (). Improvements in the detectors installed in the underground experiment have provided 2.99±.25 kg day for analysis and improvements in the analysis method have produced an exclusion limit of pb at a neutralino mass of 6.7 GeV/c 2. In addition, a thorough study of the backgrounds, corrections and systematic uncertainties has been included, indicating that this limit does not exceed pb when considering the one sigma error on the uncertainty band. ii

3 ACKNOWLEDGEMENTS It has been said that it takes a village to raise a child, and it is my personal opinion that it probably takes many villages to successfully raise a thesis. I can thank only a handful of people here, however the contributions of many others have certainly been appreciated along this journey. I would like to thank my supervisor, Tony Noble, for his direction and assistance during my time here. There has never been a deadline too tight or a submission too late for him to provide constructive feedback, which has been extremely helpful. Carsten Krauss also deserves much praise for teaching me to properly use C++, and an immense amount of credit for persevering through my struggles to learn ROOT. In addition, he has shown me how much a post-doc can accomplish and how to be a good scientist. I can only aspire to the day when threats with the hockey stick are a thing of the past. I also must thank the members of the PICASSO collaboration for their assistance during my time here. In particular, Connie Storey was a great office mate, providing me with useful input when it was needed and knowing when it was time for a break. The entire community at Queen s has been very supportive, but in particular I would acknowledge the contributions of Alex Wright for his many physics and non-physics related discussions and Chuck Hearns for being willing to help at any iii

4 Acknowledgements iv time. Finally I would like to thank my family for their unending support and Nicole Mideo for putting up with me during this entire process. I will never be able to properly express how much her support has meant.

5 STATEMENT OF ORIGINALITY The work contained in this thesis has been done primarily by myself with the assistance of members of the PICASSO collaboration, unless otherwise noted. The development of the code used for this analysis was my own, including the development of the PDF generating functions and the analysis routines. In addition, I developed the code to allow quick monitoring of the data taken in the underground experimental setup. In terms of the mechanical design work, I built a clean room for detector development, led the design and building of the temperature and pressure control systems, led the construction of the experiment superstructure and the installation of the first two TPCSs and the initial detectors in the underground environment. Several of these involved participating in safety reviews of the heating and electrical systems. I have also assisted in the creation and operation of a working detector testing site at Queen s. The successful design, installation and operation of the experiment at SNOLAB was largely my responsibility and took several years to accomplish. Finally, tasks involved in maintaining the operation of the experiment were also undertaken. This included taking data monitoring shifts as well as the installation and removal of calibration sources. v

6 CONTENTS Abstract ii Acknowledgements iii Statement of Originality v Table of Contents vi List of Figures xi List of Tables xvii Chapter. Introduction Objectives Chapter 2. Dark Matter Evidence for Existence Rotation Curves Cosmic Microwave Background Supernova Studies Summary of Evidence Candidates vi

7 Contents vii 2.2. The Axion The Neutralino Experiments Indirect Detection Experiments Direct Detection Experiments Detection State of Searches Spin-Independent Searches Spin-Dependent Searches Chapter 3. The PICASSO Experiment Detectors Composition Active Mass Gel Matrix Fabrication Temperature and Pressure Control Method of Detection Readout Location PICASSO Experimental Operation Chapter 4. Data Analysis I: Event Selection Underground Calibration Runs

8 Contents viii 4..2 Spike Cut Power Cut Pre-trigger Noise Cut Time-Binned Fourier Transform Burst Cut Multiplicity Cut Event Selection Summary Chapter 5. Data Analysis II: Signal Extraction Scope of this Analysis Detector Selection Detector Fabrication Container Damage Inappropriate Fitting Alpha Response Function Gamma Response Function Neutron Response Function Neutralino Function Fitting Exclusion Limit Fits Analysis of Previously Published Data Stability of Fits Combined Fits

9 Contents ix Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 3 6. Corrections Cut Discrimination Efficiencies Run length Correction Ambient Pressure Correction Summary Systematic Temperature and Pressure Related Uncertainties Temperature uncertainty and non-uniformity Z position pressure dependence Summary Systematic Count Rate Uncertainties Piezo efficiency Active mass measurement Cut Efficiency Uncertainty Summary Systematic Fitting Procedure Uncertainties Alpha PDF Fit Uncertainty Fit Contamination Value Uncertainty Summary Neutron Backgrounds Thermal Neutrons Fast Neutrons Summary

10 Contents x Chapter 7. Results and Discussion Results Background PDF Fits Exclusion Curve Effects of Uncertainties Discussion Significance of the Result Future Improvements Conclusion References Appendix

11 LIST OF FIGURES 2. Example rotation curve A summary of the results measuring the energy and matter densities in the Universe Spin dependent scattering interaction Spin independent scattering interaction Sample of Spin-Independent Exclusion Curves Sample of Spin-dependent Exclusion Curves PICASSO detector efficiency vs energy deposit PICASSO container in side view PICASSO container in top view Photo of a PICASSO detector Sketch of the top plate of the PICASSO TPCS Top view sketch of the PICASSO TPCS Sketch of the piezo sensors as used on the PICASSO detectors DAQ schematic Underground location of the PICASSO experimental setup Neutron flux as a function of depth in equivalent metres of water Set temperature during PICASSO WIMP runs as a function of time. 52 xi

12 List of Figures xii 3.2 Breakdown of total time into run type Sum of fourier transform histograms of 782 events in detector 72 during calibration run Location of the neutron calibration source used for the first generation DAQ Location of the neutron calibration source, independent 3 He neutron detector and PICASSO TPCSs for second generation DAQ Example of a spike event from PICASSO data Expansion of time axis for the example spike event from PICASSO data Power cut value distribution for detector 99 in runs.6.2 and Zoom of power cut value distribution for detector 99 in runs.6.2 and Examples of good signals and associated Fourier Transforms Examples of bad signals and associated Fourier Transforms Time binned Fourier transform region definition used with the second generation DAQ Example of the time-binned Fourier transform of a signal which is well-contained in the expected region Example of the time-binned Fourier transform of a signal which is not well contained in the expected region

13 List of Figures xiii 4.3 Cut value distribution for detector 75 in runs.. and.78.. This data was taken using the old DAQ system Trigger time difference, detector 99, run.62.2 The time difference is the measured time between two consecutive events Probability of having two events within time window as exhibited by detector 99 at 52 C Temperature dependent count rate for detector Live time by temperature for detectors Live time by temperature for detectors Live time by temperature for detectors Alpha-emitter spiked detector responses Fits to spiked detectors 39 and Detector response of a radon-spiked detector Fit to response of radon-spiked detector Detector response with close proximity to gamma source Detector response with close proximity to gamma source fit to gamma function Detector response with close proximity to gamma source fit to gamma function Expected detector response to neutralinos of varying masses with a total nuclear cross section of pb PDF fits to detector

14 List of Figures xiv 5.4 Alpha and gamma PDF fits for detectors Alpha and gamma PDF fits for detectors Alpha and gamma PDF fits for detectors Exclusion curve determined using detector Example neutralino response curves Effect of increasing fit cross section for 23 GeV neutralino by a factor of five PICASSO data used in () Comparison of the shape of the 5 GeV neutralino and alpha response Lack of stability of detector 75 neutralino fit Exclusion curve determined using detectors 72 and Hardware dead time fraction vs temperature for runs taken with Software dead time fractions vs temperature for detector Boiling point of C 4 F with ambient pressure variation Ambient pressure range during PICASSO WIMP runs Deviation from average ambient pressure during PICASSO WIMP runs Count rate for detector #72 with ambient pressure and dead time adjustments Temperature offset from measured value for temperature sensors Deviation from set temperature for data runs Event identification efficiency by temperature for detectors Each point represents a different run

15 List of Figures xv 6. Event identification efficiency by temperature for detectors Each point represents a different run Event identification efficiency by temperature for detectors Each point represents a different run Droplet surface based alpha PDF showing variation in function caused by a one standard deviation variation in the parameters Effects on the exclusion curve caused by varying the droplet surface based alpha PDF parameters by one standard deviation Gel based alpha PDF showing variation in function caused by a one standard deviation variation in the parameters Effects on the exclusion curve caused by varying the alpha contamination parameter by one standard deviation Temperature dependent count rate for detector 72 with background PDF fit Temperature dependent count rate for detector 93 with background PDF fit Temperature dependent count rate for detector 8 with background PDF fit Exclusion curve determined using detectors 7, 72, 93 and Range of exclusion curve due to systematic uncertainties Comparison of the exclusion curve of this analysis with results from several world-leading experiments

16 List of Figures xvi 7.7 Comparison of exclusion curve of this analysis including theoretical predictions

17 LIST OF TABLES 2. Fit values obtained from the study of three years of WMAP data MSSM particles Thermodynamic properties of Freon gases Time-binned Fourier transform area definitions Summary of effects of cuts on calibration data using the first generation DAQ Summary of effects of cuts on WIMP data using the first generation DAQ Summary of neutron count rates and efficiencies in calibration runs Summary of trigger and bubble rates during a WIMP and calibration run using the new DAQ Increase in trigger and bubble rate in a WIMP and calibration run using the new DAQ Total live time for each detector used for data taking by PICASSO during the analysis period Effective spin values for selected nuclei xvii

18 List of Tables xviii 6. Trigger rate of detectors #7, 72 and 76 during WIMP runs using first generation DAQ, in triggers/hour/gram Cut efficiencies using the first generation DAQ Total cut efficiency using the first generation DAQ Hardware dead time summary Summary of the software dead time created by the burst cut for each operational detector Effective temperatures calculated using reduced superheat equation Average detector efficiencies due to piezos for good events, averaged over all runs Active mass of current detectors Count rate uncertainty summary Thermal neutron cross sections Definition of extent of live time used in the final analysis A. Runs used in analysis taken with the first generation DAQ A.2 Runs used in analysis taken with second generation DAQ

19 Chapter. INTRODUCTION. Objectives An astonishing conclusion from modern precision astronomy is that only 5% of the matter and energy in the Universe is in forms that we know today. An understanding of the nature of the completely unknown missing energy and missing mass is one of the most active areas of research today. The missing matter is generally expected to be in a form such that it could be detected on Earth in rare interactions. Hence a great deal of effort is being expended in many experiments around the world to be the first to detect this matter. One of the experiments currently operating is known as the PICASSO (Project in CAnada to Search for Supersymmetric Objects) experiment. The detectors used by the PICASSO collaboration consist of 4.5 litre acrylic containers containing an emulsion of superheated Freon droplets in a gel matrix. In a reaction similar to that used in bubble chambers (or detectors), incoming particles will strike nuclei in the active mass (Freon in the case of the PICASSO detectors), causing the recoil of a nucleus. This nucleus will deposit energy along the path of its recoil, which will provide sufficient stimulus to cause a phase transition in the superheated droplets. This phase transition can be observed experimentally, thereby signalling the occurrence of an interaction. The enhanced spin-dependent

20 Chapter. Introduction 2 cross section of Fluorine ensures sensitivity to spin-dependent interactions, one of the possible mechanisms with which these dark matter particles will interact with matter. The use of superheated droplets as a tool for the detection of neutralinos provides an excellent mechanism to discriminate events caused by nuclear recoils from those caused by other energy depositions, such as the ionization tracks resulting from gamma, beta or alpha particles. The superheated droplets are threshold detectors, as they are able to observe all interactions above a particular energy threshold. This critical energy is controllable using the ambient temperature of the droplets, providing a temperature-dependent threshold for the energy deposition. The PICASSO detectors are contained within specially designed containers that allow accurate temperature control, enabling differentiation between types of particles based on their energy depositions. In this thesis, the process used to search for evidence of the missing matter from the recent PICASSO detector data will be described, with an emphasis on data analysis. Chapter 2 discusses the known evidence indicating that matter is missing from the Universe and contains details concerning the possible candidates which could make up this missing matter. In addition, a number of previously and currently operating experiments are briefly outlined to provide an overview of the state of experimental evidence. Chapter 3 describes the methods used by the PICASSO collaboration in detail. All operational aspects of the experiment are included, as well as the theory describing the detector thresholds. The physical components of the detectors are also

21 Chapter. Introduction 3 described in this section. A description of the mechanisms used to read signals from the detectors finishes the chapter. Accounts of the data analysis procedure begin in chapter 4 with discussion of the separation of nuclear recoil related events from other background events. In addition, the distinction between events associated with droplet nucleations and those caused by acoustic noise is also included. The data analysis continues into chapter 5, which is concentrated on estimating the possible dark matter contribution from the data. The mathematics underlying the predictions for the missing matter interaction rate are also located in chapter 5, as well as the process of fitting the temperature dependent response curves from the detectors. Studying the systematic uncertainties, backgrounds and corrections makes up chapter 6. Topics of great importance to the final result, such as the neutron background in the experimental area, uncertainties associated with the data taken and dead time corrections are defined in this chapter. The result of this work has been to establish a new limit on the cross-section for possible Dark Matter interactions with normal matter. This limit is presented in the form of an exclusion curve corresponding to a particular confidence level which is determined as a function of mass for the assumed particles. Chapter 7 discusses this result, how it is to be understood in terms of the estimated systematic uncertainties, and how these results fit when compared with other dark matter search experiments, particularly those exhibiting spin-dependent exclusion limits. The conclusion is also contained at the end of this chapter.

22 Chapter 2. DARK MATTER The fields of astronomy and cosmology have provided substantial information indicating that there is more matter in the universe than can be accounted for using current observational methods. In the past 2 years, this knowledge has driven scientists to intensify their efforts to understand the constituents of the universe using a variety of methods. In addition, theoretical particle physicists have had the opportunity to develop potential mechanisms to explain this missing matter. In the more recent past, experimental physicists have taken the initiative, creating many experiments designed to detect some direct evidence of this dark matter. These experiments may provide the opportunity to first detect and then characterize this unknown form of matter. 2. Evidence for Existence Investigation into the nature of the Universe has provided several pieces of evidence supporting the existence of dark matter. This evidence is taken from such widely ranging fields as observational and microwave astronomy, and studies of the creation of elements during the big bang, referred to as nucleosynthesis. The combination of all of this information presents a coherent picture of the structure of the missing matter in the Universe. A selection of several pieces of evidence indicating the 4

23 Chapter 2. Dark Matter 5 existence of dark matter will be discussed in detail. The majority of the evidence supporting the existence of dark matter in the universe is taken in the framework of the ΛCDM model, also referred to as the concordance model of cosmology. This is the simplest model which explains the cosmic microwave background and supernovae observations as well as the large scale structure data. The Λ represents the cosmological constant, or dark energy, a term describing the accelerating expansion of the universe, while the CDM portion of the name stands for Cold Dark Matter. In this model the missing matter is taken to be non-relativistic, non-baryonic and collisionless. This is the simplest model, which is consistent with parameters derived from the Cosmic Microwave Background, supernova studies and big bang cosmology. 2.. Rotation Curves The most simply understood piece of evidence for the existence of dark matter came from the study of the rotation curves of galaxies. The orbital velocity of the stars in a galaxy can be plotted versus the distance from the centre of the galaxy, producing curves such as the one shown in Figure 2.. In Figure 2., the data points representing the observational data from galaxy NGC 653 are shown as points with their associated error bars. In addition, a fit to this data has been divided into the contributions from several constituent components of the curve. These components are the visible disk, the gas surrounding the galaxy and the dark matter halo, as indicated in the Figure. The sum of these components results in a response which fits the data points very well.

24 Chapter 2. Dark Matter 6 Figure 2.: Rotation curve for galaxy NGC 653 from (2) Using standard Newtonian dynamics, the velocity of any particle as a function of the distance from the centre of the galaxy can be expressed as in Equation 2. and the mass function as shown in Equation 2.2, taken from reference (2). In equations 2. and 2.2, r represents the radius, the distance from the centre of the galaxy, G is the gravitational constant, M(r) is the mass of the galaxy within radius r, v(r) is the radially dependent velocity and ρ(r) is the density of the matter at radius r. GM(r) v(r) = (2.) r R M(R) = 4π ρ(r)r 2 dr (2.2) Combining Equations 2. and 2.2 along with the fact that the amount of matter detectable using visual methods diminishes as the radius from the centre increases results in an expected decrease in rotational velocity at large radius. This effect is

25 Chapter 2. Dark Matter 7 exhibited by the disk portion of Figure 2.. The continuation of a flat rotation curve at large radii implies that there is more matter present than can be seen visually. This matter is situated in a halo surrounding the galaxy, as represented in Figure 2.. The discrepancy between the observed and expected rotation curves can be explained in some theories which remove the assumption that Newtonian dynamics properly represents galactic systems. Other competing theories have been proposed which can explain the observations without including extra matter. The most prevalent of these theories is MOdified Newtonian Dynamics (MOND), first proposed by Mordehai Milgrom (3). These authors point out that all evidence of dark matter is indirect, and accurately describes this anomaly as a discrepancy between the observed mass and Newtonian prediction of velocity for a system. These theories suggest that either the observed mass or the Newtonian prediction must be incorrect. The required change to the Newtonian system can be illustrated by examining the equations before and after the modification is applied. With standard Newtonian dynamics, a test particle located a distance r from an object of mass M undergoes an acceleration due to that mass as shown in equation 2.3. a = MG r 2 (2.3) MOND would modify this equation through the introduction of a function µ(x), which gives a value of if x is very large, but a variable value for <x<. The modified expression is shown in equation 2.4.

26 Chapter 2. Dark Matter 8 ( ) a µ a = MG (2.4) a r 2 The introduction of the function µ along with a constant a allows the acceleration due to gravity to be modified only at small accelerations (when a a ) and unchanged at large accelerations when (a a ). Hence, there is no modification to the velocity profiles in the inner reaches of the galaxies where standard rotation curves can fit the observable data. The modifications mostly affect the outer portion of the galaxy and allow fits to the observed velocity profiles without the need for dark matter. While this theory can be used to explain the discrepancy in the rotation curves however, there are still several other pieces of evidence for the existence of dark matter which cannot be explained by this modification. Hence it is not the generally accepted explanation for the apparent existence of dark matter Cosmic Microwave Background When presenting details concerning the abundance of materials in the universe, the values are typically scaled by ρ c, the critical density of the universe. The definition of the critical density is shown in equation 2.5, making the assumption that the cosmological constant is zero and satisfying the condition that the universe be flat. ρ c = 3H2 8πG (2.5) In equation 2.5, H is the Hubble parameter, the rate of expansion of the universe and G is the gravitational constant. The currently accepted value for H was

27 Chapter 2. Dark Matter 9 determined by the Chandra X-ray Observatory to be 77 (km/s)/mpc with an uncertainty of 5% (4). The abundance of the constituents of the Universe can then be expressed relative to this critical value, using the symbol Ω i for the i th constituent. The form of this calculation is expressed in Equation 2.6, in which the density of the i th constituent is expressed as ρ i. Ω i = ρ i ρ c (2.6) The constituents of the Universe are typically categorized into several components: matter (Ω M ), dark energy, also referred to as the cosmological constant (Ω Λ ), and radiation (Ω r ). The matter component can be further subdivided into baryonic matter (Ω b ) and dark matter (Ω DM ). Specific species of baryons can be included separately if desired. It is also possible to include the neutrino contribution to the total energy density separately as another factor, typically Ω ν. There are many experiments which have been used to determine these energy and matter densities, the combination of which provide a rather complete understanding of the make up of the Universe. These experiments primarily study two sources of information. One of the main sources of information concerning the energy density of the Universe is the Cosmic Microwave Background (CMB). Although the existence of this radiation has been known for more than forty years, its use in the extraction of energy/matter density information has only been possible during the past decade, when technological advances allowed ultra-sensitive satellite-based detectors to be

28 Chapter 2. Dark Matter deployed. CMB experiments involve the study of photons immediately following their decoupling from matter in the early universe. In the very early Universe, the high energies prevented the protons and electrons from forming neutral atoms. As the Universe expanded, it cooled and eventually this allowed the free protons and electrons to form neutral hydrogen. Prior to this recombination, photons scattered continuously off the free ions in this hot dense plasma. After recombination, the photons no longer scattered and they became essentially decoupled from matter. These are the relic photons observed today as the cosmic microwave background. The information carried by these photons from the final scattering off the free ions and, in particular, the density anisotropy of the Universe at that time, has been preserved. Currently the Universe has expanded sufficiently to allow the background temperature to reach approximately 2.7 K, which corresponds to photons of microwave energies. These last scattered photons are observed to have small (one part in 5 ) anisotropies in temperature, characteristic of the density perturbations at that time. These small variations are separated into two varieties: primary anisotropies, which are due to the last scattering of the photons from the charged plasma and secondary anisotropies, caused by any effect after recombination. The fitting of these anisotropies to models of the scattering can provide information used to give insight into the energy and matter density of the universe. Several experiments have used innovative analysis techniques to determine several important cosmological parameters from measurements of the CMB. Currently, the most prominent results in these interpretations have come from the Wilkinson

29 Chapter 2. Dark Matter Parameter Definition Fit Value ω m Ω m h ω b Ω b h ±.73 H Hubble constant σ 8 fluctuation amplitude.958±.6 τ optical depth.89±.3 n s scalar perturbation spectrum slope Table 2.: Fit values obtained from the study of three years of WMAP data (5). Microwave Anisotropy Probe (WMAP). The simplest model used for these fits is considered to be the ΛCDM model, which can be used to describe the WMAP data well, although additional parameters are added in the final fit to achieve the best results. This model fits the fluctuations seen in the CMB using six parameters, ω m, ω b, H, σ 8, τ, and n s. These parameters represent the matter density and baryon density of the Universe, the Hubble constant, the amplitude of fluctuations, the reionization optical depth, and the slope of the scalar perturbation spectrum, respectively. Using the most recent WMAP data to derive the parameters outlined above (as well as several others used to improve the quality of the fit) results (5) in values as shown in Table 2.. One observes from Table 2. that the total matter density is measured to a high degree of precision and that it is much greater than the baryon component, clearly indicating a substantial source of non-baryonic matter in the universe.

30 Chapter 2. Dark Matter Supernova Studies Observational astronomers have also been able to derive a great deal of information by studying supernovae using instruments such as the Hubble Space Telescope (HST). Supernovae classification relies on the spectral lines in the emitted light. Of particular use to the derivation of cosmological parameters are Type Ia supernovae. These supernovae are known as standard candles as they produce a well understood characteristic luminosity over time following their explosion and have a well-defined peak luminosity. This allows their use as a known luminosity source with which to study the distance of the explosion from Earth, as well as their recession velocity (redshift). They may be identified spectroscopically as those in which there are no Hydrogen lines, but the strongly ionized Silicon line is present. The characteristic spectrum, as well as the known peak luminosity make Type Ia supernovae ideal for the study of the expansion of the universe. This expansion is driven by the energy in the universe and so these studies are sensitive to a combination of the energy density and the matter density of the Universe, Ω Λ and Ω M. Several groups have contributed to the result in this area, with the combination showing the energy density of the universe to be Ω Λ = (statistical)±.4(identified systematics) and the matter density of the universe Ω M = (statistical)±.4(identified systematics) (6). These numbers are derived assuming a flat universe, as previously outlined.

31 Chapter 2. Dark Matter Summary of Evidence The pieces of evidence outlined in the previous sections can be combined to show the state of knowledge of the universe constituents, as shown in Figure 2.2. Figure 2.2 shows the remarkable concordance between several different methods of measuring the dark energy and matter density of the universe. Using the fits shown, it is found that the most probable energy density of the universe is approximately.7 and the matter density is approximately.3. This indicates that 7% of the universe (measured in terms of energy) is made up of unknown dark energy and 3% is matter. The constraints presented by the CMB experiments indicate that the baryon fraction of the universe (Ω b ) is approximately.4, requiring non-baryonic dark matter to constitute the remaining 26% of the energy and matter in the Universe. There are other sources of evidence which have not been mentioned here, including simulations attempting to recreate the formation of structure in the universe and the matter distributions observed following the collisions of galaxy clusters (7). All of these sources of information, observed using many sources and across many scales of size, indicate that dark matter makes up a significant portion of the energy and matter density of the universe. 2.2 Candidates There are many potential candidate particles which could make up the dark matter. All of these candidates must posses several characteristics as defined by the experimental results. The first of these is that the candidates must be non-baryonic. While it is possible that some of the missing mass is in the form of non-luminous ordinary

32 Chapter 2. Dark Matter 4 Figure 2.2: A summary of the results measuring the energy and matter densities in the Universe. The combined results, from rotation curves (Clusters), the cosmic microwave background anisotropies (CMB) and the expansion rate of the Universe (Supernovae) agree with one another very convincingly and are in agreement with the big bang nucleosynthesis. These results lead to the unavoidable conclusion that the Universe is comprised largely of missing Dark Matter and Dark Energy. Taken from (6)

33 Chapter 2. Dark Matter 5 baryonic matter - for example in the form of neutron stars, planets, brown dwarfs, etc. - such objects have not been found in sufficient quantities and the CMB results clearly indicate that the majority of the missing mass is non-baryonic in nature. The candidate particles must also not interact electromagnetically, as any interaction with light would have rendered this mass detectable using standard optical techniques. Additionally, the particles should be non-relativistic, or cold. This restriction arises from the study of structure formation in the galaxy. Since dark matter makes up such a large fraction of the energy and matter density of the galaxy, it has a large effect on the formation of structure. If the particles are created relativistically, models indicate that the structures formed in this scenario would be too large and form too late in the evolution of the universe (8). The final restriction on the nature of the candidates is that the particles should have a large relic density. This requirement arises for two different reasons. Since dark matter has such a large role in the formation of structure in the universe, and evidence indicates that effects are still apparent, the particle must not decay over cosmological time scales. The second reason is that the WMAP results require a large relic density in order to obtain good fit results (5). The CMB results have defined the density of non-baryonic dark matter in the universe; however, some fraction of the baryon density of the universe remains unobserved. There are collaborations searching for this unobserved baryonic contribution to dark matter; however, the full extent has not been conclusively located. In particular, the EROS collaboration has studied microlensing (the gravitational bending of light by large masses) in the Large Magellanic Cloud to determine the amount of

34 Chapter 2. Dark Matter 6 baryonic matter which was not previously included in calculations. This experiment determined that baryonic dark matter candidates could account for approximately 8% of the halo mass (9), suggesting the existence of additional non-baryonic constituents. There are two non-baryonic candidates currently popular with experiments directly searching for dark matter. These are the axion and the neutralino, both having their origins in solutions to Standard Model problems. Both of these particles interact weakly, would have a large relic density, and are non-relativistic, satisfying the requirements on the expected properties of the dark matter candidate The Axion Quantum ChromoDynamics (QCD) has proven to be an excellent model for strong interactions in the standard model (), however there exists a lagrangian of the vacuum state which permits the violation of charge conjugation and parity (CP). If this structure were large, the neutron would possess a large dipole moment, which has not been measured and so must be unnaturally small or zero. One solution to this disparity is to introduce a new symmetry (the Peccei-Quinn symmetry) which balances the CP violating term. This symmetry is spontaneously broken, resulting in a new particle (referred to as the axion). The axion should be massless, but quantum vacuum fluctuations ruin the symmetry and provide it with a very small mass. Although experiments exist which are actively searching for the axion, no indication of this particle has been found.

35 Chapter 2. Dark Matter The Neutralino A full review of the theory supporting supersymmetry (SUSY) is beyond the scope of this work. A brief review, supplying sufficient information to allow discussion of the dark matter candidate particles, is included. The primary motivation behind the creation of supersymmetric theory is the hierarchy problem. Using only the Standard Model (SM), calculating the mass of the Higgs boson results in quadratic divergences. These divergences can be removed if another group of particles is included in the calculation, extending the SM. Each SM particle would have a SUSY partner with the spin of the partner differing from the SM particle by /2. Since none of these particles has been found to date, it is assumed that this is a broken symmetry, resulting in the particles and their partners having different masses, with the new supersymmetric partners being at very high masses, unobservable to date in particle accelerator experiments. It is interesting to note that the new accelerator complex at CERN, presently nearing completion, may well have the ability to produce and detect supersymmetric particles. Supersymmetric theories come in several varieties, differing primarily in the number of particles added. The model requiring the least additions to the Standard Model is the Minimal Supersymmetric extension of the Standard Model (MSSM), which requires only two Higgs doublets on top of the superpartners to the Standard Model particles. These doublets are required to give mass to both the up and down type quarks, as well as charged leptons. The SM particles and their MSSM partners are shown in Table 2.2. Further information on supersymmetry and the MSSM can

36 Chapter 2. Dark Matter 8 Standard Model Particles Supersymmetric Partners and fields Interaction Eigenstates Mass Eigenstates Symbol Name Symbol Name Symbol Name q=u,s,t,d,c,b quark q L, q R squark q, q 2 squark l=e,µ,τ lepton ll, l R slepton l, l 2 slepton ν = ν e,ν µ,ν τ neutrino ν sneutrino ν sneutrino g gluon g gluino g gluino W ± W boson W± wino H Higgs boson H higgsino chargino H + Higgs boson H+ 2 higgsino B B field B bino W 3 W 3 field W3 wino H Higgs boson H higgsino H 2 Higgs boson H 2 higgsino Higgs boson H 3 χ ±,2 χ,2,3,4 Table 2.2: SM particles and their MSSM partners. Adapted from (2) neutralino be found in (). As shown in Table 2.2, the neutralino is a combination of the supersymmetric partners to the gauge bosons and as such there exists more than one possibility for its constitution. There are four separate mass eigenstates possible, labelled χ, χ 2, χ 3, and χ 4 listed in order of increasing mass. The most appropriate dark matter particle is the χ, since it is the lightest of the neutralinos and, in fact, the Lightest Supersymmetric Particle (LSP). If R-parity is conserved, this particle will be stable and other SUSY particles will decay to this state. The neutralino is one particle of a broader class of particles, known as Weakly Interacting Massive Particles (WIMPs).

37 Chapter 2. Dark Matter Experiments The experiments searching for dark matter can be divided into two categories depending on the method by which the signal is generated. The first of these categories is the indirect detection experiment, in which the observable is not the particle itself, but a signal created by its decay or annihilation products. This category of experiment is in contrast to the direct detection experiments, in which the interaction of the neutralinos in the detector creates the signal Indirect Detection Experiments Currently, theories suggest that WIMPs could self-annihilate and the particles generated in this annihilation would have a characteristic signal, which will be observable. It is theorized that several types of particles can be created in this process, providing different channels for observation. Gamma Rays If the WIMP is a majorana particle (it is its own anti-particle), then self-annihilation will be expected. A constraint on the rate is that the expected annihilation cross sections of these WIMPs are very small and the density is low, resulting in a low annihilation rate under normal circumstances. However, since these particles must interact gravitationally, models predict that WIMPs will collect in areas of large mass, such as the centre of planets, stars or galaxies. If the WIMPs interact with the nuclei in these objects, they will lose energy and may drop below the escape velocity

38 Chapter 2. Dark Matter 2 for that object. Hence WIMPs are expected to be found gravitationally bound at the centres of massive objets. This increased density results in an increased rate of annihilation and provides a target for indirect searches. One method for the WIMPs to annihilate would result in the creation of gamma rays, which could then be observed using two very different methods. The first is to observe the gamma rays directly. These experiments cannot be located on Earth, as the energy of the produced gamma rays would be in the range of GeV to TeV, and would therefore interact with the Earth s atmosphere via e + e pair production. To observe the gamma rays directly, the detectors must be mounted on space based telescopes. One of the first space based gamma ray observatories was EGRET, the Energetic Gamma Ray Telescope Experiment. The EGRET apparatus was sensitive to gamma rays of energy 3 MeV to approximately 3 GeV, which provides an ideal window for looking for the signature of annihilations of low mass neutralinos. Using data representing 2 9 cm 2 seconds, the galactic centre was excluded as a source of WIMP annihilations from low mass neutralinos with a confidence level of 99.9% (2). The EGRET sensitivity will be surpassed by the Gamma ray Large Area Space Telescope (GLAST). A modification of observation techniques has allowed GLAST to improve the sensitivity of EGRET below GeV and to extend the detection range up to 3 GeV. This increased range will allow higher energy annihilations to be detected, extending the sensitivity of the search. At the time of writing, the GLAST satellite was projected to be launched no earlier than June 3, 28.

39 Chapter 2. Dark Matter 2 Experiments attempting to detect the gamma rays caused by WIMP annihilations could be located on Earth; however, the gamma rays cannot be observed directly. In this case, the secondary particles created by the gamma ray interactions in the atmosphere could be observed, using either the fluorescence caused by the development of an electromagnetic shower or using Cerenkov radiation generated by the secondary particles moving through a medium. An example of secondary particle detection is the Very Energetic Radiation Imaging Telescope Array System (VERITAS). In this case, optical telescopes are used to look for Cerenkov radiation from the particle showers in the atmosphere. The size of the shower is directly related to the energy of the gamma rays, allowing conclusions about the annihilation energy to be drawn. The VERITAS experiment has published a possible detection of a dark matter annihilation with an energy of approximately 2.8 TeV located in an area very close to the galactic centre (3). This observation (if interpreted as a detection of a dark matter annihilation) indicates a very large mass for the neutralino, outside of the accepted range of many models. There are now numerous experiments world wide searching for indirect dark matter via the indirect gamma-gamma annihilation signal, and this promises to be a fruitful area of research in the years to come. Neutrinos In addition to producing gamma rays, WIMP self-annihilations could also produce high energy neutrinos, which could be detected on Earth. This method of detection is ideal for large volume Cerenkov detectors, of which there are several currently in

40 Chapter 2. Dark Matter 22 operation. The detection technique is to observe electrons, muons or tau particles produced by the interactions of the incident neutrinos near the detector. These highly energetic charged secondaries produce Cerenkov light in the detector, which is observed experimentally. One possibility for the detection volume is ice, as is the case with the AMANDA and future IceCube project. In the current AMANDA configuration, photomultiplier tubes (PMTs) are attached in strings and buried in the ice at the South Pole. The AMANDA collaboration has set a limit on the flux of muon neutrinos from the centre of the Earth associated with WIMP self-annihilation (4) with approximately 3 days of live time. The IceCube experiment continues this endeavour by increasing the number of strings while modifying the detection technology. It is also possible to use liquid water to detect high energy neutrinos, as done by the ANTARES experiment in the Mediterranean Sea. The method is similar to that used in ice, with long strings of PMTs looking for the Cerenkov light generated by neutrinos as they traverse the active volume. In both of these cases of Amanda and Antares, the signal in the detector indicating a dark matter self-annihilation will be the presence of a muon track deposited by the charged current interaction inside the detector. In addition, these detectors are able to reconstruct the muon s track direction which then gives a measure of the galactic origin of the event. Hence these experiments can search for enhancements in the neutrino rates at the centre of massive objects.

41 Chapter 2. Dark Matter Direct Detection Experiments The second class of dark matter search experiments uses a more direct method of detecting the WIMP. Although there are many different methods of detection, all rely on having the WIMP interact with nuclei inside the detector, however rarely. The majority of these interactions will be elastic collisions with the nucleus of one of the detector s constituent atoms, which will be displaced by this collision and deposit energy along its recoil path Detection There are several ways to detect this deposition of energy, with the majority of experiments using two in combination. The methods include scintillation, ionization and heat deposition. As the event rate is expected to be very low, one has to observe these rare recoils in the presence of backgrounds from radioactivity. This is accomplished using multiple techniques to identify the signal, or by using techniques that discriminate between true recoils and background events. The use of scintillation to detect the nuclear recoil is used in many experiments using liquid noble gases as the active mass. In several of these experiments, such as DEAP, the time structure of the signals can be used to provide a method of discriminating nuclear recoils from other signals without any other method of measuring the deposit. Another technique involves the use of ionization to detect the energy deposit. Many experiments which rely on high purity germanium crystals use only the ionization signal to provide energy deposition values. The final method of detec-

42 Chapter 2. Dark Matter 24 tion is the use of heat or phonons. Experiments using superheated liquids as targets use only this method of detection as the only channel for analysis. This is possible as these detectors are largely insensitive to the minimum ionizing radiations that plague other experiments. The majority of the experiments active currently use a combination of two of these methods of receiving signals to discriminate nuclear recoils from backgrounds. Examples include the CRESST experiment which uses both phonon and scintillation detection, WARP (5) which uses both scintillation and ionization and CDMS (6) which uses ionization and phonon detection. 2.4 State of Searches There are currently many experiments attempting to be the first to be able to conclusively prove that dark matter exists. Experiments are generally grouped into two categories, depending on whether the scattering interaction between the WIMP and the nucleus is spin dependent or spin independent. The elastic scattering crosssection for each interaction type is calculated differently. For WIMPs in general, the cross-section may be calculated as shown in equation 2.7, as in (7). dσ d q = C 2 G2 F ( q ) (2.7) v 2F2 In equation 2.7, σ is the cross-section of the neutralino on the target nucleus, q is the momentum transfer, G F is the Fermi constant, v is the velocity of the WIMP relative to the target nucleus, and F is the form factor of the target nucleus. All of the interaction physics information is represented by the C term, which will change

43 Chapter 2. Dark Matter 25 depending on the type of interaction. The total cross-section can be expressed using the standard zero momentum transfer limit as shown in equation 2.8. σ = 4m 2 r v 2 σ(q = ) d q 2 d q 2 = 4G 2 F m2 r C (2.8) In equation 2.8, m r is the reduced mass, involving the WIMP and target nucleus mass as in equation 2.9. m r = m Tm χ m T + m χ (2.9) The mass of the target nucleus is expressed as m T while the WIMP mass is expressed as m χ. If the scattering takes place as shown in Figure 2.3, the experiment is referred to as spin-dependent. The cross-section is then dependent on the spins of nucleons, with the unpaired nucleon being most important. In nuclei in which there is more of one type of nucleon (proton or neutron), this nucleon is considered to be unpaired. The scattering cross-section in this case is expressed as shown in equations 2. and 2.. C spin = 8 π J + J [a p < S p > +a n < S n >] 2 (2.) σ,spin = 32 π G2 Fm 2 J + r [a p < S p > +a n < S n >] 2 (2.) J As seen in equation 2., the spin-dependent cross-section is proportional to the expectation value of the nucleon spins <S p > and <S n > (determined by <N S p N>

44 Chapter 2. Dark Matter 26 Figure 2.3: Feynman diagram of spin-dependent scattering interaction. for the proton and similarly for the neutron) and the total nuclear spin J. The determination of the constants a p and a n will be discussed in section 3. If the elastic scattering occurs with the Feynman diagrams as shown in Figure 2.4, the interaction is called spin-independent or scalar. Figure 2.4: Feynman diagram of spin-independent scattering interaction. In the spin-independent or scalar case, the cross-sections are as shown in equations 2.2 and 2.3, in which f p and f n represent the WIMP couplings to the proton and the neutron, respectively, Z represents the charge of the nucleus (the number of protons) and A represents the atomic mass number so that A-Z represents the number of neutrons.

45 Chapter 2. Dark Matter 27 C scalar = πg 2 F [Zf p + (A Z)f n ] 2 (2.2) σ,scalar = 4m2 r π [Zf p + (A Z)f n ] 2 (2.3) The spin-independent cross-section therefore increases with the square of the atomic mass number Spin-Independent Searches The majority of currently operating dark matter experiments are spin-independent experiments. These generally involve the use of a nucleus with large mass to increase the cross-section of interaction with the WIMP. These experiments take many different approaches to detect the nuclear-recoil associated energy deposition, with a sample of the results shown in Figure 2.5. Bt way of an example, of the many experiments exploring the spin-independent sector of the dark matter interaction, the XENON experiment currently has the lowest cross section exclusion limit for a range of neutralino masses, cm 2 for a WIMP mass of 3 GeV/c 2 (9). The XENON experiment uses Xenon to search for dark matter interactions, using both the liquid and gaseous phase to allow for event by event discrimination of energy deposits associated with background events. The scintillation in the liquid phase is measured directly and the ionization is measured using the proportional scintillation in the gaseous phase. The ratio of these two signals can identify nuclear from electron recoil depositions. The lower limit in energy for this discrimination is

46 Chapter 2. Dark Matter 28 Figure 2.5: Exclusion curves taken from a sample of spin-independent experiments. Plot from (8).

47 Chapter 2. Dark Matter 29 a few kev, allowing the full range of recoils to be separated. The exclusion curve shown in Figure 2.5 was generated using 58.6 live days of data with a fiducial mass of 5.4 kg. There exists one experiment which has reported a detection of dark matter, the DAMA experiment (shown as a filled area in Figure 2.5). This result was based on an exposure of kg d using the approximately kg NaI(Tl) crystals in the Gran Sasso National Laboratory (2). The analysis consisted of observing the annual modulation in the count rate. The assumption has been made that WIMPs are traveling with a Maxwellian velocity distribution relative to Earth (due to the movement of the solar system through the galactic halo), meaning that for 6 months of the year the Earth travels in the direction of the velocity and 6 months in the opposite direction. The latter six months should therefore have an increased rate due to the movement of the Earth through the WIMP wind. The DAMA collaboration has observed a fluctuation in count rate over several annual cycles, producing a result at 4 σ confidence level of the presence of a WIMP of mass GeV and a cross-section of pb (2). If one applies the standard WIMP interpretation to these results, then this result has been excluded by several experiments since this result was published; however, further investigation by the DAMA collaboration has not provided an alternative explanation for the observed modulation, extending the confidence level to 6.3 σ (22).

48 Chapter 2. Dark Matter Spin-Dependent Searches If the interaction with the target nucleus is proportional to the spins of the target and the incident particle, it is classified as a spin-dependent interaction. There are fewer experiments searching the spin-dependent sector, partially due to the difficulty in identifying appropriate target elements and the overall lower cross-section expected. The expectation value of the spin has been tabulated for several of the most common elements used in dark matter detection and these are presented in Table 5.2. The interaction rate can be optimized through the choice of target material. A plot of the current state of searches in the spin dependent sector, specifically examining interactions on the proton, is included as Figure 2.6. Presently the lowest cross-section limit of the neutralino scattering from the proton is obtained by COUPP in their preliminary limit presented in (23). The COUPP experiment uses superheated CF 3 I as the detection medium and cameras to detect the nucleations caused by recoils. This method detects the nucleations accurately; however, each event requires a recompression of the detector. This issue will be addressed further in discussions of the PICASSO experiment.

49 Chapter 2. Dark Matter 3 Figure 2.6: Exclusion curves taken from a sample of spin-dependent experiments. Plot from (8).

50 Chapter 3. THE PICASSO EXPERIMENT The PICASSO experimental apparatus uses superheated droplets of freon suspended in a gel matrix to detect the nuclear recoil energy following the interaction of a WIMP and a nucleus. The superheated state of the freon (C 4 F ) droplets ensures that small deposits of energy in these droplets will cause a phase transition to the gaseous state. The expansion of the droplets due to this boiling is fast (on the order of ns) and causes an increase in the droplet size of approximately 5 times (24). This rapid expansion causes the creation of pressure waves which are transmitted through the gel to the nine piezoelectric sensors mounted on the container. The pressure waves interact with the piezoelectric sensors to produce voltage changes which are digitized and recorded for later analysis. At the time of writing, there were eight detectors in operation two kilometres underground in the SNOLAB cavern, which reduces the muon flux drastically from that on the surface and therefore reduces the number of spallation neutrons produced near the experiment, a significant background. These eight detectors are part of a program to operate 32 detectors in the underground location, which would provide approximately 2.5 kilograms of active mass. 32

51 Chapter 3. The PICASSO Experiment 33 Superheated Droplet Detector Theory As previously stated, all direct dark matter detection experiments attempt to detect the small amount of recoil energy produced when an incoming WIMP interacts with a nucleus in the target volume. These energy deposits are predicted to be on the order of several tens of kev and must be distinguishable from other energy deposits of this magnitude. The PICASSO experiment detects this energy using superheated droplets of freon dispersed in a gel matrix. The use of superheated liquids to detect the deposit of energy by incident particles has been prevalent for decades (25); however, recent use has been made of the adjustable threshold energy of these detectors to allow for the particle discrimination. The theory describing the behaviour of superheated liquids was first outlined for bubble chambers by Frederick Seitz in 958 (26) and further developed by V.P. Skripov in 974 (27). Although this theory was intended for the bubble chamber, the principles can be applied directly to superheated droplets. The theory characterizing the expansion of superheated droplets relies on the formation of proto-bubbles in the superheated fluid which then expand to cause the phase transition throughout the liquid droplet. The equation governing the creation of these proto-bubbles is shown in Equation 3.. The derivation of this equation requires only that the proto-bubble be spherical, which is reasonable in this experimental case under discussion. Equation 3. gives the amount of energy (or work) required to create a protobubble of sufficient magnitude to cause a phase transition. This equation may be

52 Chapter 3. The PICASSO Experiment 34 broken down into the addition of the three component terms, describing the energy required to overcome the surface tension, the pressure difference and the molecular work in the phase transition, respectively. W = 4πr 2 σ πr3 (p p ) + (µ µ )M (3.) In equation 3. (taken from (27)), r represents the radius of the droplet, σ represents the surface tension of the droplet, p represents the pressure external to the proto-bubble, p is the vapour pressure inside the droplet, µ and µ are the chemical potentials of the liquid and vapour phases respectively, and M represents the mass of the inner phase. If the system is in equilibrium, equations representing the pressures and chemical potentials can be expressed as in equations 3.2 and 3.3, where the temperature of the state has been included as T. p = p + 2σ r (3.2) µ (p, T) = µ (p, T) (3.3) Equation 3.2 can be rearranged to provide an equation for the critical radius in terms of the pressures and surface tension. r c = 2σ p p (3.4)

53 Chapter 3. The PICASSO Experiment 35 Finding the critical amount of work required to cause the creation of a protobubble (W cr ) results from substituting equations 3.3 and 3.2 into equation 3.. W cr = 4πr 2 σ πr3 ( p p 2σ r ) (3.5) W cr = 4 3 πr2 σ (3.6) Substituting the radius derived from the equilibrium state (equation 3.4) into equation 3.6 gives the final equation for the critical amount of work required to form the proto-bubble. W cr = 6πσ3 3(p p ) 2 (3.7) One advantage of using superheated liquids for detection is the ability to control the threshold of the detector using the operating temperature. The temperature dependence is included in both the surface tension equation and the vapour pressure, so that equation 3.7 can be written as in equation 3.8. W cr = 6πσ3 (T) 3(p (T) p ) 2 (3.8) The above equations describe the formation of a proto-bubble held in equilibrium, with the addition of a critical amount of energy W cr (which will be referred to as E c ). In order to cause a rapid phase transition, the energy deposited by the recoiling nucleus must have a value E>E c within the radius of the proto-bubble r c. Equation 3.8 represents an idealized energy detection threshold. In practice, the stochastic nature of the energy deposition dictates that the threshold isn t a sharp

54 Chapter 3. The PICASSO Experiment 36 function, but a smooth probability distribution. Deposits of energy below E c will not cause nucleation in the droplets, while deposits near E c have some probability of causing this droplet expansion. This is described using an asymmetric sigmoid function to represent the probability of bubble formation. This function is shown in equation 3.9, in which a is an experimentally determined parameter. ( ) a(edep E c (T) P(E dep, E c (T)) = exp E c (T) (3.9) An example of this function is shown in Figure 3., in which the probability of causing a droplet expansion is plotted against the amount of energy deposited in the droplet. Efficiency Efficiency of Bubble Production as a Function of Energy Deposited and Temperature C 2 3 C 4 C 5 C Energy Deposited (kev) Figure 3.: The efficiency of PICASSO detectors plotted vs the amount of energy deposited in the droplet. Figure 3. shows the threshold nature of the PICASSO detector, as well as the

55 Chapter 3. The PICASSO Experiment 37 probability distributions for droplet expansions at a variety of temperatures. The function is no longer step-like in nature, adjusted through the use of equation 3.9. Experimental studies have shown that the constant a in equation 3.9 is very close to unity (28). 3. Detectors The PICASSO detectors consist primarily of droplets of active mass suspended in a gel matrix, contained within an acrylic container designed to allow pressurization of the gel as well as the mounting of piezo-electric sensors and temperature monitoring devices. A schematic of the PICASSO detector containers is shown in Figures 3.2 (side view) and 3.3 (top view). A photo of the detectors is included as Figure Composition There are two main components used in the PICASSO detectors, the active mass and the gel matrix used to suspend that active mass Active Mass The active mass is kept in a superheated state, requiring that the freon (currently C 4 F ) remains liquid at a temperature above its boiling point. This can be done by avoiding the exposure of the liquid to nucleation sites and by carefully heating the liquid. In this state the liquid is very sensitive to energy deposition, allowing its use as a detector of nuclear recoils.

56 Chapter 3. The PICASSO Experiment 38 Figure 3.2: Side view of the PICASSO containers showing dimensions.

57 Chapter 3. The PICASSO Experiment 39 Figure 3.3: Top view of the PICASSO containers showing dimensions.

58 Chapter 3. The PICASSO Experiment 4

59 Chapter 3. The PICASSO Experiment 4 Recent studies have indicated the possibility of using a different variety of freon (C 4 F 8 ) in the detectors. The important qualities of the freon are thermodynamic properties (the boiling and critical point), as these will determine the superheated state of the active mass droplets, and C 4 F 8 has thermodynamic properties very similar to those of C 4 F, as shown in table 3.. The advantage to C 4 F 8 is that it is significantly less expensive than C 4 F and can be obtained in a much more pure state (99.99% pure compared to 98%). Freon Formula Boiling Point ( C) Critical Point ( C) C 4 F C 4 F Table 3.: Thermodynamic properties of Freon gases It is clear from Table 3. that the thermodynamic differences between the two gases are small, indicating that the degree of superheat will be similar for both active materials. This allows either gas to be used in the detectors Gel Matrix The gel matrix serves several purposes in the PICASSO detector. The gel suspends the droplets and keep them away from the container walls, which could have surface defects potentially creating nucleation sites. The gel is also produced such that its density matches that of the active mass, which allows the droplets to be neutrally buoyant. This density matching ensures that, during the polymerization process (the transition of the gel matrix between liquid and gel, discussed in detail in section 3..4), the droplets maintain a homogeneous distribution. Without this matching,

60 Chapter 3. The PICASSO Experiment 42 they would tend to float or sink. The density match between the active mass and the gel is currently achieved through the introduction of CsCl to the gel matrix. This process allows for accurate density control; however, the heavy salt nature of CsCl means that it is very difficult to make radiopure. Studies have been undertaken which use polyethylene glycol (PEG) to match the densities, making the purification much more effective. In addition to these purposes, the gel matrix serves to contain the droplets after their phase transition. The containment of the active mass ensures that these droplets may be recompressed into a superheated liquid state. Multiple runs may then be performed with a detector, provided an adequate period of recompression is included after bubble expansion Fabrication The fabrication process occurs in several steps, with many of the details suppressed for brevity in the following description. The first step is the purification of all of the ingredients, including the water. The purification of the detector materials is vitally important, as the inclusion of alpha emitting nuclei close to the superheated droplets would cause many droplet nucleations, increasing the count rate and raising the exclusion limit calculated. The most effort has gone into the purification of the CsCl, the heavy salt used to match the density of the gel matrix and the density of the active mass. The purification process consists primarily of an ion exchange process in which Hydrous Zirconium Oxide (HZrO) attracts and binds the contaminants, allowing them to be removed by

61 Chapter 3. The PICASSO Experiment 43 filtration. Following purification, the gel matrix is prepared using all of the ingredients required to create the tri-dimensional polymer, with the exception of the final chemical required to activate the polymerization. This matrix is then degassed and cooled in the detector container to a temperature of -2 C, well below the boiling point of the active liquid, ensuring that the active mass will remain liquid once added in the next step. The active liquid is poured into the detector container and allowed to warm and the mixture is agitated using a stirring device, either a mechanical mixer or a stir bar. This agitation disperses the active mass throughout the gel matrix (at this point still a monomer) and the density matching ensures the droplets remain dispersed. The mixing speed of the viscous fluid determines the droplet size. The final step is to add the final ingredient required to start the polymerization. This process can be exothermic and is generally performed under refrigeration. The polymerization can happen very quickly (on the order of minutes) so that the droplets of active mass maintain their dispersal. The detector container can then be closed and pressurized so that the metastable state of the active mass is reached Temperature and Pressure Control The control of the temperature and pressure of the PICASSO detectors is vital to the discrimination of background events and requires the design and construction of a Temperature and Pressure Cotrol System (TPCS). In order to achieve consistent temperature throughout the detectors, heating is provided to two large aluminium

62 Chapter 3. The PICASSO Experiment 44 plates on the top and bottom of the boxes, providing a large regulatory thermal mass. Heat is introduced to the top and bottom plates through eight 25 Ω resistors, spaced in a symmetric arrangement to provide even heating to the plates. A sketch of the top plate is shown in Figure cm Transistor Board Resistor Signal Cable Holes cm Pressure Line Hole Figure 3.5: Sketch of the top plate of the PICASSO TPCS showing the placement of the resistors. The bottom plate of the TPCS is identical to the top shown in Figure 3.5 with the exception that the holes to allow the signal wires to pass through the plate are present only on the top. The transistor boards control the power to the resistors,

63 Chapter 3. The PICASSO Experiment 45 with each transistor board controlling two resistors. The top and bottom plates are connected through walls which are designed to transfer heat efficiently along the z axis of the boxes, maintaining the desired temperature and reducing the temperature gradient in the TPCS. The method chosen to provide this heat transfer was to create a double-walled design, using aluminium sheets to transfer the heat and rigid PVC insulation to maintain the temperature. The configuration chosen is shown in Figure 3.6. This method of heat transfer has been shown to be excellent in maintaining a constant temperature inside the TPCS, a vital requirement for the PICASSO experiment. 3.2 Method of Detection There are several methods that could be used to detect the expansion of a liquid droplet into a gaseous bubble. These include visual detection of the expanded droplets, observation of the bubble formation through a change in pressure or via an acoustic signal as the bubble pops. The PICASSO experiment makes use of the final method, using piezo electric sensors mounted on the detector containers for this purpose. The PICASSO piezoelectric sensors (piezos) consist of a small disk of piezo electric material mounted in a metal housing. The piezos are constructed by the PICASSO collaboration, and have shown good sensitivity to acoustic signals within the range known to be characteristic of bubble expansions (29). A sketch of the piezos used as mounted on the detectors is shown in Figure 3.7.

64 Chapter 3. The PICASSO Experiment cm cm Detector Pressure Connection Shock Absorbing Pad Aluminium Sheets Rigid PVC Foam Insulation Figure 3.6: Top view sketch of the PICASSO TPCS showing the design of the thermal transfer system.

65 Chapter 3. The PICASSO Experiment 47 Acrylic Gel Matrix Coupling compound Signal Connector Piezoelectric Material Bubble Formation Pressure Waves Figure 3.7: Sketch of the piezo sensors as used on the PICASSO detectors. The metal housing is placed in contact with the outside of the container, with additional coupling compound used to ensure an acoustic connection between the container and the piezo housing. Pressure waves are thereby transmitted from the gel matrix to the piezo Readout Each PICASSO detector has nine piezoelectric sensors mounted on the detector container, which are read out by a custom built DAQ system. Each piezo is connected to a pre-amplifier (pre-amp) by SMA cables, using a bulkhead connector to pass through the top plate of the TPCS. The nine pre-amps necessary for one detector are mounted on a pre-amp mother board, which combines the signals to be passed

66 Chapter 3. The PICASSO Experiment 48 to the ADC board using a ribbon cable. The ADC boards are connected to the collector board using CAT 6 cable and digitize each of the analogue signals that is above the programmed threshold. The collector board gathers the signals from all of the piezos from each detector and passes the signals on to the VME CPU for the addition of slow control and header information to the data file. A schematic of this setup is shown in Figure 3.8. Figure 3.8: Schematic of DAQ system used with underground experimental setup. The processing of the signals, disregarding the application of cuts (which will be discussed in Chapter 4), is performed by the VME CPU. Following the end of the run, the data files are transferred automatically to storage devices at Queen s University and Université de Montréal as well as to a backup device located adjacent to the experimental setup.

67 Chapter 3. The PICASSO Experiment Location Reduction of the radioactive background, which will be discussed more thoroughly in section 6.5, is important for the PICASSO experiment, with neutrons being of particular significance. Interactions of neutrons in the PICASSO detectors will produce a temperature dependent signal closely mimicking that of the WIMPs, requiring the neutron background to be as low and as well understood as possible. In order to reduce the neutron flux, the atmospheric muon flux must be as low as possible. Cosmic rays incident on the Earth interact with the atmosphere to produce muons. These muons can interact with the materials surrounding the experiment to produce neutrons by spallation. These neutrons are particularly problematic in that they can have a wide range of energies and therefore can cause background counts in the energy range expected from WIMP interactions in the detector. One method to avoid a significant portion of the atmospheric muons is to situate the experiment deep underground. In this setting, the overburden material absorbs a large fraction of the muons, removing these as a potential source of neutrons. The PICASSO experiment is located in the SNO cavity at the VALE-INCO nickel mine in Lively, Ontario, Canada. The location of the experiment is shown in Figure 3.9. This environment provides 6 metres water equivalent of flat overburden, enough to reduce the muon flux to approximately.27 µ/m 2 /day (3). This results in a thermal neutron flux of 444.9±49.8±5.3 neutrons/m 2 /day and a fast neutron flux of approximately 4 neutrons/m 2 /day (3). The reduction in flux compared to the surface can be seen in Figure 3., discussed in (3). The effect of this flux is dis-

68 Chapter 3. The PICASSO Experiment 5 Figure 3.9: Underground location of the PICASSO setup.

69 Chapter 3. The PICASSO Experiment 5 cussed in Chapter 6. Figure 3.: Neutron flux as a function of depth in equivalent metres of water (3). 3.3 PICASSO Experimental Operation As discussed previously, the discrimination of non-nuclear recoil events in the PI- CASSO detector requires data to be taken at a range of temperatures. In order to facilitate this discrimination, the detectors in the PICASSO underground setup are scanned in temperature by taking WIMP runs at many temperatures. The lowest temperature possible is approximately 9 C, close to the laboratory ambient temperature of roughly 7 C. The detectors have not had data taken at temperatures above 55 C due to the drastic increase in trigger rate at these temperatures. A chronological presentation of the runs taken that are within the scope of this analysis is shown in Figure 3..

70 Chapter 3. The PICASSO Experiment 52 Run Set Temperature C) Set Temperature ( TPCS TPCS /9/6 //6 3/2/6 2/3/7 2/5/7 2/7/7 /9/7 //7 //8 Run Start Date Figure 3.: Set temperature during PICASSO WIMP runs as a function of time.

71 Chapter 3. The PICASSO Experiment 53 WIMP runs (in which data are taken to be analyzed for use in WIMP search data sets) are taken when the pressure of the detectors is released to the ambient pressure. These runs have a finite length due to the buildup of events in the detector. After roughly 25 events in any detector, re-pressurization is necessary. In the current PICASSO setup, detectors are pressurized at pressures of between 5.5 and 6 bar for 5 hours. This time has been shown to be sufficient to fully restore the detectors to their pre-droplet expansion state. WIMP runs nominally last 4 hours; however, due to the constraint on the total number of events, this length can be shortened. Runs with set temperatures over 45 C generally do not last 4 hours and runs above 5 C are usually taken in several runs of one hour length. This allows the total number of events to remain below the limitation. In order to observe how much time is being spent in pressure and WIMP runs, a summary is presented here. The total time during each week is divided into the time spent in WIMP runs, pressure runs, calibration runs, other unidentified runs and downtime. The breakdown of this time is shown in Figure 3.2. Unidentified runs can occur when the pressure or temperature of the WIMP run is not stable or the operator mis-identifies a run. Down time is generally accumulated when PICASSO scientists are working on or around the experimental setup. In order to minimize the cost of operations by not having personnel continuously travel to the experiment site, the operation of the detectors may be (and usually is) conducted remotely. Control of the temperature, pressure and data taking are accessible from a remote computer, allowing an operator to start and stop data and

72 Chapter 3. The PICASSO Experiment 54 PICASSO run time summary Fractional Time Spent.8.6 Unidentified runs Pressure runs Calibration runs WIMP runs Downtime Weeks Since September 2, 26 Figure 3.2: Breakdown of total time spent underground into run type. pressure runs and change the temperature without being underground. These access issues have also necessitated the development of an on-line run monitoring tool which can be used by an operator to ensure the proper functioning of the detectors. The quantities which can be kept under observation using this tool include the temperature of all active TPCSs, the pressure applied to the TPCSs, the deviation from the set temperature and the number of events in all active detectors as well as the time distribution of these events. This monitoring can alert the operator to any problems during running, allowing these to be properly dealt with. In addition to the on-line monitoring, a near-line analysis has been provided to check the quality of the runs. This web page plots the history of each detector, showing the average count rate at all temperatures at which data has been taken.

73 Chapter 3. The PICASSO Experiment 55 On the same plot, the last five runs are marked in a distinct manner. If a significant deviation exists between the rate taken in the latest runs and the rates of the previous runs, the collaboration has the chance to identify a potential problem before proceeding with further data collection.

74 Chapter 4. DATA ANALYSIS I: EVENT SELECTION The analysis of PICASSO data begins with the separation of signals associated with droplet expansion from those in which the trigger was caused by electronic effects or acoustic noise in the surrounding areas. This is known as bubble selection. Several tests have been designed to make the separation between acoustic background signals ( noise ) and the desirable signals. There are characteristics which can be associated with the noise and can therefore be used to distinguish these from the signals. In the first step, the signals are filtered using a band pass filter. This filter removes frequencies below 2 khz and higher than 2 khz, and uses a rounded frequency mask (to avoid potential problems near these frequencies when calculating the Fourier transform). These regions of the signal are filtered out as they contain no information relevant to the droplet expansion and have been associated with problematic noise. These values may be justified by examining a histogram of the power in the Fourier Transform of a calibration run. The nature of this calibration will be discussed in detail in section 4..; however, it involved the inclusion of a neutron source in close proximity to the detectors. The histogram shown in Figure 4. shows the results from the addition of the power histograms for 782 events in 56

75 Chapter 4. Data Analysis I: Event Selection 57 detector #72. Histogram of Fourier Transform of Events in Detector 72, Run Frequency (khz) Figure 4.: Sum of fourier transform histograms of 782 events in detector 72 during calibration run.9.. It is clear from Figure 4. that there is very little information in the detector signals at frequencies higher than 6 khz and below 2 khz the noise increases dramatically. The small bump just below 2 khz results from an increase in the sensitivity of the piezos at that frequency. To be conservative, the upper frequency limit was set at 2 khz. In addition to the filtering process, if the signal has a DC level offset from V, it is adjusted back to V at this stage. The identification of bubble events is accomplished though the use of several cuts (defined as the result of using characteristics of the data to separate noiserelated events from bubble-expansions). The first cuts are applied to the individual waveforms collected from the piezos. These first round cuts are known as the time-binned Fourier transform cut, the spike cut, the power cut, and the pre-trigger noise cut. If the waveform passes these cuts, it is considered to be associated with

76 Chapter 4. Data Analysis I: Event Selection 58 a droplet-expansion event. The second round of cuts require that there be at least four piezos which contain signals identified as bubbles, and that this event be separated from the previous event by more than the time defined in the burst cut. All of these cuts will be discussed individually in their respective sections. In addition, the sacrifice (the number of bubble events which are misidentified) will be determined for each cut. These events, calculated as a fraction of the number of triggers, will be accounted for in Chapter Underground Calibration Runs The determination of the cut values and their efficiencies requires the use of calibration runs. Two separate calibration sources have been used at different times in the underground PICASSO setup. At this stage of PICASSO operations, there is insufficient calibration data to completely establish the cut efficiencies under all operating conditions. With this constraint, this analysis has been carried out with the best estimates possible, with the uncertainties accounted for in the error estimations. The first calibration source used was a 252 Cf source (.2 µci) placed at the centre of the TPCS on a specially designed stand. This stand placed the calibration source equidistant from all detectors. An illustration of the location of the source and detectors inside the TPCS is shown in Figure 4.2. A well understood AmBe calibration source was installed during the use of the second generation DAQ, but the location was changed. Due to the installation of another TPCS (containing four detectors) in the interim, and the addition of a 3 He neutron detector in the PICASSO frame, the source was placed outside of the TPCS.

77 Chapter 4. Data Analysis I: Event Selection 59 23" Detector Detector 2 23" Cf source Detector 3 Detector 4 Figure 4.2: The location of the neutron calibration source used for runs taken with the first generation DAQ.

78 Chapter 4. Data Analysis I: Event Selection 6 The location is shown in Figure 4.3. Figure 4.3: The location of the neutron calibration source, independent 3 He neutron detector and PICASSO TPCSs for runs taken with the second generation DAQ. Figure 4.3 shows a top view of the PICASSO apparatus in the underground location, resulting in TPCS and 2 being shown in the same quadrant Spike Cut The first class of events which must be eliminated from the data to be analyzed are referred to as spike events. These events have one or more signals which are distinctive in shape, having a very short rise time, and generally having an amplitude at or near the maximum voltage of the system. These signals were not present in

79 Chapter 4. Data Analysis I: Event Selection 6 the data collected using the first generation DAQ, but became a significant source of background in the second generation DAQ data. An example of one of these events is shown in Figure 4.4, with the signals from all nine channels for this event included. The spike signal is shown in channel four of this event. There is a rapid voltage drop to -7 mv, followed by a slower return to the baseline voltage. This is characteristic of all of these events. The cause of these events is under investigation. It is worthy of note that in Figure 4.4 the channels other than channel four (containing the spike) show some deviation from V in the expected trigger range. The difference in time between the signals in other channels and that in channel four may be used to determine the timing of the events. A zoom in time of the event shown in Figure 4.4 is shown in Figure 4.5, with the time axis zoomed to the range between 24 and 28 µs. It is clear from Figure 4.5 that channel four triggers the event, passing the 3 mv threshold at 256 µs. The majority of the other channels do exhibit some deviation from their nominal level; however, these deviations occur later, usually after 26 µs. This further supports the hypothesis that the spike in channel four is responsible for these deviations. It should also be noted that the deviations in the other channels are of very small magnitude, on the order of 2 mv at maximum, which is not seen in bubble events. Additionally, the lack of these events in the first generation DAQ suggest the DAQ system as the likely cause. Finally, spike events happen primarily in one channel of the detector. An example is seen in run.6.2 (a 4 hour WIMP run at a temperature of 4 C) which contains the event shown in Figure 4.4. In detector 72 during this run, there were 84 identified spike events. Of these, 6 took

80 Chapter 4. Data Analysis I: Event Selection 62 Figure 4.4: Example of spike event taken from run.6.2, event #737. place in channel zero and 2 in channel two. The remaining 2 events occurred in channel one (7) channel three (3) and channel four (2). Channels five, six, seven and eight had no spike events.

81 Chapter 4. Data Analysis I: Event Selection 63 Figure 4.5: Expansion of time axis of example of spike event taken from run.6.2, event #737. As a final confirmation of the noise-related nature of these events, if the spikes are unrelated to bubble events, the rate of spike events should not differ between WIMP and calibration runs. Using the data from run.6.2 (as discussed above),

82 Chapter 4. Data Analysis I: Event Selection 64 detector 72 had 84 events identified as spike events in 4 hours, a rate of 2. spike events per hour. Examination of run shows that this 32 hour calibration run at 4 C had events identified as spike events in 32 hours, a rate of 3.2 spike events per hour. In order to determine if this increase is significant, two runs were studied which were taken separated by a period of pressurization. Run.647.2, a hour WIMP run at 3 C had 25 spike events in detector 72, a rate of 2.5 spike events per hour. Run.649.2, a 4 hour calibration run at 3.75 C had 66 spike events in detector 72, a rate of.65 spike events per hour. Within these large fluctuations, the spike event rate is not observed to change between WIMP and calibration runs at the same temperatures. Consideration of the combined evidence indicates that these events are not associated with bubbles and should be removed from the analysis stream. In order to accomplish the removal of these signals from the data, a cut was created which integrates the signal over a fixed time window and then takes the absolute value of the result. The advantage to this method is that it exploits the asymmetry of the signal over the range chosen (events associated with bubbles are generally symmetric about V). In the analysis of the second generation DAQ, the range over which the signal was summed was from sample number 24 to sample number 248. These limits were chosen due to the location of the trigger at sample 24. In these spike events, the DAQ system is triggered by the large spike, fixing the spike location in time. It should also be noted that, in this example, all channels fail the Fourier Transform cut and only three pass the power cut. The limiting value for this cut was set using a study of the spike events themselves.

83 Chapter 4. Data Analysis I: Event Selection 65 These events are easily identified by eye and the cut value can be calculated using the procedure previously described. It was found that setting this cut value at 2 mv removed all the spike events without removing any of the data events. Signals with this degree of asymmetry are not associated with any droplet expansion events. The ease of identification of these signals makes the efficiency of their removal from the analysis stream very close to %. A scan of some of the data by hand shows that all spike events are properly identified and there are no droplet-expansion associated events removed using this cut Power Cut Another problematic class of signals are those associated with events with very small amplitudes. An examination of the data showed that signals with very low power in the Fourier transform spectrum could pass the time-binned Fourier transform cut, which will be discussed in detail in section The majority of these signals have a flat spectrum; however, there are some which, by random processes, have enough power within the droplet-expansion associated region to pass the time-binned Fourier transform cut. The removal of these signals is difficult, as they pass the remainder of the tests, but are clearly not identifiable as signals due to their small overall amplitudes. In order to remove these signals, a new cut was created which identifies signals which are too weak to be properly identified. The fraction of events misidentified due to their low overall amplitude was small prior to the installation of the second generation DAQ; however, the cut was retroactively applied to all data collected from the

84 Chapter 4. Data Analysis I: Event Selection 66 first generation DAQ. The reason for this change is the extended sensitivity of the second generation DAQ, to be discussed in section As the sensitivity of the DAQ system increased, the trigger thresholds of the piezos was decreased. With the sensitivity of the second generation DAQ system, these thresholds approached the limits of the random noise in the acquisition electronics. In order to identify and separate these weak signals, the absolute value of the prepared signal voltage was added for each bin in the range defined by the power window. This range is the same as the range used for the spike cut and encompasses the area known to contain the signal for good events. The resultant summed value is then divided by the number of bins in the range to give an average absolute per bin voltage in this range. If this value is lower than the set value, the signal is rejected. The set value for this cut was determined through extensive study of signals during both data and calibration runs. Examples of the distribution of this cut value are shown in Figure 4.6 for both a calibration run (.657.2, a 3.6 hour run taken at 4 C starting August 9, 27) and a WIMP run (.6.2, a 4 hour run taken at 4 C starting July 3, 27). In Figure 4.7 the relevant portion of Figure 4.6 has been expanded to illustrate the difference between these runs more clearly. It is clear from Figure 4.7 that the inclusion of the AmBe neutron source external to the detectors causes a change in the distribution of the power cut value. The distribution shows an increase in the number of events with a power cut value over approximately 2 mv, indicating the increase in the average amplitude for droplet expansion associated events. The apparent separation in the distribution occurring at

85 Chapter 4. Data Analysis I: Event Selection 67 Average Absolute Amplitude Distribution, Detector 99 Events 35 3 WIMP Run Calibration Run Average Absolute Amplitude (mv) Figure 4.6: Power cut value distribution for detector 99 in runs.6.2 and

86 Chapter 4. Data Analysis I: Event Selection 68 Average Absolute Amplitude Distribution, Detector 99 Events 25 2 WIMP Run.6.2 Calibration Run Average Absolute Amplitude (mv) Figure 4.7: Zoom of power cut value distribution for detector 99 in runs.6.2 and

87 Chapter 4. Data Analysis I: Event Selection 69 roughly 2 mv has not been explained; however, the inclusion of the neutron source must be responsible. This is possibly due to the kinetics of the events and the effect of the droplet distribution for short range internal alphas and long range external neutrons. The lower peak contains the noise present in the WIMP run as well as the smaller energy deposits due to the always present alpha or neutron induced nuclear recoils. This area is being further explored for use in particle identification. A study of the signals showed that events which should be identified as bubbles may have average amplitudes lower than the 2 mv separation. Further studies were carried out examining the events which occur below this limit. It was found that there were still events with smaller amplitude which would be considered to be bubbles by eye. In order to produce a final value for this cut, a lower bound of.2 mv average amplitude per bin was chosen to be the limit of detectability by the DAQ. Any signals with average per bin amplitude lower than this should not be associated with bubbles Pre-trigger Noise Cut A small number of the signals have noise prior to the trigger time which is not characteristic of bubble events. In order to remove these signals from the data analysis, a cut was created which restricts the amount of pre-trigger noise a signal may have. This is accomplished by cutting signals based on the root mean square (RMS) value of the signal before the trigger. This cut also removes a class of event referred to as re-triggers. These events are artifacts of the DAQ system and are easily identifiable. In these cases, the same

88 Chapter 4. Data Analysis I: Event Selection 7 event is recorded twice, offset in time by a small amount. The first occurrence is at the properly defined trigger time, while subsequent events are an exact replica of this signal with the exception that the trigger point is moved within the event. These are clearly an artifact of the DAQ system and would be multiply counted. These can also be detrimental to the analysis, as these events will generally pass all other cuts until the fraction of the signal contained within the time-binned Fourier transform range becomes small compared to the baseline noise after this region. The use of the pre-trigger noise cut completely removes these rare but clearly not droplet-associated events. For the current data analysis, the pre-trigger noise cut is set to remove events with a pre-trigger noise RMS of mv. The noise before the trigger of real events is almost always smaller than mv Time-Binned Fourier Transform The primary tool used in separating the bubble signals from those caused by noise of any other kind is the information in the frequency spectrum, obtained by performing a Fourier transform on the signal. Studies of the Fourier transforms of signals associated with droplet expansions have shown that the majority of the power in these signals is contained between 2 and 2 khz in the frequency spectrum. Example signals are shown in Figures 4.8 and 4.9. The examples in Figures 4.8 and 4.9 show signals which have the majority of the power spectrum of the signal contained within the lower half of the frequency range (2-7 khz, shown in Figures 4.8(a) and 4.8(c)) as well as those with the power more

89 Chapter 4. Data Analysis I: Event Selection 7 (a) Signal Example (b) FFT Example (c) Signal Example 2 (d) FFT Example 2 Figure 4.8: Examples of good signals and associated Fourier transforms evenly distributed across the entire range, as in Figures 4.9(a) and 4.9(c). Although the signal shown in Figure 4.9(c) is clearly different from the other good events, Figure 4.9(a) shows that a signal may look good during a quick visual inspection, but have a Fourier transform which contains an unusually large high-frequency component and is unlikely to be a real bubble event. A knowledge of the characteristic power spectrum of droplet expansions provides a simple method of distinction from acoustic noise events which can be combined with additional information to supply further discrimination. As an additional discrimination tool, the Fourier transform of the signal can be taken at particular time intervals (set to 8 µs for the old DAQ, 4 µs for the new DAQ), providing time

90 Chapter 4. Data Analysis I: Event Selection 72 (a) Signal Example 3 (b) FFT Example 3 (c) Signal Example 4 (d) FFT Example 4 Figure 4.9: Examples of bad signals and associated Fourier transforms dependent information about the power spectrum of the signal. Since the DAQ trigger time is fixed in the signal (bin #52 for the first generation DAQ, 24 for the second), the power spectrum should show that the power in the known frequency range associated with droplet expansions (2-2 khz) at this time should be significantly higher than in the remainder of the signal. In order to measure this, the time-binned Fourier transform has been separated into different time and frequency areas based on the values previously discussed. The section divisions are shown in Figure 4.. There are more regions defined here than are eventually used in the bubble determination. All areas were explored to find the best discrimination power.

91 Chapter 4. Data Analysis I: Event Selection 73 Figure 4.: Definition of the regions for the time-binned Fourier transform characterization of droplet expansions. The case shown applies to data taken with the second generation DAQ The limits on the areas identified as A and B are also presented numerically, as they differ for the different DAQ generations, in Table 4.. The change in the time windows shown in Table 4. was necessitated by the change in the DAQ system. While both systems have a data acquisition rate of 4 khz (one sample every 2.5 µs), the old DAQ recorded 52 samples before the trigger while the new DAQ records 24. In addition, the event length is 496 µs in the former and 248 µs in the latter. The fixed location of the trigger (in time) on these plots allows for time-based discrimination of the frequency content of the signal. Since the trigger is known to be at channel 24 (for the second generation DAQ) and the frequency is known to be between 2 and 2 khz, this region can be identified as being associated with

92 Chapter 4. Data Analysis I: Event Selection 74 Description Generation Value Generation 2 Value Time Window Low Edge µs µs Time Window Boundary 38 µs 22 µs Time Window Boundary 2 35 µs 55 µs Time Window High Edge 496 µs 248 µs Frequency Window Low Edge khz khz Frequency Window Boundary 2 khz 2 khz Frequency Window Boundary 2 2 khz 2 khz Frequency Window High Edge 9 khz 9 khz Table 4.: Definition of the areas used for droplet expansion discrimination using the timebinned Fourier transform. droplet expansion events, labelled as region B in Figure 4.. Region A is then identified as the pre-trigger portion of the transform, while region C is the tail portion, primarily containing any ringing of the primary signal event. This longer tail region was studied, but shown not to improve significantly on the discrimination power compared to the use of areas A and B alone, and was not used in order to keep the number of cuts to a minimum. The examples shown previously can also be shown in the time-binned Fourier transform view, with the power shown in colour, as shown on the scale. Included here are the transforms corresponding to the signals shown in Figure 4.8(a) (Figure 4.) and Figure 4.9(c) (Figure 4.2). Figure 4. shows the majority of the power of the time-binned Fourier transform contained within the droplet expansion associated region, while Figure 4.2 shows the power continuing throughout the extent of the signal. This is further evidence that the signal shown in Figure 4.9(c) would not be identified as being associated with a droplet expansion.

93 Chapter 4. Data Analysis I: Event Selection 75 Figure 4.: Time-binned Fourier transform data showing the characteristic frequencies in the signal as a function of time within the signal. This case corresponds to the signal shown in Figure 4.8(a) The signal is well contained within the expected region. Figure 4.2: Time-binned Fourier transform data showing the characteristic frequencies in the signal as a function of time within the signal. This case corresponds to the signal shown in Figure 4.9(c). In this case, the signal is not well contained within the expected region, with a significant amount of power even at 2 µs into the event.

94 Chapter 4. Data Analysis I: Event Selection 76 The use of the ratio of the region values removes any amplitude dependence on the signal, which is beneficial when analyzing very small signals. Using the first generation DAQ, the defined cut required that the power contained in the area defined as B divided by the area defined as A be larger than 6, while in the second generation this ratio was increased to 9. This ratio is known as the cut value. The increase reflects an increase in sensitivity after the installation of the second generation DAQ. A distribution comparing the Time Binned Fourier Transform cut (cut ) value from a calibration run (run number..) to that from a WIMP run (.78.) is shown in Figure 4.3 for detector 75. A higher rate detector was chosen to illustrate better the difference in the distributions. Normalized Cut Value for Detector 75 Normalized Number of Events WIMP Run.78. Calibration Run Cut Value Figure 4.3: Cut value distribution for detector 75 in runs.. and.78.. This data was taken using the old DAQ system.

95 Chapter 4. Data Analysis I: Event Selection 77 A similar illustration does not exist for the second generation DAQ system. Although a neutron source was installed in the frame to provide calibration results, the location of the source was not sufficiently close to the detectors to provide a significant increase in the rate of expansion-associated events. This will be further discussed in section 4.. In order to set the cut value for the second generation DAQ, events were examined individually and the value for cut was determined using these signals. In this case, events were first chosen by eye which were considered to be good events. Additionally, events were found which had small cut values and the cuts were adjusted to predominantly select good events. As a measure of the efficiency of this cut, the event acceptance statistics for the two runs used here will be useful. In a calibration run at 35 C (..), detector 7 accepted 58.3% of the triggers (after the other first round cuts had been applied) and detector 72 accepted 6.3% of these events. These acceptances can be compared to those derived from a WIMP run at the same temperature (.377.), in which detector 7 accepted 3.3% of the triggers and 72 accepted 38.9%. The significant increase in acceptance during the calibration run indicates that the majority of the neutron-related events are being properly identified Burst Cut The first cut used in the data analysis stream which is not based on the signals from the piezos is referred to as the burst cut. This burst cut is used to remove events that are introduced by the detectors themselves. Subsequent to the installation of the new DAQ system, a number of events were observed which occurred almost

96 Chapter 4. Data Analysis I: Event Selection 78 immediately after the previous event. The explanation for these events has not been adequately determined yet; however, there are two probable contributions. The first is that the DAQ system is re-triggering on the same event, producing a false new event several times in a very short period of time. A trigger is generated if the signal amplitude is above a set threshold, meaning that signals including a great deal of ringing could generate a new event. This theory is supported by the evidence that many of the events have a time separation of. s, the minimum time difference possible using the DAQ system. An example of the distribution of time between events is shown in Figure 4.4, which shows the data from detector 99 in run.62.2, taken at 52 C (63.5 events/hr/g, representing the highest rate, and therefore the worst case scenario ). A second potential explanation of the burst events is that the expansion of one droplet in the PICASSO detector triggers the expansion of other droplets. There is some evidence to support this theory, as not all burst events are separated by the. second time difference predicted by the limitation of the DAQ system, as would be predicted by the re-triggering events. These larger time differences (still less than one second) may be explained by the transmission of pressure waves in the detector container, or by a slow mechanical process in the gel matrix, triggering the formation of another bubble within the gel. The rate of real triggers in the PICASSO detectors occurring at random times should approximate a Poissonian distribution. Making this assumption allows the determination of the probability of two events occurring within a given time interval. As an example, the probability of having two or more events within a given time

97 Chapter 4. Data Analysis I: Event Selection 79 Trigger Time Difference, Detector 99, Run.62.2 Number of triggers Time between events (s) Figure 4.4: Trigger time difference example, detector 99, run The time difference is the measured time between consecutive events. window is plotted in Figure 4.5 using an average rate equal to that in detector 99 at 52 C. This is a high rate detector and so represents the worst case in terms of removing accidental coincidences during a WIMP run. Using the probabilities shown in Figure 4.5, a window could be set which should not remove a large number of true events. One second was chosen as the final value, as given the rate for detector 99 at 52 C the probability of having a second event within one second of the first is approximately.5 4. It is worth noting again that Figure 4.5 depends on the rate of events in the detector and, that in the example shown, the highest rate detector has been chosen, so that probabilities for

98 Chapter 4. Data Analysis I: Event Selection 8 Probability of Having 2 Events Within Specified Period Probability Time (s) Figure 4.5: Probability of having two events within a given time window, as exhibited by detector 99 at 52 C. other detectors will be lower. This probability is small enough that few events not causally associated with the previous event will be removed. Due to the higher rate during calibration runs, the portion of events removed will be more significant, and these need to be corrected for in these cases Multiplicity Cut The final cut applied to the data is to count only events which have four or more piezo signals (of a possible nine) which have been identified as being associated with a bubble as good events. The requirement to have four signals was enforced largely because some detectors used in the analysis do not possess all nine piezos. Studies

99 Chapter 4. Data Analysis I: Event Selection 8 have been finished which vary this cut to values from three to five with no significant change compared to a cut value of four. If the requirement is set any higher, some detectors are unable to achieve any good events, due to missing or malfunctioning piezos. This is very conservative as, in principle, all functioning piezos mounted on the detector should fire during an event. 4. Event Selection Summary In order to show the effects of the individual cuts on the data, tables showing the number of events removed by each cut have been prepared for both the first and second generation DAQ during calibration runs. For the first generation DAQ, the 252 Cf source is used as discussed in section 4... Since the source is approximately equidistant from the four detectors installed, the rate should be roughly equal in these detectors. In these runs, one of the detectors (number 75) has been removed from the list. This detector was equipped with only a single, five channel DAQ board at this time, causing the number of good events to be artificially reduced. Three runs have been included at three different temperatures. The number of events cut by each individual cut are shown in Table 4.2. It should be noted again that the spike cut was designed to remove a specific class of events which were present only in the second generation DAQ system. There were none of these events observed during the use of the first generation DAQ, explaining why Table 4.2 shows no triggers which are removed by the spike cut. Further, the pre-trigger noise cut has very little effect in the first generation DAQ runs, while the fraction cut due to this noise becomes more significant after this DAQ system was

100 Chapter 4. Data Analysis I: Event Selection 82 Events removed by cuts Detector Triggers Burst Pre-Trigger Spike Power Fourier Bubbles Noise Run.6.: 3 hour calibration run at 2.5 C Transform Run.9.: hour calibration run at 28 C Run..:.5 hour calibration run at 35 C Table 4.2: Summary of the effects of the cuts on calibration data as used in the PICASSO data analysis using the first generation DAQ. replaced. For the purposes of comparison, typical WIMP runs at these temperatures have been analyzed and the results are presented in Table 4.3. It is clear from Table 4.3 that detectors #7 and 72 have so few events that statistical studies of the efficiencies would not produce useful results; however, based on these small numbers the fraction of events cut by the individual cuts seem to be commensurate with those shown for the calibration runs. The strength of the 252 Cf source is known (.2µCi), so the cut efficiency can be determined. Previously, the detector efficiency to neutrons in the temperature ranges discussed here was determined to vary between -5 2 counts/neutron/g cm 2 (). The count rates for the runs in Table 4.2 have been determined and are

101 Chapter 4. Data Analysis I: Event Selection 83 Events removed by cuts Detector Triggers Burst Pre-Trigger Spike Power Fourier Bubbles Noise Run.84.: 3 hour WIMP run at 2.5 C Transform Run.22.: 45 hour WIMP run at 28 C Run.93.: 3 hour WIMP run at 35 C Table 4.3: Summary of the effects of the cuts on WIMP data as used in the PICASSO data analysis using the first generation DAQ. shown in Table 4.4 along with the efficiency calculated for each run. Table 4.4 shows that the calculated efficiencies to neutrons is relatively constant for each of these detectors after the cuts are applied while the trigger efficiencies can be quite different. Further, the efficiencies calculated are consistent with those calculated during previous neutron calibrations. These factors indicate that the cuts are functioning properly and removing acoustic noise signals while keeping the majority of the bubble events. It is more difficult to analyse the cut efficiencies for the second generation DAQ. As discussed previously, a neutron source has not yet been placed in an appropriate location to calibrate the detectors while the second generation DAQ has been used. This setup is planned for the next series of calibration runs. None the less, it is

102 Chapter 4. Data Analysis I: Event Selection 84 Detector Trigger Rate Trigger Efficiency Bubble Rate Bubble Efficiency (cts/g/hr) (cts/n/g cm 2 ) (cts/g/hr) (cts/n/g cm 2 ) Run.6.:3 hour calibration run at 2.5 C 7.38±.3 (4.27±.47) 3.5±.2 (3.55±.42) ±.5 (6.65±.56) 3.7±.2 (3.62±.43) ±.2 (3.8±.43) 3.2±. (3.46±.39) 3 Run.9.: hour calibration run at 28 C 7.79±.36 (3.33±.6) 2 5.3±.26 (.64±.) ±.35 (3.8±.6) ±.28 (2.2±.2) ±.26 (2.3±.) ±.24 (.63±.) 2 Run..:.5 hour calibration run at 35 C ±.56 (7.94±.29) ±.35 (3.±.5) ±.57 (8.53±.3) 2.95±.36 (3.38±.6) ±.4 (4.8±.2) ±.32 (2.99±.4) 2 Table 4.4: Summary of neutron count rates and efficiencies in calibration runs. constructive to examine the data which is available. The number of bubbles, triggers and the respective rates are presented in Table 4.5. The increase in rate due to the inclusion of the neutron source for each detector at this temperature is shown in Table 4.6. The issues with the calibration runs using the new DAQ are obvious upon examination of Table 4.6. The increase in trigger rate with the inclusion of the neutron source (unaffected by any data cuts) varies from 8.49 to 2.55 times. Attempts have been made to explain these increases using Monte Carlo simulations of the path of neutrons in the underground setup, which is difficult as the water shielding was modified to allow the insertion of the 3 He counter and an exact description is not available. As a result, this has not provided a fully satisfactory explanation for the variable rates observed in Table 4.6. Other issues being pursued are the threshold

103 Chapter 4. Data Analysis I: Event Selection 85 Detector Triggers Trigger Rate Bubbles Bubble Rate (triggers/hour) Run.626.: 4 hour WIMP run at 46.5 C bubbles/hour Run.66.: 2.4 hour calibration run at 47 C Table 4.5: Summary of trigger and bubble rates during a WIMP and calibration run using the new DAQ Detector Trigger Rate Increase Bubble Rate Increase Table 4.6: Increase in trigger and bubble rate in a WIMP and calibration run using the new DAQ

104 Chapter 4. Data Analysis I: Event Selection 86 behaviours of the various detector types. In addition to the variation in the increase in trigger rate, the absolute trigger rate increase is also low (with the exception of detector 7). An increase in trigger rate of several times has not proved significant enough for accurate studies of the cut efficiencies. Due to these factors, efficiencies during the period of the new DAQ have been estimated using the results from the old DAQ.

105 Chapter 5. DATA ANALYSIS II: SIGNAL EXTRACTION After the undesirable background events have been separated from those caused by the expansion of the superheated droplets, an analysis of the temperature-dependent count rate is required to identify the particles responsible for these events. The typical count rate, as a function of temperature, is shown in Figure 5.. This spectrum is a sum of alpha, gamma and neutron backgrounds with a potential WIMP signal. The analysis is designed to extract the WIMP signal, or put a limit on its possible contribution. To do this requires that we understand the shapes of the spectra expected due to the alpha particles, gamma rays, neutrons and WIMPs. These will be discussed in the subsequent sections. 5. Scope of this Analysis The analysis presented in this thesis begins with the installation of the 4.5 litre detectors in the underground experiment (September 2, 26, run.69.) and ends as of December 3, 27 (run.84.2). A full list of the runs used, including the temperatures and lengths of the runs, is located in the appendix. The list of detectors available for this analysis, as well as their live times, is presented in Table 5.. The live time for each detector has also been summed according to the temperature of the run, with the results shown in Figures 5.2, 5.3 and

106 Chapter 5. Data Analysis II: Signal Extraction 88 Averaged Count Rate for Detector 72, Statistical Error Only Count Rate (events/hr/g) Temperature ( C) Figure 5.: Temperature dependent count rate for detector 72 showing the experimental data.

107 Chapter 5. Data Analysis II: Signal Extraction 89 Run Live Time by Temperature, Detector 7 Run Live Time by Temperature, Detector 7 Live Time (kg d).8 Live Time (kg d) Temperature ( C) Temperature ( C) (a) Detector 7 (b) Detector 7 Run Live Time by Temperature, Detector 72 Run Live Time by Temperature, Detector 73 Live Time (kg d) Live Time (kg d) Temperature ( C) (c) Detector Temperature ( C) (d) Detector 73 Figure 5.2: Live time broken down by temperature for detectors 7 to 73

108 Chapter 5. Data Analysis II: Signal Extraction 9 Run Live Time by Temperature, Detector 75 Live Time (kg d).5.4 Run Live Time by Temperature, Detector 76 Live Time (kg d) Temperature ( C) (a) Detector 75 Run Live Time by Temperature, Detector Temperature ( C) (b) Detector 76 Run Live Time by Temperature, Detector 78 Live Time (kg d) Live Time (kg d) Temperature ( C) (c) Detector Temperature ( C) (d) Detector 78 Figure 5.3: Live time broken down by temperature for detectors 75 to 78

109 Chapter 5. Data Analysis II: Signal Extraction 9 Run Live Time by Temperature, Detector 93 Run Live Time by Temperature, Detector 94 Live Time (kg d).2.8 Live Time (kg d) Temperature ( C) Temperature ( C) (a) Detector 93 (b) Detector 94 Run Live Time by Temperature, Detector 99 Run Live Time by Temperature, Detector 6 Live Time (kg d) Live Time (kg d) Temperature ( C) (c) Detector Temperature ( C) (d) Detector 6 Run Live Time by Temperature, Detector 8 Live Time (kg d) Temperature ( C) (e) Detector 8 Figure 5.4: Live time broken down by temperature for detectors 93 to 8

110 Chapter 5. Data Analysis II: Signal Extraction 92 Detector Number Live Time (kg d) Total Table 5.: Total live time for each detector used for data taking by PICASSO during the analysis period. 5.2 Detector Selection Due to the preliminary nature of several aspects of the PICASSO experiment during the time of data-taking for this analysis, not all of the detectors shown in the previous section produced results which could be included in this study. Several detectors had to be removed from the analysis, for reasons to be outlined in the following sections Detector Fabrication The fabrication of the PICASSO detectors is a complex procedure (as briefly outlined in Section 3..4). As experience with the fabrication and purification methods has increased, the detectors produced have improved in quality. Specifically for the

111 Chapter 5. Data Analysis II: Signal Extraction 93 detectors involved in this run, detectors #7 and 7 were purified using the previous method (using HTiO) instead of the current method (using HZrO). In addition to this removal, detectors #77 and 78 underwent a problem during manufacture, causing the active mass to behave in an unexpected manner. Finally, detector #94 was manufactured outside of the clean room, reducing its reliability. These fabrication issues produced results which are unassociated with the alpha particle and gamma ray PDFs, requiring the removal of these detectors from the analysis Container Damage While detectors were located at the testing facility there was an accident involving the pressurization system. During this incident, the pressure delivered to the detectors exceeded the set amount, causing the destruction of one of the containers under pressurization. Detectors #75 and 76 were also connected to the pressure system at this time and, although they were not destroyed, these containers have exhibited temperature responses since this incident which do not behave as the other detectors. Currently it is thought that these containers became cracked during the over-pressurization, and these cracks produce acoustic noise during temperature or pressure changes, causing bubbles to be identified in the detector. For that reason, these detectors have been excluded from the analysis Inappropriate Fitting After the exclusion of the detectors due to hardware concerns, the remaining detectors were processed using the exclusion fitting program previously discussed. The

112 Chapter 5. Data Analysis II: Signal Extraction 94 exclusion curve of each detector was analyzed as any discontinuities in the exclusion curve indicate that the PDFs used for fitting the alpha particle and gamma ray responses are inappropriate. This procedure causes the removal of detectors #73, 99 and 6. The final detectors used will then be #72, 93 and Alpha Response Function In order to properly extract the potential WIMP signal, the detector response functions of the other bubble-inducing contaminations must be well understood. The first of these responses is the response of the detector to alpha particles. The probability distribution function (PDF) for the alpha particles is extracted from data taken using specially prepared spiked detectors at the Université de Montréal. Two detectors were used; detector # 39 spiked with 2 Bq of 24 Am and detector # 56 with 2 Bq of 238 U. Plots of the two data sets are included in Figure 5.5. Alpha Spiked Calibration Data, Detector 39 Alpha Spiked Calibration Data, Detector 56 Efficiency (events/decay) Efficiency (events/decay) Temperature [ C] (a) Detector #39 response Temperature [ C] (b) Detector #56 response Figure 5.5: Detector responses of alpha-emitter spiked detectors #39 and #56. It is noted that the efficiency (in events/decay) varies between detectors #39 and #56 by nearly a factor of two. However, these overall efficiencies determined by the Université de Montréal differ by this factor likely due to the difficulty in knowing

113 Chapter 5. Data Analysis II: Signal Extraction 95 the equilibrium status of the 238 U chain. Most important is that the shape of the response (the purpose of this section) is unchanged by this overall scaling. A parameterization of these responses is required for their use in the exclusion curve fitting programs. The function chosen should have a rounded onset, as well as a plateau for a temperature region indicative of the maximum sensitivity of the detectors to alpha particles, before the onset of sensitivity to gamma particles. The function chosen is an asymmetric sigmoid, which has a functional form as shown in equation 5.. R = P + P ( + e [ (T P 3 ln(2 /P 4 ) P 2 )/P 3 ] ) P 4 (5.) Although equation 5. has a constant term (P ) which would account for a flat count rate at all temperatures (due to acoustic noise, for example), this term has been fixed to be zero in all data fits described in this document (although it can have a non-zero value in the spiked detector fits). This affects the analysis only by achieving a better fit to the detector temperature response at higher temperatures. The fits of this function to the first spiked detector response are shown in Figure 5.6. In the case of the calibration runs, the constant offset (representing a background count rate) has not been fixed to be zero. These calibration runs were taken at the Université de Montréal in an environment on the surface, increasing the count rate at these lower temperatures due to the higher neutron flux. In both of the cases shown, the fit value for the background count rate is of the order of 7 events/decay; indicating that this is not a large effect. However, the inclusion of this

114 Chapter 5. Data Analysis II: Signal Extraction 96 Alpha Spiked Calibration Data, Detector 39 Alpha Spiked Calibration Data, Detector 56 Efficiency (events/decay) χ 2 / ndf 5.5 / 23 p 7.867e-7 ±.928e-7 p.77 ±.538 p ±.483 p ±.228 p ± Efficiency (events/decay) χ 2 / ndf / 23 p 2.942e-6 ± 7.48e-7 p.65 ± 8.587e-5 p ±.368 p ±.2272 p ± Temperature [ C] (a) Detector 39 alpha spiked response fit Temperature [ C] (b) Detector 56 alpha spiked response fit Figure 5.6: Fits to the detector responses of alpha-emitter spiked detectors 39 and 56. offset significantly improves the quality of the fit for these calibration runs taken on the surface with a higher neutron background rate. More recently, another detector was produced for use in the determination of the alpha calibration curve. In this case, 226 Ra was injected into the detector during the manufacturing process. The absorption of 226 Ra or the resulting daughter ( 222 Rn) by the freon or the surfactant located on the surface of the droplets could result in the alpha emitter being concentrated on the droplets, providing a slightly different alpha response to that seen if the emitter is isotropically distributed throughout the gel matrix, as is expected for 24 Am and 238 U. The difference in the responses is that the location of the emitter on the surface of the droplets results in the possibility that the recoiling nucleus will enter the droplet, providing sufficient energy to cause a nucleation site. This will be further discussed in section The count rate from this spiked detector is shown in Figure 5.7, which makes it clear that the response of this detector to the 226 Ra spike is very different from the response of the 238 U or 24 Am spiked detectors, as seen in Figure 5.5.

115 Chapter 5. Data Analysis II: Signal Extraction 97 Radon Spiked Detector Calibration Data Count Rate (events/hr/g) Temperature [ C] Figure 5.7: Temperature dependent count rate for a detector spiked with 226 Ra. In order to fit this second alpha spiked detector response, a sigmoid function was determined to be a better fit. This expression for this function is shown in equation 5.2. R = P + P + e (P 2 (T P 3 )) (5.2) In this equation, parameter represents the offset from a zero baseline, parameter represents the amplitude of the signal, parameter 2 represents the steepness of the slope and parameter 3 represents the offset in the turn on from zero. Parameters and are obviously strongly correlated at high temperatures; however, their inclusion in this functional fit improves the quality of the fit at low temperatures. Parameter can be ignored for detectors in the low background environment underground. The fit of this function to the data is shown in Figure 5.8. The function is a reasonable fit above 2 C, where the WIMP search data exists. The fit below 2 C

116 Chapter 5. Data Analysis II: Signal Extraction 98 is not relevant for this analysis and is a better fit when a combination of both alpha PDFs is used to fit the actual data. Count Rate (events/hr/g) Radon Spiked Detector Calibration Data χ 2 / ndf 27.6 / 2 p.468 ±.326 p 4.7 ± 2.76 p ±.37 p ± Temperature [ C] Figure 5.8: Fit to the count rate in the detector spiked with 226 Ra. The fits shown in Figures 5.6(b) and 5.8 will be used in the fitting of the alpha response to the count rates obtained from the detectors. 5.4 Gamma Response Function The PDF for the gamma response of the detectors was also determined using data collected while including a radioactive source in the experimental setup. In this case, a 22 Na source was placed adjacent to a detector while a full temperature scan of the count rate was taken. Since the gamma response is observed to affect the detectors only at temperatures higher than approximately 45 C, only high temperature runs were analyzed. The resulting temperature dependent count rate is shown in Figure 5.9.

117 Chapter 5. Data Analysis II: Signal Extraction 99 Gamma Calibration Data Efficiency (events/decay) Temperature [ C] Figure 5.9: Temperature dependent count rate for detector adjacent to 22 Na source. The data shown in this plot extend far beyond the functional range of any detectors used for taking data for analysis purposes, as the maximum temperature of these calibration runs is approximately 7 C while the maximum for the underground detectors is 55 C. The full gamma response is fit with the same function as that used to fit the surface based alpha spiked detector, shown in equation 5.2. The onset of sensitivity of the detectors to gamma rays as well as the plateau are governed by the same equations as those used for the alpha particles, suggesting the use of the same equations. The result of the fit is shown in Figure 5.. Because of the limits on the temperature range in the underground environment, the full gamma range need not be fit, and only the lower temperatures shown in Figure 5.9 will be relevant for data fitting purposes. The fits to this function are then found to be exponential, with the functional form as shown in equation 5.3.

118 Chapter 5. Data Analysis II: Signal Extraction Gamma Calibration Data Efficiency (events/decay) χ 2 / ndf 3.6 / 4 p -2.85e-7 ±.87e-7 p.3658 ±.348 p ±.4985 p ± Temperature [ C] Figure 5.: Temperature dependent count rate for detector adjacent to 22 Na source fit with gamma response function 5.2. y = e []+[] T (5.3) This exponential form fits the function with parameter representing the amplitude of the exponential curve and parameter representing the exponential slope. As stated previously, the data will be fit without including the plateau region, as this is far beyond the temperature capability of the underground detectors. An example of the fit is shown in Figure 5.. Although the function 5.3 appears to describe the response adequately in the functional range, it is not useful to determine the apparent onset of the gamma response, as this value will be entirely determined by the level of the alpha plateau in count rate. As the alpha contamination is driven lower, the apparent gamma onset will move to lower temperatures. In addition to this complication, the functional

119 Chapter 5. Data Analysis II: Signal Extraction Gamma Calibration Data Efficiency (events/decay) χ 2 / ndf.78 / 9 p ±.936 p.8949 ± Temperature [ C] Figure 5.: Temperature dependent count rate for detector adjacent to 22 Na source fit with gamma response function 5.3. temperature range of the detectors does not permit the full gamma response curve to be explored. This creates an issue because the fit of the sigmoid will not converge without some indication of the plateau level. For this reason, the sigmoid for the γ response was not used in the actual detector fit, but instead the simple exponential version of 5.3 was found to describe the data well. 5.5 Neutron Response Function Neutron calibrations are a valuable tool to understand the performance of the detectors. However, at present the background rates are dominated by α and γ contamination and a parameterization of the neutron PDF has not been generated. This is further discussed in section 6.5. The response of the detectors to neutrons will be a convolution of the neutron spectrum with the probability of bubble formation, previously discussed in section 3

120 Chapter 5. Data Analysis II: Signal Extraction 2 in equation 3.9. The differential energy spectrum of muon-induced neutrons in the SNOLAB environment has been calculated in (3). A characterization is provided for this spectrum; however, this is accurate only at neutron energies above MeV. In future generations of purer PICASSO detectors, alphas will not be the limiting factor, and a complete understanding of the neutron spectrum and response will be required. The count rate of neutrons in the PICASSO detectors will be discussed further in section Neutralino Function The mathematics for the determination of the neutralino function has been discussed in Chapter 2. However, the terms relating to the detector response for PICASSO must be understood in greater detail. The majority of this section is derived following (32) closely. It is important to know the range of recoil energies possible given the energy of the incoming dark matter particles (represented by E ). After some algebra, it can be shown that, for an incoming neutralino of mass M DM, a target nucleus of mass M T and an angle between the incoming track and the recoiling track θ, the recoil energy of the nucleus E R in relation to the energy of the incoming particle (E ) can be expressed as shown in Equation 5.4. E R = ( ) 4MDM M T (M DM + M T ) 2 cos2 θ E (5.4) In order to simplify this equation, a kinematic factor, r, can be separated and this is expressed in Equation 5.5.

121 Chapter 5. Data Analysis II: Signal Extraction 3 r = 4M DMM T (M DM + M T ) 2 (5.5) In order to determine the spectrum of nuclear-recoil energies, the total rate of dark matter particles incident on the Earth must be known, and this will be expressed as R. The event rate (per unit mass), R, will be in units of s kg. These units are generally chosen in keeping with a fixed mass density of dark matter in the halo, resulting in a mass-dependent flux. With the assumption that the velocity distribution of the neutralinos is Maxwellian, the differential recoil spectrum can be shown to be as expressed in equation 5.6. dr de R = R E r e E R/E r (5.6) The rate of neutralinos striking the detector dependent on the recoil energy is vital for the characterization of the neutralino response curve in a detector. However, there are several corrections which must be applied to equation 5.6 in order to accurately reflect the count rate observed by experiments on Earth. These corrections include taking account of the velocity of the Earth through the dark matter halo, the energydependent efficiency of the detector, the cross-section for spin-dependent and spinindependent experiments, and the form factor correction due to the finite size of the nucleus. The use of these corrections can be incorporated into equation 5.6 to give equation 5.7, which contains the additional terms for the modified spectral function (S(E), which contains the Maxwellian form of the neutralino spectrum shown in equation

122 Chapter 5. Data Analysis II: Signal Extraction 4 5.6), the nuclear form factor (F(E)) and the interaction correction which varies according to the dominant method of interaction (I). dr de R = R S(E)F 2 (E)I (5.7) The first term to be examined in detail is the rate of counting the incident dark matter particles. The differential rate on a target with an atomic mass A (in AMU) can be calculated using equation 5.8, where N is Avogadro s number, σ is the crosssection per nucleus and n is the number density of dark matter particles with a velocity v. (Note: the number density depends on the mass of the dark matter particles, as it is the mass density of the galaxy which is assumed.) dr = N σvdn (5.8) A If the zero-momentum transfer assumption is made (in which case the crosssection is constant and will be written as σ ), equation 5.8 can be integrated to find the total rate R (the finite size of the nucleus will be dealt with later). R = N A σ vdn (5.9) R = N A σ n < v > (5.) The rate calculation shown in equation 5. uses the mean particle density n, which is calculated by dividing the dark matter density (ρ DM ) by the mass of the

123 Chapter 5. Data Analysis II: Signal Extraction 5 dark matter particles (M DM ). If the velocity of the Earth (v E ) is included in the calculations, the differential particle density can be defined as dn = n k f( v, v E)d 3 v (5.) where k is a normalization constant so that the integration of dn from a velocity of zero to the escape velocity (v esc ) is n. The velocity distribution used in equation 5. is assumed to be Maxwellian, as shown in equation 5.2 with a mean velocity of v. f( v, v E ) = e ( v+ v E) 2 /v 2 (5.2) The integration required to calculate k can then be expressed as in equation 5.3. k = vdn = 2π dφ + vesc d(cos θ) e ( v+ v E) 2 /v 2 dv (5.3) For the purpose of these calculations, it will be assumed that the neutralinos do not leave the galaxy, i.e. that v esc =. As described in (32), this is an excellent approximation. Using this assumption, the integration in Equation 5.3 can be performed to give the value shown in 5.4. k = (πv 2 )3/2 (5.4) This value of k can then be substituted into equation 5.9 along with the expansion for n to give equation 5.5, where R is the event rate per unit mass assuming that

124 Chapter 5. Data Analysis II: Signal Extraction 6 the velocity of the Earth in the dark matter halo (v E ) is zero and that the escape velocity (v esc ) is infinite. R = 2 N ρ DM σ π /2 v (5.5) A M DM The constants in equation 5.5 can be scaled to the generally accepted values, resulting in equation 5.6. R = 53 M DM M T σ pb ρ DM.4GeV/c 2 /cm 3 v 23km/s (5.6) Detailed calculations, additionally accounting for the real escape velocities, the annual orbit of the Earth around the sun, and the daily rotation of the Earth have been made. These lead to a more precise expression, with a several percent variation in the count rate annually (). The observation of this annual variation would be a strong indication of the existence of dark matter. The form factor shown in equation 5.7 must be modified to include an adjustment due to the finite size of the nucleus. The standard expression for the cross-section is expressed in equation 5.7. σ(qr n ) = σ F 2 (qr n ) (5.7) In equation 5.7, r n is a characterization of the effective radius of the target nucleus. The qr n term can be expressed in terms of the atomic mass of the nucleus in AMU (A), the recoil energy of the nucleus (E R ) and the appropriate experimentally determined constants a n and b n describing the nuclear radius.

125 Chapter 5. Data Analysis II: Signal Extraction 7 qr n = A /2 E /2 R (a na /3 + b n ) (5.8) The correction term due to the nuclear form factor can now be calculated using terms derived from the shell model applied to the individual nucleus, which can be expressed as: F 2 (qr n ) = S(q) S() (5.9) where S(q) = a 2 S (q) + a 2 S (q) + a a S (q) (5.2) with the a i values determined experimentally using the coupling strength of the W boson to the proton or neutron. The S xy terms are the isoscalar, isovector and interference term, respectively (33). A commonly used approximation (32) for the spin-dependent form factor is shown in 5.2. F(qr n ) = sin qr n qr n (5.2) Values for the form factor have been determined for 9 F, the nucleus of interest in the PICASSO experiment. Given the small A value for this nucleus, calculations have been carried out using r n =2.8 fm and q = kev, a large momentum transfer. Using these values, the F 2 correction term, given by equation 5.2 was.97, very close to unity. As the momentum transfer is reduced in value, this value will approach

126 Chapter 5. Data Analysis II: Signal Extraction 8 unity, as seen in equation 5.2, so the assumption that the form factor correction is unity is justified, as the momentum transfers will be small. The remaining quantity in equation 5.7 is the interaction term I. As previously stated, this is the interaction term between the neutralino and the nucleus, which will be different in the spin-dependent and spin-independent cases and also depending on the SUSY model used to define the neutralino and the interaction process (34). Only the spin-dependent case will be examined here, as this is of most interest to the PICASSO experiment. Using the same formalism used in (32), the I term can be defined as in equation 5.22, when I s is used to denote the spin-dependent interaction term. σ = 2G2 F π 4 r2 I s (5.22) In equation 5.22, σ is the effective cross-section of the dark matter particle, r is the reduced mass of the neutralino and the target nucleus, previously defined in equation 2.9, and G F is the Fermi constant. The spin-dependent interaction term I s can be expressed as in equation 5.23 (32). I s = [a p < S p > +a n < S n >] 2J + J (5.23) In equation 5.23, the a p and a n terms represent the spin dependent coupling of the neutralino to the nucleons, J represents the nuclear spin and <S p > and <S n > are the expectation values for the spin content of the proton and neutron group, respectively, in the nucleus. The values for these constants are then important in

127 Chapter 5. Data Analysis II: Signal Extraction 9 Nucleus Z J <S p > <S n > 7 O 8 5/ F 9 / Na 3/ Si 4 / Ge 32 9/ Nb 4 9/ I 53 5/ Xe 54 / Table 5.2: Effective spin values for nuclei relevant to dark matter searches, taken from (35). determining the effectiveness of a nucleus to interact with dark matter. These values have been tabulated for a selection of nuclei currently in use in dark matter search experiments and are shown in Table 5.2. The values in Table 5.2 are derived primarily from the Extended Odd Group Model (EOGM) described in (36). This variant of the odd group model calculates the contribution of both nucleons (proton and neutron), regardless of which is the unpaired nucleon. The expected spin for the odd (unpaired) nucleon proceeds as in the odd group model, as shown in equation 5.24, in which µ is the magnetic dipole operator and the free-nucleon g factors are also used. S odd = µ gl odd J g s odd gl odd (5.24) Note that the subscript odd replaces either proton or neutron, dependent on the structure of the nucleus. In order to calculate the paired nucleon spin expectation value, the calculation of the isoscalar magnetic moment is required, as shown in equation 5.25.

128 Chapter 5. Data Analysis II: Signal Extraction µ IS = J +.76(S odd + S even ) + µ x (5.25) In the isoscalar calculation, the µ x term represents a correction term to µ, which has been shown to be small. This allows the calculation of the expectation value of S even with knowledge of S odd and several physical parameters. The results of these calculations are shown in Table 5.2. It is worthy of note that <S p > is quite large for 9 F, the active target used in the PICASSO project. The correction terms to this point have specified an experiment only through the use of a particular target nucleus. In addition to these four correction terms, the experimental sensitivity must also be considered in the calculation of the expected count rate. Equation 5.7 will now be rewritten as shown in equation dr de = R S(E)F 2 (E)Iǫ(T, E) (5.26) In equation 5.26 the sensitivity of the detector has been included as ǫ, dependent on both temperature T and nuclear recoil energy E. This detector efficiency has been previously outlined in equation 3.9. Combining these two equations gives a proper representation of the expected count rate in the PICASSO detector. In order to determine the rate as a function of deposited energy at any given energy range, equation 5.26 must be integrated over the temperature range which would be visible in the detector. This is shown in equation 5.27, with the minimum visible energy denoted E min and maximum energy E max.

129 Chapter 5. Data Analysis II: Signal Extraction R obs = Emax E min R S(E)F 2 (E)I s ǫ(t, E)dE (5.27) While the majority of the terms in equation 5.27 are independent of temperature, the dependence in the detector efficiency remains, enforcing the temperature dependence of the observed count rate. Hence R obs is properly expressed as R obs (T), including the temperature dependence. The efficiency term, without consideration for the efficiency of the analysis cuts, was calculated previously in equation 3.9. The expected count rate can be plotted using this formalism, with the results shown in Figure 5.2. For demonstration purposes, these were calculated for a fixed neutralino total spin-dependent nuclear cross section of pb. It should be noted that this is not the proton-neutralino cross-section, but the cross-section of the neutralino interacting with the entire nucleus. 5.7 Fitting The fitting of the temperature dependent count rate to the PDFs outlined above will either provide evidence for a non-zero contribution from neutralinos or determine the maximum cross-section which can be excluded at a 9% Confidence Level (CL) if no neutralino signal is detected. The method for performing these fits is outlined below. The first step is to determine the shapes of the alpha and gamma response curves. In order to identify the alpha responses accurately, the functional form of all three responses (gel- and droplet-based alphas, and gamma responses) are fit to the spiked data curve, and all parameters are fixed to the values obtained from these fits.

130 Chapter 5. Data Analysis II: Signal Extraction 2 Expected Neutralino Response using PICASSO Detectors Count Rate (events/hr/g) GeV Neutralino 5 GeV Neutralino GeV Neutralino 5 GeV Neutralino Temperature ( C) Figure 5.2: Expected response to neutralinos in PICASSO detectors for varying neutralino masses with a total nuclear cross section of pb.

131 Chapter 5. Data Analysis II: Signal Extraction 3 Only the overall scale of each curve is subsequently allowed to vary. Once a fit has been obtained for each of these three response curves, the shape of the combined response curve is determined by fixing the scale factor for the droplet-based alpha and gamma responses as a ratio of the gel-based alpha response. This ensures that the overall shape of the background spectrum will not vary during the subsequent fitting processes. The full function used to fit the detectors as described in the previous sections is shown in equation The equation has been divided into sections to show the three different responses which are, in order, the gel-based alpha emitter response, the droplet surface based alpha emitter response and the gamma response, respectively. The multiplicative parameters are shown here, with P representing the offset from a zero count rate (fixed to zero in the final fits), P showing the contamination level of the gel-based alpha emitter response, P 2 showing the contamination of the droplet surface based alpha emitter response, and P 3 representing level of the gamma response. ( ) R = P + P ( + e [ T 3.4ln(2/ ) 24.6)/3.4)] ) ( ) +P 2 + P + e 2.76 (T 4.3) 3 ( (5.28) e T) An example of the result of this fitting strategy is shown in Figure 5.3. Figure 5.3(a) shows the full range (in order to show the minimal contribution for the surface alpha response). A version of the same plot zoomed in to the region of interest is shown in Figure 5.3(b).

132 Chapter 5. Data Analysis II: Signal Extraction 4 Count Rate (events/hr/g) PDF Fits to Detector 72 Data Detector 72 Data Old Alpha Response Gamma Response New Alpha Response Combined Response Temperature ( C) (a) Full range view of fit Count Rate (events/hr/g) PDF Fits to Detector 72 Data Detector 72 Data Old Alpha Response Gamma Response New Alpha Response Combined Response Temperature ( C) (b) Zoom of fit Figure 5.3: Example of fitting of PDFs to detector 72. The fitting procedure has been carried out for all detectors within the scope of this analysis (those shown in Table 5.) and the resultant fits are shown in Figures 5.4, 5.5 and 5.6. It is apparent from Figures 5.4 and 5.5 that the PDFs as generated by the spiked detector data do not adequately fit several of the detectors which have taken data in this phase of the PICASSO experiment. Specifically, the response of detectors 75 and 76 (with the fit shown in Figures 5.5(a) and 5.5(b) respectively) do not fit the expected alpha or gamma responses. The primary difference is the count rate at low temperature, which deviates strongly from the equations determined using the spiked detectors. This will be discussed further in section 7.5. The lack of an appropriate PDF for the alpha and gamma responses in these detectors resulted in their removal from the data analysis. This reduces the integrated live time accrued in the experiment. However the unusual slope of the temperature response is unexplained to this point and therefore these cannot be included in the subsequent steps of the analysis. Note that, during this period of PICASSO opera-

133 Chapter 5. Data Analysis II: Signal Extraction 5 Count Rate (events/hr/g) PDF Fits, Detector 7, Statistical Errors Only χ 2 / ndf 238 / 6 p ± p.46 ±.8899 p2.368 ±.626 p3.339 ±.4798 Count Rate (events/hr/g) PDF Fits, Detector 7, Statistical Errors Only. χ 2 / ndf 362 / 9 p ± p.783 ±.9757 p2.2 ±.853 p3.982 ± Temperature ( C) (a) Detector Temperature ( C) (b) Detector 7 Count Rate (events/hr/g) PDF Fits, Detector 72, Statistical Errors Only. χ 2 / ndf 9 / 3 p ± p.4543 ±.522 p ±.442 p ±.24 Count Rate (events/hr/g) PDF Fits, Detector 73, Statistical Errors Only. χ 2 / ndf / 3 p ± p.4296 ±.397 p ±.7787 p ± Temperature ( C) (c) Detector Temperature ( C) (d) Detector 73 Figure 5.4: Alpha and gamma PDF fits for detectors 7 to 73 Count Rate (events/hr/g) PDF Fits, Detector 75, Statistical Errors Only. χ 2 / ndf 7524 / 73 p ± p.3662 ±.2489 p ±.37 p ±.269 Count Rate (events/hr/g) PDF Fits, Detector 76, Statistical Errors Only χ 2 / ndf 526 / 78 p ± p.4626 ±.2429 p ±.76 p ± Temperature ( C) (a) Detector Temperature ( C) (b) Detector 76 Count Rate (events/hr/g) PDF Fits, Detector 77, Statistical Errors Only. χ 2 / ndf 2.27 / 8 p ± p.424 ±.6885 p ±.92 p3.45 ±.356 Count Rate (events/hr/g) PDF Fits, Detector 78, Statistical Errors Only. χ 2 / ndf / 8 p ± p.494 ±.725 p ±.55 p3.349 ± Temperature ( C) (c) Detector Temperature ( C) (d) Detector 78 Figure 5.5: Alpha and gamma PDF fits for detectors 75 to 78

134 Chapter 5. Data Analysis II: Signal Extraction 6 Count Rate (events/hr/g) PDF Fits, Detector 93, Statistical Errors Only χ 2 / ndf 7.22 / 46 p ± p.2838 ±.388 p ±.338 p3.955 ±.384 Count Rate (events/hr/g) PDF Fits, Detector 94, Statistical Errors Only χ 2 / ndf / 25 p ± p.474 ±.655 p2.24 ±.529 p3.234 ± Temperature ( C) (a) Detector Temperature ( C) (b) Detector 94 Count Rate (events/hr/g) PDF Fits, Detector 99, Statistical Errors Only. χ 2 / ndf / 4 p ± p.745 ±.22 p ±.9758 p ±.7598 Count Rate (events/hr/g) PDF Fits, Detector 6, Statistical Errors Only. χ 2 / ndf / 6 p ± p 4.624e-5 ±.2499 p ±.222 p ± Temperature ( C) (c) Detector Temperature ( C) (d) Detector 6 Count Rate (events/hr/g) PDF Fits, Detector 8, Statistical Errors Only. χ 2 / ndf 34.9 / 9 p ± p.4238 ±.358 p ±.3229 p ± Temperature ( C) (e) Detector 8 Figure 5.6: Alpha and gamma PDF fits for detectors 93 to 8

135 Chapter 5. Data Analysis II: Signal Extraction 7 tions, numerous new detector purification methods were developed and tested, with various of levels of success. It is not therefore unexpected that many of these detectors will have responses as yet not understood and it may not be valid to compare these to the detectors which were calibrated with the sources. The behaviour of bubbles in the underground environment is different from those on the surface due to the substantially increased pressure underground, affecting the shape of the response. The change in response is caused by the change in the boiling point of the Freon and this must be taken into account during the fitting process. This was accomplished using the spiked detector data to give the temperatures of the onset of the plateau and fitting the data from the underground detectors to this temperature by adjusting the boiling point of the active mass, and therefore the effective temperature. The data taken underground fits well with the data taken on the surface, provided this effective temperature correction is made. Further discussion of the effective temperature correction can be found in section Exclusion Limit Fits The intent of this fitting procedure is to determine the maximum detectable neutralino cross-section over a range of masses. This is achieved by fixing the mass in the neutralino response in equation 5.27 and fitting the data to the combined alpha, gamma and neutralino responses. In this combined fit, the only parameters allowed to vary are the overall scale of the background count rate (the alpha and gamma responses) and the cross-section of the neutralino. In order to preserve the quality of the fits, the ratio of the two alpha responses is fixed during the fitting process. This

136 Chapter 5. Data Analysis II: Signal Extraction 8 allows the removal of one parameter from the final response, which was important when the number of data points was limited. The total function used to fit the detectors is then a combination of the non-nuclear recoil related responses (shown in equation 5.28) and the expected neutralino rate (shown in equation 5.27). The results of the exclusion curve fitting for detector 72 are shown in Figure 5.7, showing the best exclusion fit using one detector that has been obtained from this analysis. Exclusion Curve Determined Using Detector 72 Cross-Section (pb on proton) Neutralino Mass (GeV) Figure 5.7: Exclusion curve determined using detector 72. Provided that the fit cross-section is consistent with zero (as is the case in all of the fits to this data), once the fit cross section is obtained for each trial neutralino mass, the 9% confidence level is determined using the uncertainty established by

137 Chapter 5. Data Analysis II: Signal Extraction 9 the fit for the neutralino cross section. The positive uncertainty associated with this fit value is taken, and the final exclusion value is the addition of the fit cross section and.64 times the uncertainty to give the 9% confidence level value. The result of performing this procedure for a range of neutralino masses is shown in Figure 5.7. The exclusion values in this figure have been converted to the crosssection on the proton using the conversion equation given in (37) and shown in equation 5.29, in which µ p is the reduced mass of the proton, µ T is the reduced mass of the target nucleus, J is the total nuclear spin and < S p > is the expectation value of the proton group spin. σ p = σ 3 J 4 J + µ 2 p µ 2 T < S p > 2 (5.29) Using equation 5.29, the value for the cross-section obtained from the fit is converted to the cross-section of the neutralino scattering from the proton, providing the final result. For the exclusion limits, it is assumed that the incoming WIMP scatters using a spin-dependent interaction on the fluorine nucleus, which defines the values used in equation The total nuclear spin J= 2 and < S p >=.44. As an example of the set limits, several illustrative plots have been prepared. Shown in Figure 5.8 are the count rates due to the neutralino at a mass of GeV and 23 GeV resultant from the fit to detector 72. These values have been picked as they give two different limits of the count rate. The peak exclusion limit (at a 9% CL) obtained from detector 72 occurs at approximately 23 GeV, with a cross-section of approximately. pb on the proton, converted from a total fit cross-section of

138 Chapter 5. Data Analysis II: Signal Extraction 2.82 pb. The limit at lower neutralino mass is higher in cross-section; for a GeV neutralino mass, the cross-section fit at a 9% CL is 2.2 pb on the proton, converted from 3.8 pb overall. Neutralino Fit Response for Detector 72 Count Rate (events/hr/g) -3-4 GeV Neutralino Response 23 GeV Neutralino Response Temperature ( C) Figure 5.8: Example of neutralino response curves fit to detector 72 at and 23 GeV at a 9% confidence level. The differences in the neutralino responses shown here appear exaggerated due to the scale of the plot. In order to further demonstrate the validity of the cross-section fit, Figure 5.9 shows the effect of increasing the 9% confidence level exclusion limit cross-section by a factor of five. It is clear from Figure 5.9 that increasing the cross-section gives a response curve which does not fit the data as appropriately as the unscaled version.

139 Chapter 5. Data Analysis II: Signal Extraction 2 Detector 72, 23 GeV Neutralino Fits Count Rate (events/hr/g) - 23 GeV Neutralino Exclusion Plot 23 GeV Neutralino 5X Increased Cross Section Temperature ( C) Figure 5.9: Effect of increasing fit cross section for 23 GeV neutralino by a factor of five.

140 Chapter 5. Data Analysis II: Signal Extraction Analysis of Previously Published Data In order to verify the correct operation of the code used to determine the exclusion values from the detector response, the data used in () was analyzed using the method created for this analysis. This resulted in a peak exclusion cross-section of 2.69 pb on the proton at a WIMP mass of 23.7 GeV at a 9% confidence level. This can be compared to the result in (),.3 pb on the proton at 29 GeV. There are several reasons for these differences. The dominant reason is that the background PDFs have changed from those used in (). The newer calibration curves use the data collected from the larger volume detectors, which may not be appropriate to the smaller versions. Additionally, the method described in this analysis also takes into account the response of the detectors to gamma rays during the fitting process, which was not included in previous analysis. This method functions well for data which includes temperatures high enough to observe the start of detector sensitivity to gamma rays. The data taken with the previous phase of detectors is shown in Figure 5.2, and does not include temperatures at which gammas would be detected. In the absence of the detector showing a response to gammas, the fitting procedure discussed in this document attempts to include a gamma response, which reduces the sensitivity of the exclusion procedure Stability of Fits Since the fits to the data are taken in steps of neutralino mass, and the values of the fits to the alpha and gamma contributions to the data are allowed to vary, one test

141 Chapter 5. Data Analysis II: Signal Extraction 23 Official PICASSO Data - Det 4 (Temperature Plot) Count Rate (events/hr/g) Temperature [ C] Figure 5.2: PICASSO data used in ().

142 Chapter 5. Data Analysis II: Signal Extraction 24 of the stability of the fits is to examine the contamination scale values from the fits as the neutralino mass is changed. These plots have been produced for all of the active detectors; however, only two examples are discussed here. In the examples resulting from fits to detector 72 the scale of the background obtained from the fit is very stable, showing no deviation to.%. This is not generally the case, as some other detectors have difficulty fitting the response of high mass neutralinos, above approximately 2 GeV. At masses higher than this, there begins to be a degeneracy between the expected neutralino response and the detector alpha response. This can be seen in Figure 5.2 in which the expected neutralino response curve for a 5 GeV neutralino is plotted with the alpha curve, scaled to allow comparison. An example of an alpha curve plot for a detector which does not fit the alpha response derived from the calibration data well is shown in Figure 5.22 for detector 75. It is clear from Figure 5.22 that the fit is much less stable across mass values for this detector than for detector 72, as discussed previously. This is in part due to the degeneracy between the shape of the alpha and the neutralino response curves and in part due to the fact that the background PDFs do not describe this detector background well. This stability provides a tool to separate usable detectors from those which should not be used in the final result.

143 Chapter 5. Data Analysis II: Signal Extraction 25 Comparison of Large Mass Neutralino and Alpha Response Curves Count Rate (arbitrary units) Alpha Response -7 5 GeV Neutralino Response Temperature ( C) Figure 5.2: Comparison of the shape of the 5 GeV, pb expected neutralino response with alpha response.

144 Chapter 5. Data Analysis II: Signal Extraction 26 Scale value by mass for Detector 75 Fit Scale Value Mass (GeV) Figure 5.22: Value of the fit contamination scale over mass for detector 75 indicating the lack of stability of the fit.

145 Chapter 5. Data Analysis II: Signal Extraction Combined Fits The next step in the analysis process is to include more than one detector in the fit to determine the exclusion limit. The algorithm used for fitting the combined detectors is slightly different from that used for the one detector process. The process used to fit the alpha curves is the same as that described in the previous section for the one detector procedure performed for each detector to be used in the creation of the exclusion curve. Similar to the one detector process, the ratio of the droplet-based alpha contamination to the gel-based alpha contamination and the gamma contamination are fixed using the fit to the data. As discussed previously, the freon boiling point has been adjusted at this stage, taking account of the difference in ambient pressure between the surface and the underground detectors. The neutralino cross-section is fit while fixing the neutralino mass and determining the 9% confidence level for the cross-section. The chi-squared value is calculated for each detector using the traditional method and then summed over the detectors used in the analysis, as shown in equation 5.3, where O T is the observed count rate at temperature T, R T is the expected count rate and R is the count rate uncertainty at that point. χ 2 combined = detectors temperatures O T R T R (5.3) This chi-squared combination is then used as figure of merit and minimized to find the cross-section. In this way, the combination of the detectors increases the active mass and therefore the exposure used in the fit while recognizing that each

146 Chapter 5. Data Analysis II: Signal Extraction 28 detector can have different ratios of the background PDFs. The effect of this combination is that detectors which do not fit the predicted background count rate spectrum well may interfere with detectors which do, and can thus cause a decline in the limit of the exclusion curve. An example is shown in Figure 5.23, which presents the exclusion curve generated by using detectors 72 and 75. Exclusion Curve Using Detectors 72 and 75 Cross-Section (pb on proton) 2 Neutralino Mass (GeV) Figure 5.23: Exclusion curve determined using detectors 72 and 75 showing effect of using detectors which do not exhibit the predicted alpha response. It is clear from Figure 5.23 that the inclusion of detectors with count rates which are not adequately described by the known alpha responses can be ruinous to the fitting required to determine the exclusion curve. Not only is the exclusion value increased significantly (as seen when comparing Figures 5.23 and 5.7), but the

147 Chapter 5. Data Analysis II: Signal Extraction 29 shape of the 9% confidence level curve also ceases to be smooth, with discontinuities between adjacent trial neutralino masses.

148 Chapter 6. BACKGROUNDS, CORRECTIONS AND SYSTEMATIC UNCERTAINTIES The study of the backgrounds, run time corrections and systematic uncertainties associated with the PICASSO project is vitally important, as it is for all direct dark matter detection experiments. The final results of the uncertainties calculated here must be applied to the count rate, and will be tabulated for clarity at the end of the chapter. The final results will be applied to the count rate, calculated as shown in equation 6.. These corrections have not been applied to any plots previously shown in this thesis. CountRate = # bubbles active mass (g) length of run (h) (6.) The corrections and uncertainties associated with the PICASSO experiment can be divided into five categories depending on the manner of their inclusion in the final analysis. These are: Corrections, to account for measured efficiencies associated with the analysis cuts as well as the run length and effective temperature (Section 6.). Systematic uncertainties in determining the temperature and pressure inside the detector (Section 6.2). 3

149 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 3 Systematic uncertainties in determining the count rate at a given temperature (Section 6.3). Systematic uncertainties associated with the fitting procedure (Section 6.4). Systematic uncertainties associated with neutron backgrounds (Section 6.5). The first category includes the efficiency corrections (discussed in Chapter 5), which must be applied to the terms in equation 6. directly. These corrections are not uncertainties, but modifications to the values for the terms in equation 6.. The same method is applied to account for changes to the run length and effective temperature. The second category are the systematic uncertainties which are accounted for in the response of the detectors by modifying the temperature itself. These include not only uncertainties on the temperature measurement, but also in the pressure of the droplets themselves. The equations used to make the conversion between pressure and temperature uncertainty will be discussed in this section. Thirdly, the uncertainty directly associated with the count rate will also be discussed in detail. This will include bubble detection and identification uncertainties as well as any corresponding to the terms in equation 6.. The uncertainty associated with the fitting procedure itself will be discussed and quantified. Although this uncertainty must be calculated during the fitting process, an example is included to show the typical effect. Finally, the effects of the neutron backgrounds are discussed and their effect on the uncertainty in the count rate included. A summary of these uncertainties will

150 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 32 conclude the chapter. 6. Corrections There are three corrections which must be applied to the count rate. The first is to account for events improperly removed by the bubble cuts discussed in Chapter 5. The efficiency of the cuts will be estimated and accounted for in the number of bubble events recorded. The remaining corrections are the correction of the run length due to system dead time and the temperature due to the ambient pressure fluctuations in the underground setup. 6.. Cut Discrimination Efficiencies Although the cuts outlined in Chapter 5 are required to remove acoustic noise and electrical interference related events from the data, these cuts may remove appropriate bubble events. In order to account for this, the efficiency of the cuts has been calculated and will be applied to the number of bubble events recorded. Determining the cut efficiencies relies on the neutron calibration data taken during PICASSO operations. In order to determine which neutron events have been inappropriately removed, the average rate during WIMP runs at the available neutron calibration temperatures will be determined. The first generation DAQ has neutron calibration runs taken with three viable detectors (#7, 72 and 76) at three temperatures: 2.5, 28 and 35 C. Examining the first generation WIMP runs at these temperatures results in the rates shown in Table 6., with the rates shown in triggers/hr/g. During the time in which the first generation DAQ was used with this

151 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 33 configuration of detectors, there were two runs taken at 2.5 C, five runs taken at 35 C and one run taken at 28 C. The result shown is an average if there exists more than one run at that temperature. Temperature 7 Trigger Rate 72 Trigger Rate 76 Trigger Rate 2.5 C C C Table 6.: Trigger rate of detectors 7, 72 and 76 during WIMP runs using first generation DAQ, in triggers/hour/gram Although the effects of having only one run at 28 C are apparent in this table (with the rate in detectors #72 and 76 decreasing while the temperature increases, contrary to the expected reaction), this does show that, in comparison with the rates during the neutron calibration runs (as shown in Table 4.4), the increase in rate due to the inclusion of the neutron source is dominant. It is therefore a valid assumption that all of the counts in the calibration runs are due to neutrons. An exception to the method of applying the cuts to determine their efficiency will be made for the burst and spike cuts. Since these cuts are well motivated and remove events which are attributable to the DAQ electronics, these events will be removed prior to the efficiency calculation. The results of this study are shown in Table 6.2. The pre-trigger noise and spike cuts have not been included in this table due to their removal of zero events in the first generation DAQ. The efficiency of the cut will be calculated as a sacrifice, determining the percentage of neutron triggers which are removed by each cut.

152 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 34 Detector # Temperature Adjusted Power Efficiency Fourier Efficiency ( C) Triggers Cut Transform Cut % 8 2.4% % % % % % % % 4.% % % % 3 3.8% % 62.8% % % Table 6.2: Cut efficiencies using the first generation DAQ Due to the limited range of calibration runs available for study, Table 6.2 shows no trend in temperature. Therefore, the estimated efficiencies will have no temperature dependence. Further adding to the difficulty, calibration runs are available for only detectors #7, 72 and 76. While further study is required, an estimation of the efficiency will be applied to all detectors and that estimation will be made using these numbers. The efficiencies of the power and Fourier transform cuts can be combined into one cut efficiency. The total number of events cut in each run are shown in Table 6.3. Using the efficiencies shown in Table 6.3, an average efficiency has been estimated. The average of the efficiencies shown is 28.±2.8%. This is the final value which will be used for the uncertainty.

153 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 35 Detector # Temperature Adjusted Total Events Efficiency C Triggers Cut % % % % % % % % % Table 6.3: Total cut efficiency using the first generation DAQ 6..2 Run length Correction The third correction which must be applied to the calculation of the count rate concerns the length of the run. The initial calculation for the run length is the time at which the run began subtracted from the time at which the run finished. This is not an accurate measure of the actual length of the run, which should be the live time of the system, requiring that all dead time be removed. The dead time during PICASSO data collection (WIMP) runs is calculated in two separate portions, the hardware portion and the software portion. The hardware correction is determined at the VME computer, which counts each instance of receiving a trigger with a size of zero samples to be a missed trigger. This indicates that the DAQ system is still processing the previous trigger when this trigger was recorded. In this case, the DAQ increments the number of missed triggers as well as adding the time between the trigger calls to the hardware dead time. This hardware dead time is summed and included in the DAQ run summary statistics.

154 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 36 A summary of the hardware dead time calculation is shown in table 6.4. Detector # Live Time (s) Hardware Dead Hardware Dead Time (s) Time (%) % % % % % % % % % % % % % Table 6.4: Summary of the hardware dead time calculated by the VME computer The hardware dead time is proportional to the trigger rate, which results in a temperature dependence. The hardware dead time fraction (calculated by dividing the dead time recorded by the DAQ system by the unadjusted run length) is plotted against the run temperature in Figure 6. for detector #72. As shown in Figure 6., the dead time fraction calculated at the DAQ computer is approximately constant and below.% for most temperatures below 45 C. At temperatures higher than 5 C, the dead time can approach % for most detectors. While this is not a significant reduction in the live time, the temperature dependence means that it can influence the shape of the temperature dependent detector response. The calculation of the second portion of the dead time is performed in the software

155 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 37 Hardware Dead Time Fraction by Temperature, Detector 72 Percentage of Run Dead (%) Temperature ( C) Figure 6.: Hardware dead time fraction vs temperature for runs taken with detector 72

156 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 38 during the analysis of the runs and is due to the events cut by the Burst Cut. A discussion of the method of application and parameters of this cut was included in Chapter 4. Invoking this cut results in the discarding of events, rendering the detector effectively dead. The amount of time cut due to this cut must be summed and included in the total dead time. As discussed in section 4..6, the burst cut used in the analysis of the PICASSO data removes triggers occurring within one second of each other. The dead time must then be increased if a trigger occurs within this one second window after the previous trigger. If this happens the time between the two triggers must be considered dead time, and is added to the total dead time. If another trigger does not occur within the one second window, one second must be added to the dead time. This calculation is carried out for and applied to all runs separately, although a large effect is only seen at runs of high temperature, greater than approximately 45 C and with calibration runs. A summary of the effect of this dead time cut on all detectors which have been underground is tabulated in Table 6.5. The temperature dependence of the software cut is similar to that of the hardware cut, as shown in Figure 6.2 for detector 72. As can be seen by comparing Figures 6. and 6.2, the software dead time is more significant to the live time calculation than the hardware dead time. Even when analyzing detectors which have the fewest burst cut events, the dead time fraction can approach % at 55 C. The detectors with the highest rates can approach 5%, which can result in a significant change in the detector response curve.

157 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 39 Percentage Dead Time Due to Burst Cut, Detector 72 Percentage of Run Dead (%) Temperature ( C) Figure 6.2: Software dead time fraction vs temperature for detector 72

158 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 4 Detector # Live Time (s) Burst Cut Dead Burst Cut Dead Time (s) Time (%) % % % % % % % % % % % % % Table 6.5: Summary of the software dead time created by the burst cut for each operational detector The effect of both dead time calculations on the final detector response curves has been calculated and is incorporated into the final analysis. It is clear that the software dead time calculation dominates this addition, so that the resulting corrections resemble those shown in Figure Ambient Pressure Correction In order to determine the temperature dependent count rates, it is important to determine the effective temperature of the detector correctly. The location of the PICASSO experimental setup in an active mine results in fluctuations in ambient pressure. During WIMP runs, the detector pressure is released to the environment, so any changes in ambient pressure can impact the count rate. The effect of the ambient pressure fluctuations will cause a change in the counting

159 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 4 rate of the detectors due to their threshold detector nature, as discussed in section 3. This theory indicates that the detectors require a critical amount of energy (E c, equation 3.8) to be deposited within a critical radius (r c, equation 3.4) in order to cause a bubble expansion. Both of these equations involve a term p (p -p ), the difference between the pressure external to the droplet (the ambient pressure) and the vapour pressure in the droplet. Significant changes in the external pressure of the droplet will then affect the threshold energy of the detector. These variations will be accounted for using the reduced superheat equation, first proposed by Francesco d Errico in 2 (38) to normalize the comparison between emulsions of superheated liquids. s = T T b T c T b (6.2) In Equation 6.2, s represents the degree of superheat, T b is the boiling point and T c is the critical point of the active mass. Change in ambient pressure will alter the boiling point of the liquid, allowing for an effective temperature to be calculated based on the reduced superheat being equal at the different pressures (and hence different boiling points). s = T T b T c T b = T 2 T b2 T c T b2 (6.3) Equation 6.3 can be solved for the new effective temperature T 2 as shown in equation 6.4.

160 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 42 [( ) ] T T b T 2 = (T c T b2 ) + T b2 T c T b (6.4) The changes in ambient pressure will affect the boiling point of the C 4 F in a manner characterized by the Antoine equation (39): log(p) = A B T + C (6.5) where P is the ambient pressure (in mmhg), T is the temperature (in C) and A, B and C are coefficients particular to the fluid used. The coefficients have been collected in (39) and in the case of C 4 F are given in equations 6.6, 6.7 and 6.8. A = (6.6) B = 2.58 (6.7) C = (6.8) The effect of the ambient pressure variation on the boiling point of C 4 F is shown in Figure 6.3. It is clear from Figure 6.3 that the boiling point will change significantly as the ambient pressure changes, which (in combination with Equation 6.2) provides the mechanism to adjust the effective temperature of the detector to reflect the change in ambient pressure. The pressure in the SNOLab environment is affected by several factors, including the location and activity of air handling fans used throughout the mine to provide fresh air. These fans can be cycled on and off during the day. The ambient pressure

161 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 43 Boiling Point of C F with Ambient Pressure Variation 4 4 F C) C 4 F Boiling Point ( Ambient Pressure (bar) Figure 6.3: Boiling point of C 4 F with variation in ambient pressure

162 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 44 has been monitored by SNO personnel and this data has been made available for analysis. There are problems with this monitoring system which can result in days of missing measurements; however, the majority of WIMP runs have associated pressure information. The ambient pressure measured in the SNOLAB area has been presented in (3), and the data have been provided for analysis by the PICASSO collaboration. The maximum and minimum ambient pressures taken during each data run are plotted in Figure 6.4, showing the range over which the pressure can vary. Ambient Pressure Range During WIMP Runs Pressure Range (Bar) /26 /26 /27 3/27 5/27 7/27 9/27 Run Start Date Figure 6.4: Ambient pressure maximum and minimum during PICASSO data runs until September 27 Taking the average pressure during data runs gives a value of.228 bar. The

163 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 45 deviation from this average pressure for each run can be calculated and is shown in figure 6.5. Ambient Pressure Deviation From Average Ambient Pressure Deviation (bar) /9/6 //6 //7 3/3/7 2/5/7 2/7/7 /9/7 Run Start Date Figure 6.5: Deviation from average ambient pressure (.228 bar) during PICASSO data runs until September 27 As seen in Figure 6.5, the largest ambient pressure deviations are approximately ±.2 bar from the average. Using the average pressure of.228 bar, this is a variation of.63%. Taking temperatures at both the lowest and highest temperatures used in the PICASSO data acquisition, this change can be quantified with the results shown in Table 6.6. In this case, the effective temperature given is calculated in relation to the detector having an ambient pressure of.228 bar, the average underground ambient pressure.

164 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 46 Detector Temperature Effective Temperature Effective Temperature ( C) at.28 bar ( C) at.248 bar ( C) Table 6.6: Summary of effective temperatures calculated using the maximum ambient pressure swing (±.2 bar) Another correction must be applied to the pressure which is complementary to the ambient pressure correction discussed in this section. The hydraulic system used to pressurize and depressurize PICASSO detectors involves lengths of tubing which are routed out of the detectors vertically and connect to the hydraulic manifold, a distance from the superstructure. In this configuration, when the pressure at the manifold is released to atmospheric pressure, the mineral oil remaining in the hydraulic lines creates a negative pressure on the detector, corresponding to the height difference between the detectors and the manifold. This pressure is measured by a gauge placed immediately outside of the TPCS and is subtracted from the ambient pressure to determine the final pressure to which the detector is subjected, and which is the proper pressure to be used in the temperature correction. The results shown in Table 6.6 indicate that the effective temperature change due to the ambient pressure variations in the underground laboratory is a significant alteration in the temperature spectrum of the detectors. The pressure correction due to the mineral oil pressure is constant and has therefore not been added to this plot. The difference between the set and the adjusted temperature at the maximum and minimum ambient pressure exceeds the. C uncertainty on the temperature measurement (to be discussed in section 6.2) and therefore must be included in the

165 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 47 final analysis Summary These three corrections (for the cut efficiencies, live time and ambient pressure) have been applied to the data, with the results shown in Figure 6.6 for detector #72. The systematic error on the cut efficiency has not been included in this plot, as it will be included in section Count Rate For Detector 72 Count Rate (events/hr/g) - Unadjusted Rate Adjusted Rate Temperature (C) Figure 6.6: Count rate for detector #72 before and after application of ambient pressure and dead time adjustments The corrections have had a larger effect on the count rate at high temperatures, due to the larger dead time, although the temperature correction due to the changes in ambient pressure is not as significant.

166 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties Systematic Temperature and Pressure Related Uncertainties In addition to the uncertainties associated with the measurement of the detector temperature, there exist several other uncertainties which are most easily evaluated as temperature uncertainties Temperature uncertainty and non-uniformity Great effort has been expended towards the goal of maintaining a uniform temperature across all of the detectors. This effort includes the construction of special temperature control systems to provide uniform heating and the inclusion of many temperature monitoring devices in the experimental setup. The data from one of these temperature sensors mounted on the outside of the detector container is recorded while the DAQ system is running and is stored for each run. The variation in the recorded temperature of the temperature sensors has been measured by placing a long string of properly sealed sensors in a water bath at a fixed temperature and plotting the deviation of the temperature reported by the various sensors from the temperature of the first sensor. This process was repeated several times (4), with the results of one run at 7.7 C shown in Figure 6.7. The accuracy of the temperature sensors taken from Figure 6.7 is typically at or below. C, so that value will be used for the measurement uncertainty. The spread of the temperatures measured during data-taking runs can be used to define the standard deviation of the temperature measurements for each run, and this value has been plotted in Figure 6.8 both in temperature and as a fraction relative

167 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 49 Figure 6.7: Temperature offset from measured value for temperature sensors at 7.7 C

168 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 5 to the set temperature. C) Deviation ( Absolute Temperature Deviation from Set Point Relative Deviation (%) Relative Temperature Deviation from Set Point Temperature ( C) Temperature ( C) (a) Absolute Temperature Deviation (b) Relative Temperature Deviation Figure 6.8: Deviation from the set temperature for runs taken until December 3, 27 The temperature spread from the set point as shown in Figure 6.8(a) is less than.8 C, and in most cases is commensurate with the. C uncertainty set previously. This is partially due to the run selection process which eliminates runs with large temperature deviations as they are considered to be unstable runs. As seen in Figure 6.8(b), this variation results in an uncertainty of less than.6% in the majority of the data runs. The larger standard deviation seen at lower temperatures reflects the difficulty in controlling the temperature accurately as the set point approaches the ambient temperature of the experimental environment. The significance of this issue will be reduced when the planned upgrades to the system (including a source of cooling) are completed Z position pressure dependence The critical energy required for nucleation in the droplets is dependent on the ambient pressure in the gel, as shown in equation 3.5. This pressure external to the droplets

169 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 5 will be affected by the weight of the gel above each individual droplet, creating a z-dependence in the ambient pressure. The magnitude of the pressure change can be determined using the known quantities of the PICASSO gel matrix. The density of the gel is 594 kg/m 3, as it has been matched to that of freon. The height of the gel in the detectors is 32.5 cm. Using the equation for the pressure difference due to a fixed height of an incompressible fluid, p = ρgh (6.9) this difference in pressure between the top and bottom of the detector is calculated to be bar. As previously stated, the average ambient pressure of the PICASSO experimental setup is.228 bar, meaning that this variation is 4.4% relative to the average. This variation in pressure can be expressed in the form of an effective temperature change using the method utilized for the ambient pressure fluctuation. An increase in pressure of bar is not negligible compared to the ambient pressure fluctuation. If it is assumed that the droplet distribution in the detector is homogeneous, the uncertainty associated with the ambient pressure of any particular droplet must be increased by the temperature equivalent to bar. This corresponds to an effective temperature range of 8.5 to 9.5 C at an ambient temperature of 9 C and a range of 54.7 to 55.2 C at an ambient temperature of 55 C. This uncertainty will be added to the overall temperature uncertainty.

170 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties Summary Considering the temperature-related error results in an uncertainty of. C on each temperature point due to the uncertainty of the temperature measurement error and the variation in detector temperature during WIMP runs. In addition, a temperature-dependent uncertainty must be added due to the z-position pressure dependence, which increases the uncertainty by approximately.3 C. 6.3 Systematic Count Rate Uncertainties One additional class of uncertainties is that which can be applied directly to the count rate calculation, expressed in equation 6.. These uncertainties directly affect the number of events or the active mass Piezo efficiency The efficiency of the piezos has been calculated individually in order to determine several aspects of the detector efficiency. The calculation of the piezo efficiency proceeds by determining the number of times that an individual piezo is involved in an event identified as a bubble event, and dividing that by the number of bubble events in that run. This ensures that the efficiencies are not affected by external factors such as malfunctioning piezos or an increased number of triggers in the runs. Event Identification Efficiency The DAQ system used by the PICASSO experiment is currently configured to trigger when the voltage from the piezos passes a fixed threshold. This configuration works

171 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 53 well for large signals, but the amplitude of the signal has been shown to be temperature dependent, with lower temperatures producing signals of lower amplitude. The event identification efficiency for the detector can be calculated using the piezo efficiencies. Since the current requirements for the identification of a bubble event are that four piezos register a waveform associated with the expansion of a droplet, the four highest piezo efficiencies are multiplied to give an efficiency for the detector during that run. These efficiencies can be plotted with respect to temperature and these plots are shown in Figures 6.9, 6. and 6.. Good Event Efficiency Detector 7 Good Event Efficiency Good Event Efficiency Detector 7 Good Event Efficiency Temperature ( C) Temperature ( C) (a) Detector 7 (b) Detector 7 Good Event Efficiency Detector 72 Good Event Efficiency Good Event Efficiency Detector 73 Good Event Efficiency Temperature ( C) (c) Detector Temperature ( C) (d) Detector 73 Figure 6.9: Event identification efficiency broken down by temperature for detectors 7 to 73. Each point represents a different run. It is clear from the efficiency plots that the event identification efficiency is close to unity for the majority of the runs. Runs with an efficiency of one will not require any

172 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 54 Good Event Efficiency Detector 75 Good Event Efficiency Good Event Efficiency Detector 76 Good Event Efficiency Temperature ( C) Temperature ( C) (a) Detector 75 (b) Detector 76 Good Event Efficiency Detector 77 Good Event Efficiency Good Event Efficiency Detector 78 Good Event Efficiency Temperature ( C) (c) Detector Temperature ( C) (d) Detector 78 Figure 6.: Event identification efficiency broken down by temperature for detectors 75 to 78. Each point represents a different run.

173 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 55 Good Event Efficiency Detector 93 Good Event Efficiency Good Event Efficiency Detector 94 Good Event Efficiency Temperature ( C) Temperature ( C) (a) Detector 93 (b) Detector 94 Good Event Efficiency Detector 99 Good Event Efficiency Good Event Efficiency Detector 6 Good Event Efficiency Temperature ( C) Temperature ( C) (c) Detector 99 (d) Detector 6 Good Event Efficiency Detector 8 Good Event Efficiency Temperature ( C) (e) Detector 8 Figure 6.: Event identification efficiency broken down by temperature for detectors 93 to 8. Each point represents a different run.

174 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 56 adjustment for the number of events. If the efficiency differs from one, an uncertainty is introduced into the measurement. For the runs which have efficiencies less than one, this efficiency will provide an additional uncertainty when applied to the total number of bubbles. In these cases, the systematic uncertainty in the number of droplet expansion events will be increased to incorporate the possible missed events due to a reduced event identification efficiency. The average efficiency associated with the piezos for each detector is shown in Table 6.7, averaged over all of the runs since the underground installation, which should give an overall impression of the efficiency of the detectors. Detector # Average Efficiency (%) Table 6.7: Average detector efficiencies due to piezos for good events, averaged over all runs It is clear from Table 6.7 that the detector efficiencies to good events are quite high for almost every detector. The lowest average efficiency is shown to be 82.7% in detector 99. This discrepancy may be in part due to the change in active mass

175 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 57 in this detector. As discussed previously, the active ingredient in the detectors was chosen to be C 4 F early in the experimental history. Following this choice, it was discovered that a different freon (C 4 F 8 ) possessed almost identical thermodynamic properties and could be obtained in a more purified state. Detector 99 contains C 4 F 8 as the active mass, which may explain the reduction in good event efficiency. One additional possible explanation for the large drop in efficiency in detector 99 is that this is one of the first saltless detectors produced for study. The previous detectors (as discussed in Chapter 3) were made with a gel matrix which contains CsCl in order to balance the density of the gel matrix with that of the active mass. In detector 99, there is no CsCl and, instead of matching the densities, the gel is held together by viscosity during polymerization using a polyethylene glycol gel. This substitution makes radiopurification much easier; however, the full response of the detectors has not been studied as thoroughly as that for the detectors using C 4 F. Missed Trigger Efficiency In addition to this event identification efficiency, the probability that a trigger was missed must also be calculated. In the PICASSO experimental setup, if any of the piezos exceed the trigger voltage, the system is sent a trigger and all channels are read out. The probability of missing a trigger is then given by equation 6., N P missedtrigger = ( ǫ i ) (6.) where ǫ i is the event identification efficiency of the i th piezo and N is the number of piezos currently in use on the detector. This discounts piezos which are missing or i=

176 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 58 manually turned off during the run. The probability that any detector has missed a trigger is very small, as all the active piezos must have a small efficiency. Calculations show that this probability is less than 2 %, and therefore can be considered negligible in this analysis Active mass measurement The active mass in the PICASSO detectors has been measured and the appropriate uncertainty has been recorded. Each detector has the active mass weighed during fabrication, determined by the difference before and after the C 4 F is incorporated into the detector. This method depends on the accuracy of the measurement and there may be active mass lost during the detector fabrication process. For all detectors used in the current phase of data collection, the values of the active mass and the associated error are tabulated in Table 6.8. There are several methods used to check the amount of active mass in the detectors. The first is to cut the detector into thin slices, count and estimate the size of the droplets in the slices and then add up the volume of the droplets. This can be a very accurate method, but it requires the destruction of the detector, is time intensive and is only valid if the distribution of droplets in the gel is homogeneous. Another method is to calibrate the active mass using a neutron source with a known flux and use the number of signals counted from the detectors to calibrate the active mass. The uncertainty in this method is larger, however, and the strict constraints

177 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 59 Detector # Measured Active Mass (g) Uncertainty (g) Relative uncertainty % % % % % % % % % % % % % Table 6.8: Active mass and associated uncertainty for detectors used in PICASSO Phase II on the temperature control make experimentation difficult. The final method is to use Monte Carlo simulations of the detector response and neutron calibration data to fit for the the value of the active mass. This method has proved successful in the past, with the first phase detectors undergoing this study. Extensive work is currently underway to improve the Monte Carlo simulations to provide a more accurate estimate of the active mass. None of these post-fabrication methods have been applied to the detectors installed in the current phase, however, suggesting that the most accurate information available is the measurement of the active mass during the manufacture of the detectors.

178 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties Cut Efficiency Uncertainty As discussed in section 6.., there is a systematic uncertainty associated with the efficiency of the bubble cuts, which has been determined to be 2.8% using the data available and must be included in the systematic uncertainties Summary The uncertainty applied to the count rate will consist of the contribution due to the active mass measurements, the event identification efficiencies and the cut efficiencies. The summary of the effects of these uncertainties is shown in Table 6.9, in which the event identification uncertainty has been calculated at 55 C, in order to provide the maximum effect. The event identification uncertainty is temperature dependent, as discussed in section Detector # Event Identification Active Mass Cut Efficiency Total Uncertainty Uncertainty Uncertainty %.6% 2.8% 3.% 7.%.6% 2.8% 2.9% %.6% 2.8% 3.% 73.2%.6% 2.8% 2.9% %.% 2.8% 6.2% %.% 2.8% 3.% 77.4%.% 2.8% 2.9% 78.6%.% 2.8% 2.9% 93.94%.% 2.8% 3.% % 3.7% 2.8% 3.6% %.2% 2.8% 24.6% 6 3.3%.9% 2.8% 3.3% 8 7.3% 2.% 2.8% 4.9% Table 6.9: Summary of the uncertainty applied to the count rate for all detectors

179 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties Systematic Fitting Procedure Uncertainties The systematic errors involved in the fitting procedure comprise two separate components. The first is the uncertainty involved in fitting the PDF to the alpha calibration data. The second component is the uncertainty returned by the combined fit to the detector count rate. This uncertainty is handled separately and must be determined after the PDF uncertainties have been included. In these sections, the effects of the uncertainties have been studied using detector #72 only. This is appropriate only due to the fact that this detector is the standard by which all detectors have been judged and that the effects of variations on the parameters in this detector can be extended to the remainder of the detectors Alpha PDF Fit Uncertainty The fit of the alpha PDFs to the calibration data described in section 5.3 provides uncertainties on the parameters returned by the fit. As there are two separate alpha response curves, representing alpha particles in the active droplets and alphas in the gel, these will be tested individually. In order to determine the effects of the uncertainties associated with the alpha PDFs, the values of the parameters of the fit have been varied by one standard deviation (as returned by the fit to the calibration data) and the exclusion curve calculated with the altered values.

180 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 62 Droplet Surface Based Alpha Particles The equation for the droplet surface based alpha particles is given in equation 5.. The fitting of this equation to the calibration data is discussed in Section 5.3, with the results from the fits shown in Figure 5.6. The uncertainties obtained from this fitting process have been applied to these parameters, with results as shown in Figure 6.2. Count Rate (events/hr/g) Alpha Curve Parameter Variation One sigma parameter increase One sigma parameter decrease Temperature ( C) Figure 6.2: Droplet surface based alpha PDF showing variation in function caused by a one standard deviation variation in the parameters. Visually, increasing and decreasing the parameters by one standard deviation gives a result which is not significant; however, the effect on the final exclusion curve must be determined. The fitting process to determine the exclusion limits has been carried out with the variations, with the results shown in Figure 6.3.

181 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 63 Exclusion Curve Variations - Detector 72 Cross-Section (pb on proton) - -2 Unaltered Fit Parameters Parameters Reduced by One Standard Deviation Parameters Increased by One Standard Deviation 2 Neutralino Mass (GeV) Figure 6.3: Effects on the exclusion curve caused by varying the droplet surface based alpha PDF parameters by one standard deviation. The change in the result is visible on this plot, but is not large enough to be significant. Varying the parameters by one standard deviation changes the exclusion level at 6.69 GeV from.36 pb on the proton (decreasing the parameters) to.34 pb on the proton (increasing the parameters). This variation of approximately.5% will be included as a systematic error in the final result. Gel Based Alpha Particles The effects of the one standard deviation variation of the parameters in the PDF for the gel based alpha particles is shown in Figure 6.4. The variation of these parameters showed no effect on the final exclusion limit, and will not be included in the systematic errors.

182 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 64 Gel Based Alpha Response Count Rate (arbitrary units) Parameters Reduced One Standard Deviation Parameters Increased One Standard Deviation Temperature ( C) Figure 6.4: Gel based alpha PDF showing variation in function caused by a one standard deviation variation in the parameters Fit Contamination Value Uncertainty As discussed in section 5.7, a contamination parameter is determined for the two alpha responses as well as the gamma response, and this parameter is used to determine the potential visible neutralino signal in the data. The values returned by the fitting procedure will be varied in a manner similar to that for the PDF uncertainty, with the exception that the ratio of the two alpha responses will be altered instead of the contamination levels of the responses themselves. Unlike the previous section, it is now appropriate to include variations in the fit contamination level for the gamma function, the results of which will also be included. Plots of the variations are not included, as the changes are not significant enough

183 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 65 to be detected visually. Alpha Particle Emitter Contamination Varying the level of the alpha particle emitter contamination by one standard deviation has the effects shown in Figure 6.5. Exclusion Curve Variations - Detector 72 Cross-Section (pb on proton) - -2 Unaltered Contamination Parameters Increased Contamination Parameter Ratio Reduced Contamination Parameter Ratio 2 Neutralino Mass (GeV) Figure 6.5: Effects on the exclusion curve caused by varying the alpha contamination parameter by one standard deviation. The effects of this change are more significant than those discussed previously. Lowering the contamination parameter ratio by one standard deviation has the effect of increasing the exclusion limit at 6.6 GeV to.5 pb on the proton from.4 pb on the proton, for a total change of 9.4%. The change in the curve as the parameter ratio is increased is more obvious. The fit obtained using these parameters does not make sense and has a reduced chi-squared value which is much higher than those

184 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 66 from the other fits. Furthermore, the chi-squared value changes significantly with the neutralino mass, a behaviour which is not seen in the other fits. The results from this fit will not be used in the final result. The change in the alpha contamination parameter fit will then be used as the result from the lowering of the parameters, which adds 9.5% to the total uncertainty. Gamma Ray Emitter Contamination In a similar manner to the change shown by changing the gel based alpha PDF, the gamma contamination parameters have no effect on the final result obtained from the exclusion fitting process Summary The only variations which had an effect on the final exclusion curve are those associated with the droplet surface based alpha PDF and the alpha contamination. These effects are small, however and contribute 9.5% to the final uncertainty. 6.5 Neutron Backgrounds Extensive studies have been performed on the neutron flux in underground environments, as this can be a background which is difficult to distinguish from a dark matter signal. Neutrons can interact with nuclei in the target material to produce recoils which closely mimic those caused by dark matter interactions. In particular for the PICASSO project, neutron background studies have been undertaken to determine accurately the flux of neutrons as well as their spectrum, and the effectiveness of the

185 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 67 water shielding surrounding the experimental setup Thermal Neutrons Thermal neutrons are primarily produced in underground environments by fission and (α,n) reactions in the rock and fission in the shielding and detector materials. The first source is most prevalent for the PICASSO experiment, as great care was taken in choosing construction materials which had little radioactive contamination. The inclusion of Uranium and Thorium in the rock surrounding the SNO cavern in the Creighton mine is responsible for the majority of the thermal neutron flux. Approximately 9% of this flux is caused by (α,n) reactions in the rock, with the alpha particle being produced primarily by the decay of 238 U and 232 Th. This alpha particle can scatter from another nucleus, freeing a neutron. The remaining % of the thermal neutron flux is due to the fission of 238 U producing neutrons which thermalize after undergoing multiple scattering interactions in the rock. The flux of thermal neutrons in the SNOLAB cavity has been measured using gas counters filled with BF 3 and 3 He contained in varying thicknesses of moderators. The results of extensive work determining the background as well as subtracting extraneous counts has resulted in a final value for the thermal neutron flux of 444.9±49.8±5.3 neutrons/m 2 /day (3). The effect of these neutrons on the PI- CASSO experiment will be through the activation of the constituent elements of the detectors and containers. The thermal neutron capture cross-sections are shown for the majority of the elements of the detectors in Table 6.. These values are taken from the Evaluated Nuclear Data File (ENDF) (4).

186 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 68 Isotope Process Cross-Section (barns) total 4.97 C (natural) elastic n,γ total C 6 O 7 O 9 F Cl (natural) 35 Cl 33 Cs 34 Cs 35 Cs Continued on Next Page... elastic n,γ total 4.34 elastic 4.32 n,γ.93 3 total 4.73 elastic 3.87 n,γ n,α.235 total elastic n,γ.95 2 total 5.2 elastic 6.78 n,γ 33.5 n,p.355 n,α O( 9 ) total 65.2 elastic 2.9 n,γ n,p.499 n,α.85 4 total elastic 4.98 n,γ total 66. elastic n,γ 4.2 total 3.78 elastic 25.48

187 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 69 Isotope 36 Cs 37 Cs Table 6. Continued Process Cross-section (barns) n,γ 4.2 total 5.77 elastic 3.89 n,γ.39 n,α total 5.4 elastic n,γ.3 n,α Table 6.: Thermal neutron cross-sections on PICASSO constituent elements. Values taken from ENDF/B-VI database. It is clear from the values in Table 6. that the most important reaction is the (n,p) reaction on 35 Cl. The remainder of the reactions are extremely rare or have a cross-section which is very low. In addition, it is important to note that in the range of current operating temperatures, the PICASSO experiment is insensitive to gamma particles. The incoming thermal neutrons, in collision with the nucleus, will produce a proton of maximum energy 598 kev. This proton could then produce a nuclear recoil which would be of sufficient energy to cause a nucleation in the active mass, producing a false positive signal. The approximate rate of this reaction can be calculated. If the assumption is made that the detectors are entirely composed of CsCl (which will produce a rate which is too high), and that the volume of the container is 4.5 litres, there will be atoms of 35 Cl in the detector. If the cross-section of this reaction is

188 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 7 taken to be.499 barns, as shown in Table 6., and the thermal neutron flux is not mediated by the water shielding,. protons will be produced per day in the PICASSO detectors. In a very worst case scenario, each proton produced from the neutron production on 35 Cl will be detected by the detectors and identified as a bubble event. This results in a rate of events/g/hr (using an average value of 8 g active mass), which is negligible compared to even the lowest counting rates included in this study, being at least an order of magnitude lower Fast Neutrons The effect of thermal neutrons on the PICASSO detectors is indirect, with only the products of neutron capture producing signals in the detectors. Fast neutrons have enough energy to cause nuclear recoils, producing these false droplet nucleations directly. The fast neutron flux is also more difficult to measure, although the inclusion of water shielding surrounding the detectors thermalizes most of these neutrons through multiple scattering interactions. The most accurate number available for the fast neutron flux in the SNOLAB cavity is 4 neutrons/m 2 /day (3), although this number has associated with it a great deal of uncertainty. Assuming that the flux is isotropic, only the surface area of the detectors is required to determine the count rate due to these fast neutrons. The dimensions of the detectors are given in Figures 3.2 and 3.3. Using these values, the cross sectional area of the detectors is approximately m 2. The neutron flux impinging on these detectors without shielding would then be 52 neutrons/day,

189 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 7 which equates to a rate of neutrons/hr/g (using an active mass of 8 g). This rate is significant in comparison to the count rates obtained from the lowest rate detectors currently located in the underground setup. In order to reduce this flux, the detectors underground are surrounded by water, contained in water cubes and sealing the superstructure. The water cubes used in the PICASSO setup are 3 cm by 3 cm by 3 cm, resulting in a volume of 27 litres. Monte Carlo simulations have been performed to characterize the effect of this shielding on the neutron flux, with the result that a reduction of approximately 2 times the incident neutron flux (28). This reduces the neutron rate to 4. 3 neutrons/hr/g. The final reduction to this count rate is the detector efficiency to neutrons. As discussed previously in section 4., the detector efficiency to neutrons has been determined to be below 5 2 counts/neutron/g cm 2. Applying this efficiency to the neutron rate results in a count rate of 2 4 events/hr, which is insignificant compared to the rates of the detectors currently in use, being at least an order of magnitude lower than the rate of the lowest count rate detector. 6.6 Summary The results of the studies of uncertainties are summarized as follows. The corrections to the count rate due to the run length, ambient pressure and cut efficiencies have been applied to the data from the individual detectors. The summary of detector count rate uncertainties is shown in Table 6.9, the uncertainty due to the fitting procedure must be applied at the time of fitting, and the neutron background rate

190 Chapter 6. Backgrounds, Corrections and Systematic Uncertainties 72 is shown to be insignificant at the current count rates.

191 Chapter 7. RESULTS AND DISCUSSION 7. Results The result of the work described previously is to create an exclusion curve in spite of the fact that to date no indication of the existence of dark matter has been found using the PICASSO detector. Due to the temperature-dependent count rate response differences in several of the detectors underground, these results have had to be excluded from the final fit result. The detectors used in the final analysis are shown in table 7., along with the live time for each detector. The total exposure analyzed for this result is a significant reduction from that taken by all detectors (2.99 instead of kg d). The justification for the removal of the remainder of the detectors from the analysis is that the alpha response functions obtained from the calibration data (discussed primarily in section 5.3) do not describe the data. There are many potential explanations for this discrepancy, which Detector Number Live Time (kg d) Total 2.99 Table 7.: Definition of the extent of the live time used in the final analysis presented in this document. 73

192 Chapter 7. Results and Discussion 74 will be discussed further in Section Background PDF Fits The fits to the background PDFs are shown in figures 7., 7.2 and 7.3. Detector 72 Background Fit Count Rate (events/hr/g) - Data Background Fit Temperature ( C) Figure 7.: Temperature dependent count rate for detector 72 with background PDF fit. The fits of the background functions to the data shown in this figure exhibits a range of quality. The fits to detector 72 are quite good, with small deviations at low temperatures. The fits to detector 93 are adequate, with a larger deviation at low temperatures. The fits to detector 8, although the data are limited due to the lower live time, are more than adequate for the requirements of the determination of the exclusion limits.

193 Chapter 7. Results and Discussion 75 Detector 93 Background Fit Count Rate (events/hr/g) Data Background Fit Temperature ( C) Figure 7.2: Temperature dependent count rate for detector 93 with background PDF fit.

194 Chapter 7. Results and Discussion 76 Detector 8 Background Fit Count Rate (events/hr/g) - Data Background Fit Temperature ( C) Figure 7.3: Temperature dependent count rate for detector 8 with background PDF fit.

195 Chapter 7. Results and Discussion Exclusion Curve The exclusion curve for the combined detectors derived from the live time shown in Table 7. has been calculated and is shown in Figure 7.4. Exclusion Curve Using Detectors 72, 93, 8 Cross-Section (pb on proton) Neutralino Mass (GeV) Figure 7.4: Final exclusion curve determined using detectors 72, 93 and 8. The exclusion curve shown in Figure 7.4 has a maximum exclusion limit (minimum cross-section) of pb on the proton at a neutralino mass of 6.7 GeV. 7.4 Effects of Uncertainties As discussed in Chapter 6, calculations of the backgrounds, corrections and systematic uncertainties have been undertaken to determine the effects of these changes to

196 Chapter 7. Results and Discussion 78 the count rate on the exclusion curve. The systematic uncertainties and backgrounds have been calculated for the detectors used in the final determination of the exclusion curve, and the count rate has been adjusted accordingly. Increasing the count rate by a factor of one standard deviation also increases the exclusion limit a commensurate amount, while lowering the count rate also lowers the exclusion limit. This effect is shown in Figure 7.5 with the range between the upper and lower exclusion curves shown. Exclusion Range Using Detectors 72, 93, 8 Cross-Section (pb on proton) Neutralino Mass (GeV) Figure 7.5: Range of exclusion curves due to systematic uncertainties. The shape of this range shows that there is very little effect at low neutralino masses. As the neutralino mass increases, the effect also increases with the crosssection at the maximum exclusion limit (at 6.7 GeV) being restricted between 2.6

197 Chapter 7. Results and Discussion 79 and pb on the proton. 7.5 Discussion 7.5. Significance of the Result The significance of the result from this work, when compared to the results from other direct dark matter search experiments is shown in Figure 7.6, which includes spin-dependent limits calculated using the cross-section of the neutralino and the proton. Figure 7.6: Comparison of the exclusion curve of this analysis with results from several world-leading experiments. Data taken from (8). The effect of this analysis on the world-leading results for the spin-dependent cross-section on the proton is clear from Figure 7.6. The result from the previous

198 Chapter 7. Results and Discussion 8 phase of the PICASSO experiment has been decreased by almost two orders of magnitude, roughly corresponding to the increase in live time (33.4 kg d for this analysis,.98 kg d for the previous) combined with the improvements in the analysis process, such as the inclusion of the gamma response in the fitting process, the extension of the temperature range of the fit and the use of Minuit as the fitting tool. In addition to achieving the lowest experimental exclusion curve, it is vital that these limits be compared to theoretical calculations of the predicted neutralino cross section. Theories have been presented in (42) and (34) outlining the predicted neutralino mass/cross section space derived from the MSSM (Minimal Supersymmetric Model) and CMSSM (Constrained Minimal Supersymmetric Model) theories. These predicted regions are illustrated in Figure 7.7. It is clear from this plot that the results of this analysis do not approach the theoretical limits. This shortfall may be remedied using several different approaches, which will be discussed further. This work s result should be compared with the ongoing results from other recent dark matter search experiments. When considering the spin-dependent dark matter interaction, PICASSO is the world leader, as previously discussed. There is a great deal of interest in the spin independent interaction, however, which has placed a great deal of emphasis on all results from direct detection experiments. In particular, the limits presented by the currently operating noble gas experiments (such as Xenon and DEAP mentioned in section 2.4.) as well as their successors and the solid state experiments such as CDMS have generated much attention from the scientific community. It is hoped that competition between spin dependent dark matter search

199 Chapter 7. Results and Discussion 8 Figure 7.7: Comparison of exclusion curve of this analysis including theoretical predictions. Data taken from (8).

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