Master Thesis. Timing and calibration of the ATLAS RPC trigger chambers

Master Thesis Timing and calibration of the ATLAS RPC trigger chambers Joris Hartman ATLAS Department, NIKHEF Supervisor: Peter Kluit June 2009

Abstract ATLAS is the largest experiment of the LHC at CERN. Its research is focused on a wide area, including Higss search. The Muon Spectrometer forms the outermost part of ATLAS. It consists of precision measurement chambers and trigger chambers. One type of trigger chambers are Resistive Plate Chambers (RPC). RPCs are used in the barrel of the Muon Spectrometer. The RPC trigger chambers are designed to provide a fast trigger signal. Because an RPC consists of several sub-elements, the timing information of these elements has to be precise and thus calibrated. To study this calibration, the time differences between orthogonal strip times are used. These time differences are the input for a method based on matrix inversion. A linear system is constructed and solved, leading to corrections which can be applied to individual strip times. Several solutions are combined to improve these corrections. The time differences and corrections are stored in a hit database. The corrected time distributions improves the resolution on submodule level from 3.7 ns to 2.7 ns and, in the case where more than one peak is present, peaks are merged in a single peak. This proofs the principle of the used calibration method, which can be extended to be applicable to other elements in the Muon Spectrometer to calibrate the whole system.

tän froneøn brotoìc åd santa, tän pˆjei mˆjoc jènta kurðwc êqein. Aeschylus, Agamemnon (l. 176-178) Šneu fðlwn oîdeèc éloit n z n, êqwn t loip gaja pˆnta Aristotle, Nicomachean Ethics (VIII 1155a5) 1

Contents 1 Introduction 5 1.1 Research project.................................... 5 1.2 Standard model..................................... 5 1.3 Large hadron collider.................................. 6 1.4 Outline of thesis.................................... 9 2 ATLAS and the muon detectors 10 2.1 ATLAS......................................... 10 2.1.1 Inner detector.................................. 11 2.1.2 Calorimeters.................................. 11 2.1.3 Muon Spectrometer.............................. 12 2.1.4 Trigger system................................. 12 2.1.5 Precision trackers................................ 13 2.2 Coordinate system and identification scheme of chambers............. 14 2.2.1 Coordinate system............................... 14 2.2.2 Identification of chambers........................... 15 3 RPC structure and operation mechanism 17 3.1 Global overview..................................... 17 3.2 Structure of an RPC.................................. 17 3.3 Operation of an RPC................................. 18 3.4 Level-1 trigger system................................. 19 4 Data set and timing 22 4.1 Cosmic particles.................................... 22 4.2 Data set......................................... 22 4.3 Introduction on timing................................. 26 4.4 Logical division of an RPC.............................. 27 2

5 Correction of strip times 29 5.1 Data........................................... 29 5.1.1 Data preparation................................ 29 5.1.2 Chamber identification............................. 29 5.2 Time differences.................................... 29 5.2.1 Acquiring time differences........................... 30 5.3 Time solving...................................... 31 5.3.1 Matrix construction.............................. 31 5.3.2 Correcting strip times............................. 32 5.4 An example: R.B2L.4A3.M2.S0............................ 32 5.5 Stability of the corrections............................... 33 6 Results 35 6.1 Data selection...................................... 35 6.2 Determination of time corrections........................... 35 6.3 Application of time corrections............................ 37 6.3.1 Single-peaked distributions.......................... 37 6.3.2 Double-peaked distributions.......................... 39 6.4 Interpretation of the corrected data.......................... 40 7 Conclusion and outlook 41 7.1 Conclusion....................................... 41 7.2 Outlook......................................... 42 References 43 A Single-matrix solutions 44 B Identifier scheme and hit database 46 B.1 Unique identifier.................................... 46 B.2 Hit database...................................... 47 C Software 48 C.1 Main........................................... 48 C.2 createstripmap.................................... 48 C.3 sorthitsbymodule................................... 49 C.4 loopoverhits...................................... 49 C.5 addhittodatabase and getcorrection....................... 50 C.6 Matrix functions.................................... 50 3

D Student s contributions 51 D.1 Master project..................................... 51 D.2 CERN Summer School................................. 52 D.2.1 Segments.................................... 52 D.2.2 Kalman fit................................... 52 4

Chapter 1 Introduction 1.1 Research project The trigger system of the ATLAS muon spectrometer plays a crucial role in the detection of muons. Where the precision chambers, like Monitored Drift Tubes, are designed to have a high resolution on position, the trigger chambers have to provide a fast and precise time measurement. The Resistive Plate Chambers or RPCs are part of this trigger system. Each RPC consists of several detector elements which, when combined, are designed to reach a resolution of 1 ns. The same holds for the combination of RPCs in different regions of the Muon Spectrometer. To be able to provide this resolution, the RPCs have to be calibrated. During my research project, I analysed the timing information of the RPCs to investigate timing problems and to try to correct these to improve the calibration. The RPC data used in this analysis were taken in cosmics runs in several sections of ATLAS. Different runs have been taken in 2005-2008. The data used in this thesis are M5 data, taken from October 22nd till November 5th 2007. Using this cosmic data, first time relations within single chambers were analysed. From this, corrections to the data could be constructed. Using these corrections, other time relations were corrected, often resulting in a significant improvement of the data. 1.2 Standard model Particle physics is focused on research of the elementary particles, the smallest building blocks in our universe. The current model describing these particles and their interactions is the Standard Model (SM) [1]. The Standard Model has proven to be a solid model, which is capable of describing these interactions with high precision. The SM describes several types of particles. Six quarks, divided in three families, are the building blocks for hadrons, like protons and neutrons. There are six leptons, such as the electron, and 3 types of gauge bosons, particles responsible for the interactions or elementary forces. The SM has three families of particles (see table 1.1). The first family contains the up (u) and down (d) quarks and the leptons electron (e) and the associated electron neutrino (ν e ). Most matter we know of in the universe is made of these particles and essentially there are no more particles needed to build our visible universe. Nevertheless, two other families of particles exist. The second family consists of the charm (c) and strange (s) quarks, together with the muon (µ) 5

and the muon neutrino (ν µ ). The third family has the top (t) quark, the bottom (b) quark, the tau (τ) particle and the tau neutrino (ν τ ). The only difference between these particles and the particles from the first family is their mass. The gauge bosons are not part of one of these families. The photon is responsible for the transmission of the electromagnetic force, has no charge and no mass. The weak force is carried by three bosons, the W ± and Z 0 bosons. These particles do have a mass of respectively 80.4 GeV and 91.2 GeV and the W boson is either positively or negatively charged [2]. The strong force is carried by 8 different gluons, which are massless but do have a colour charge. All of the particles in the SM have been observed in particle physics experiments. Family 1st 2nd 3rd Up-type u c t Down-type d s b Leptons e µ τ ν e ν µ ν τ Table 1.1: The particles in the standard model. The three up-type quarks have charge + 2 3e, the three down-type quarks have charge 1 3 e. Although the SM describes the elementary particles and their interactions with an unsurpassed precision, there are some problems with the model. One of these problems is the nature of the mass of the particles. In a model of spontaneous symmetry breaking, the particles acquire mass through interaction with a Higgs field. The associated field particle is the Higgs boson. The mass of the SM Higgs boson is experimentally limited to m H > 115 GeV because of experiments at LEP, while from theory it follows that m H < 700 GeV in order to let the SM not break down [2]. This mass range will be covered by the new LHC accelerator. One of the important decay channels is H ZZ 4µ. In figure 1.1 a simulation of such a decay is shown, where the four muon tracks are clearly visible. Therefore the muon spectrometer in ATLAS is important for the detection of the Higgs particle. Of course the branching ratio for this decay channel is strongly dependent on the mass of the Higgs particle. In figure 1.2 the branching ratios of the Higgs particle decay into different final states are shown. 1.3 Large hadron collider CERN, the European Organization for Nuclear Physics located at the Swiss-French border near Geneva, was founded in 1954. The research at CERN is focused on fundamental particle physics and it is one of world s largest institutes in this field. CERN is a collaboration of 20 European states and is located at the Swiss-French border. Since the foundation of CERN, several accelerators have been build. The previous large accelerator at CERN was the Large Electron Positron collider (LEP). LEP was built in a tunnel of 27 km circumference and an average depth of 100 m underground. With LEP, precise measurements on the W ± an Z 0 boson mass were performed by several experiments. Although some data showed evidence of a The nature of the top quark is not yet completely known. It is possible, for example, that the top quark has a different charge than 2 e. Top physics is also an important field of research at ATLAS. 3 Other types of Higgs bosons, for example in supersymmetric models, can have masses which are as low as 79 GeV. 6

Figure 1.1: A simulation of a Higgs decay to µ+ µ µ+ µ. The four muon tracks are highlighted. Figure 1.2: The branching ratios of Higgs decay to different final states for different Higgs masses. The Higgs to W W (dashed blue line) will decay in four leptons, for example muons, who can be detected by the muon spectrometer of ATLAS. As can be seen, this is the preferred decay for Higgs masses > 150 GeV. 7

possible Higgs candidate, LEP was closed in 1999 for the construction of the new accelerator LHC. The Large Hadron Collider (LHC), is the new particle accelerator at CERN. It has been built in the tunnel of LEP, so it has the same circumference. One of the main purposes of LHC experiments is the detection of the by theory predicted Higgs particle. LHC had its first successful beam at September 10th 2008. LHC uses superconducting magnets of 8.4 Tesla for the acceleration of protons. Two beams will be circulating in opposite directions by the use of special designed split-field dipole magnets. Several other types of magnets, such as quadrupoles, will be used to contain the beam in the beam pipe and focus the beam. The beams of protons will be collided at an collision energy of 14 TeV with a peak luminosity of 10 34 cm 2 s 1 [3]. The beam will have 2808 bunches, of 1.15 10 11 protons each. The RF frequency of LHC is 400.8 MHz, while the bunch frequency is 40 MHz. This gives a time interval of the bunch crossing of 25 ns. The collision products will be measured at four locations where experiments have been placed, one of which is point 1, where ATLAS is situated. There are four large experiments at the LHC. ATLAS, a general purpose detector, will be discussed in more detail below. CMS is also a general purpose detector, and uses only a solenoid magnet instead of a solenoidal and toroidal magnet as in ATLAS. LHCb is a detector specifically for B physics and ALICE will be used to analyse collisions of heavy ions, like lead nuclei. The location of the experiments around LHC is shown in figure 1.3. Figure 1.3: Overview of the location of the four experiments around LHC. 8

1.4 Outline of thesis This thesis contains seven chapters and four appendices describing the research, its results and some of the necessary background information. Chapter 2 describes the ATLAS experiment. An overview of the detectors in ATLAS is given and in more detail the components of the muon spectrometer. Also the coordinate system and naming convention used in this thesis is explained. Chapter 3 contains a description of the RPC detectors in some detail. Chapter 4 gives a short overview of the data used and introduces the basic principles of the timing. Also the logical division of RPC chambers used during analysis will be discussed. Chapter 5 covers the method which has been developed for the calibration and chapter 6 contains the results and their interpretation. Chapter 7 gives a conclusion and an outlook for further research. Appendix A contains an additional result. Appendix B describes the used identifier scheme and hit database. The developed software is described in appendix C. Appendix D contains an overview of the work done for this thesis and at CERN during the summer school in 2006. 9

Chapter 2 ATLAS and the muon detectors ATLAS is a general purpose detector located at CERN and part of the LHC project. In this chapter a more detailed outline of the properties of ATLAS with emphasis on the muon system will be given. Also the coordinate system and chamber identification convention used in ATLAS and throughout this thesis will be introduced. 2.1 ATLAS ATLAS, A Toroidal LHC Apparatus, is a general purpose detector. It is the largest of the four experiments, has dimensions of 46x25 m and weighs approximately 7000 metric tons. ATLAS consists of several detector elements, placed in layers from the interaction point radially outwards. One of the main purposes of ATLAS is the detection of the predicted Higgs particle. Other research areas are top physics, supersymmetry, B physics and exotics. Figure 2.1: A schematic overview of the ATLAS experiment. The different detector elements are shown. In figure 2.1 the different detector elements of ATLAS are shown, while figure 2.2 shows a transverse view of the barrel detector with the location of the detectors. In the following, these element will be discussed in short. The muon spectrometer will be discussed in more detail in the next section. 10

Figure 2.2: Transverse view of the barrel of ATLAS. 2.1.1 Inner detector The inner detector is the detector closest to the beam pipe and thus to the interaction point. It has to be capable of processing at the interaction rate of 40 MHz and discriminating the tracks of different bunch crossings [4]. The pixel detector being the innermost layer of the inner detector is only 4 cm away from the interaction point. This requires extremely radiation hard detectors which is provided by the silicon technology used in the pixel detector. The intermediate layer consists of a silicon strip tracker or semiconductor tracker (SCT), while the outermost layer is made of gas-filled straws, the Transition Radiation Tracker (TRT). The SCT and TRT have elements both in the barrel and in the endcap. These detectors are contained in a superconducting solenoidal magnet of 2 T. The inner detector is 6 m long and has a radius of 2 m. The inner detector allows a precise reconstruction of charged particles. 2.1.2 Calorimeters The calorimeter can be divided in two parts. The electromagnetic calorimeter (ECAL) is designed for the measurement of the energy and position of electrons and photons. The hadronic calorimeter (HCAL) measures the energy and direction of hadronic particles, such as jets. Also from this missing transverse momentum of an event can be calculated. The ECAL is a leadliquid-argon (LAr) detector and the hadronic calorimeter uses plastic scintillator plates within 11

an iron absorber. 2.1.3 Muon Spectrometer Two magnets are in use in ATLAS. The inner detector is contained in a solenoidal magnet of 2 T. The muon spectrometer has a toroidal magnet consisting of eight superconducting coils. The field of this magnet is not perfectly toroidal. Figure 2.3: An overview of the different types of muon chambers in ATLAS in both the barrel and the endcap. The muon spectrometer forms the outermost layer of detectors of ATLAS. The barrel part is situated in and outside the toroidal magnet and the endcap parts are placed at the two ends of ATLAS. Four types of chambers are in use in the muon spectrometer, two types of trigger chambers (RPC and TGC) and two types used for precision measurements (MDT and CSC). In the barrel only MDT and RPC chambers are used, while the endcap consists of TGC and CSC chambers. Figure 2.3 is a 3D view of the muon chambers and their position within the muon spectrometer. 2.1.4 Trigger system The trigger of the muon spectrometer uses the RPCs in the barrel and the TGCs in the end-cap region. The level-1 trigger is performed by electronics mounted on both detectors. The purpose of this trigger is to reduce the data rate from 40 MHz, which is the bunch-crossing frequency, 12

to about 75 khz. There are two thresholds for the trigger, the low trigger for p t > 6 GeV and the high trigger for p t > 20 GeV particles [5]. In the case of a trigger, the whole detector will be readout. The result of this readout is sent to the level-2 software trigger, which reduces the data rate to about 1 khz and is based on Regions of Interest (ROIs). The final trigger is the offline level-3 trigger or event filter. It reduces the data rate to 100 Hz and the results are stored for further analysis. Resistive plate chambers A Resistive Plate Chamber (RPC) is a trigger chamber which is used in the barrel section of the muon spectrometer. It consists of two gas gaps, both equipped with a plane of readout strips in two perpendicular directions. According to the naming convention explained below, the RPCs are called B1S/L, B2S/L and B3S/L, where the final S or L stands for RPCs in either the small or large sections. In the next chapter the RPCs are discussed in more detail. Thin gap chambers Thin Gap Chambers are used in the end-cap for the trigger and are used to measure the azimuthal coordinate also measured by the MDTs. TGCs have a structure similar to multi-wire proportional chambers, with the characteristics that the wire-wire distance which is greater than the anode-cathode distance [6]. They are, just as the RPCs designed to have a good time resolution and also have a good granularity to provide a sharp cut-off on the muon momentum. 2.1.5 Precision trackers Monitored drift tubes In the barrel and end-caps, the Monitored Drift Tube chambers (MDTs) provide precision measurements. An MDT chamber consist of two multi-layers, that contain three or four layers of tubes. The aluminium tubes have a diameter of 30 mm and are filled with a gas mixture of Ar/N 2 /CH 4 in a mixing ratio of 91/4/5 and at a pressure of 3 bar[6]. In the middle of the tube a tungsten wire is located, the anode. The detection principle is based on the ionisation of the gas when a charged particle passes through the tube. The created electrons drift towards the anode. From the drift time to the wire the distance of the particle to the wire can be determined with an average resolution of 80 µm [7]. Cathode strip chambers The Cathode Strip Chambers (CSC) are used in the forward region where a high counting rates are expected. The CSCs cover the pseudorapidity range η = 2 to η = 2.8 and provide an average spatial resolution of 80 µm [6]. They are multiwire proportional chambers with strip readout. The short drift time is less than 30 ns. They are equipped with a second strip plane for the measurement of the transverse coordinate. 13

Figure 2.4: Global right-handed cartesian coordinate system of ATLAS. The z-axis is along the beam pipe, and the x-axis is pointed towards the centre of LHC. 2.2 Coordinate system and identification scheme of chambers 2.2.1 Coordinate system In ATLAS a cartesian coordinate system has been defined. This global coordinate system is shown in figure 2.4. It is a right handed coordinate system, with the z-axis following the beam line and the x-axis pointing to the centre of the ring, so the y-axis points upward. The origin of this system lies in the centre of the detector. Furthermore, ATLAS is along the z-axis divided in two sides. The A side (Geneva side) is the part with z > 0, while the C side (Jura side) is the part with z < 0. The central plane (z = 0) is designated with the letter B. Instead of spherical coordinates, normally the azimuthal angle φ is used in combination with the pseudorapidity η. The angle φ is defined in the x-y plane, with φ = 0 at x = 0, and the polar angle θ in the z-y plane, with θ = 0 along the positive z-axis. The pseudorapidity η is defined as η = ln[tan( θ 2 )]. So θ = 40.4 η 1, while for θ = 90 η = 0. Based on the pseudorapidity we can define different regions in the muon spectrometer. The barrel is the region with η < 1, while the end-cap is the region with η > 1. To further identify the location of a muon chamber, 16 sectors are defined along φ. As can be seen in figure 2.5 sector 1 corresponds to φ = 0 and odd sectors are situated between barrel magnet coils, while even sectors are covered by barrel magnet coils. The chambers in odd sectors are larger than the ones in even sections, so they are called respectively large and small chambers. Finally, muon chambers are identified by their distance R from the beam line with 14

Figure 2.5: Muon spectrometer sectors in ATLAS. The chambers in the odd sections are called large and in the even sections small chambers. the chambers with smallest R being called inner and with the largest R outer chambers and in between the middle chambers. 2.2.2 Identification of chambers The identifier of a muon chamber has the generic format X.YYY.ZZZZ, where every element gives specific information about its location. In this section, only the identifiers relevant to this thesis are being described. The first digit X is either R for RPC chambers or M for MDT chambers. The second series of digits YYY consists of (1) the region of the chamber, which in this case is always B for barrel, (2) the station s location based on the distance R, so I for inner, M for middle or O for outer, and (3) whether the chamber is a large (L) or small (S) one. For RPC chambers, the second digit is a number identifying the trigger plane, and can take the values 1, 2 or 3. The last four digits ZZZZ give (1) the location along the z-axis, starting at 1 for z = 0 (2) at which side the chamber is, A or C side and (3) the sector number from 1 to 16. 15

An identifier for a chamber is for example R.B3L.3A7. This is a large RPC chamber in the third trigger plane in the barrel. It is the 3rd chamber from the centre at the A side and is located in the 7th sector. The third trigger plane is located at the outer MDT chambers, so this RPC chamber is attached to chamber M.BOL.3A7. This notation will be used in the following chapters. 16

Chapter 3 RPC structure and operation mechanism Resistive Plate Chambers (RPC) are part of the level 1 trigger system of the muon spectrometer. They are used only in the barrel, as in the endcap TGC chambers are used for trigger. Because all analysis described in this thesis was done with data from RPC chambers, this chapter contains a more detailed description of the structure of these chambers. Both the hardware, the trigger system as the read-out will be described in the following sections. 3.1 Global overview RPCs are gaseous parallel-plate detectors. The time resolution of a RPC is in the order of 1 ns [6], which is sufficient for trigger chambers. The strip width is between 30 and 40 mm, depending on the trigger layer [6]. The construction of RPCs was constrained by some important principles. First of all the thickness of the chamber had to be limited to avoid multiple scattering. As they are trigger chambers, the timing resolution should be high, in the order of 1 ns, and RPCs have to be able to distinguish different bunch crossings. Because they consist of two orthogonal strip planes, the combination of measurements of these planes can lead to a second measurement of the space coordinate. The readout of RPCs is based on metal strips. These strips detect the avalanche of electrons created when a charged particle, in this case a muon, passes through the gas in the detector. The RPCs are operated at 8.90 ± 0.15 kv. 3.2 Structure of an RPC An RPC consists of several units which are combined to form a functioning chamber. Figure 3.1 shows a cross section of a RPC chamber. The smallest functional unit is a gas volume or gas gap, which is according to the ATLAS naming convention called the counter of the RPC. A gas volume is made of two Bakelite plates of 2 mm thick kept apart from each other by insulating spacers. These spacers determine the size of the gas gap which is 2.00 ± 0.01 mm. The size of the gas gaps is limited by the size of Bakelite plates available, so the maximal length of a gas gap is 3.2 metres. If larger chambers are required, for example in the large middle and outer chambers, two identical gas gaps are glued together to form a larger chamber. The resulting dead zone from such a combination is 14 mm in ϕ. 17

On top of the plates a layer of graphite paint is spread which is connected to the high voltage or provide the grounding. To insulate the readout strips from this layer, a PET film is placed between them. The readout strips form together with the front-end electronics a strip panel, as shown in figure 3.2. On one of the plates the strip panel is oriented in the ϕ direction, that is orthogonal to the MDT wires, while on the other plate they are oriented in the perpendicular η direction. The main gas used in the RPCs is tetrafluorethane (C 2 H 2 F 4 ). This is a high density gas which leads to high primary ionisation of about 60 electron-ion pairs per centimetre when a charged particle passes through it. Furthermore, it has a relatively low operating voltage. As primary quencher a small amount of iso-butane (C 4 H 10 ) is added. As a third gas sulphurgexafluoride is added, the reason for which is explained below. So the gas is a mixture of C 2 H 2 F 4 /C 4 H 10 /SF 6 with a mixing ratio of 94.7/5/0.3. The gas pressure is 1.0 ± 0.5 mbarabove atmospheric pressure. A doublet consists of two gas volumes put together in a single structure, which is also called a unit. Such a doublet is a complete RPC and is mounted on a MDT chamber. This means that an RPC has four strip planes, two in the η and two in ϕ direction. The strips are 30 to 40 mm wide and in case of the ϕ strips cover the full width of the chamber, which is up to 108 cm. Two identical η strip planes cover the length of the chamber with a maximum length of 249 cm. The propagation time is less than 11 ns. The η strip planes are connected, so double hits can be measured in the η plane. The strips are placed 2 mm from one another, with a grounded strip in the middle of this space. As is shown in figure 3.1 the doublet is placed in a supporting structure and, to avoid dead zones, there is an overlap in the z (or η) direction. 3.3 Operation of an RPC When a charged particle crosses the RPC gas gap, it loses energy and ionises the medium. Because of an electric field applied in the medium, the electrons and ions created by the ionisation drift towards the anode and cathode. During this drift process, electrons can gain additional energy if the field strength is high enough, which results in the additional ionisation. This process, or avalanche, continues and is cumulative, so the total number n(x) of free electrons is described by n(x) = n 0 e (αx) n 0 being the initial number of electrons, α is the so called first Townsend coefficient and x is the distance from the anode. In principle the charge created during this process is unlimited, but in Figure 3.1: Cross section of an RPC chamber showing a sandwich of two doublets with dimensions. 18

Figure 3.2: Overview of the read-out strips. The different components and front-end electronics are shown. practice there is a certain limit at which there is a breakdown. If this limit is reached, the RPC is operating in streamer operation and the result is the measurement of an additional amount of induced charge after the avalanche signal, as is shown in figure 3.3 b and c for different operating voltages. For the high rate conditions in which the RPC should operate, this is an unwanted situation. Therefore the amount of charge created should be somehow limited. In the ATLAS RPCs this is done using a quencher gas, which is sulphur hexafluoride (SF 6 ). This gas is capable of suppressing the streamer by taking some of the energy created during the avalanche. Using this gas mixture, the RPC works in avalanche operation, which results in a signal as shown in figure 3.3 a. The signals produced by an RPC in avalanche mode typically have a signal of 5 ns FWHM an a jitter of 1.5 ns. The signals of the strips are sent to an 8-channel chip in the front-end electronics. So each front-end box receives the signals of eight strips. 3.4 Level-1 trigger system The level 1 trigger system consists of the hardware elements, the associated electronics and the algorithms used for triggering. The level 1 trigger is a low-level online trigger. The level 1 trigger hardware in the barrel consists of RPCs and their electronics. As has been described in the previous section, an RPC has two gas gaps both with 2 readout strip layers, one in the η and one in the ϕ plane. An RPC unit thus has a total of 4 readout strip layers, 19

Figure 3.3: RPC signals in different operation modes. Figure a shows the signal when in avalanche mode at voltage of 9.4 kv. In figure b (9.6 kv) and c (10.2 kv) the avalanche signal is followed by a streamer. The gas mixture is C 2 H 2 F 4 /C 4 H 10 /Ar in ratio of 83%/7%/10%. Figure 3.4: The components of the barrel muon trigger. The location of the RPCs on the MDT chambers are shown. Because RPC3 is placed below the outer chamber, this is a so-called small sector. 20

the signals of which are processed by the front-end electronics. The signals from the front-end are send to either the ϕ or η coincidence matrix (CM) chip. These chips perform most of the level 1 trigger algorithm. For the low p t trigger, the results of 2 adjacent ϕ and 2 adjacent η CM chips are send to a low p t Pad Logic board (PAD) [8]. For the high p t trigger a similar set-up is in use, where the CM also receives the result of the low p t CM. The result is send to the high p t PAD, which combines the results of both triggers. This result is send to the Sector Logic. In the barrel, the trigger system consists of three RPCs, which are shown in figure 3.4. The first two RPCs are placed below and above the middle MDT chambers. These two RPCs together form the low p t trigger. These RPCs are named according to the naming convention B1S and B2S or B1L and B2L. So the second digit increases with the distance from the beam line R and the last digit indicates whether the RPCs are on a small or large MDT. In the low p t trigger, a Figure 3.5: Location of RPC electronics on the modules. An ROI is an overlap of two CM chips. The results of a ROI are processed by the PAD. trigger is accomplished when 3 or more out of 4 gas gaps register a hit in a certain region. This region is determined by the hit in the B1 chamber, from where the trigger region is determined in the B2 chamber. This is based on a muon with p t > 6GeV. Both in the ϕ and η projection these criteria are applied and a trigger is only valid if in both projections the 3 out of 4 criterion is met. The third RPC is placed on the outer chamber, either a below a BOS or a above BOL. This chamber performs the high p t trigger for muons with p t > 20 GeV. When a hit is registered in the first RPC, the so called pivot plane, the trigger algorithm will search for a hit in the second RPC. The region in which this search is defined in a cone with the centre of the cone a path in the direction of the interaction point. The size of the cone determines the cut on the p t, which is visible in figure 3.4. This is done in both the ϕ and η projection. The results of these triggers are combined to Regions-of-Interest (RoI), which is an overlap of two CM regions. The location of the electronics on the RPC is shown in figure 3.5. The external clock frequency is 40 MHz, while the internal clock of the CM is 320 MHz, which means that a bunch crossing is divided in 8 bins, each 3.125 ns in size. All data from an RPC is associated to such a time bin. 21

Chapter 4 Data set and timing All data analysis on the RPCs has been done with cosmic data. Several sectors in the muon spectrometer were readout during 2005-2008. This allowed to test the detector by the measurement of cosmic muons. In this chapter a short introduction on the characteristics of cosmic particles will be given, followed by an overview of the sectors involved in the cosmic runs and the data used for analysis. 4.1 Cosmic particles The Earth s atmosphere is constantly bombarded with cosmic particles, originating from sources like the sun, distant stars or supernovae. When a particle hits the atmosphere it creates lighter particles, due to collisions with molecules. Most of the incident particles are protons, which typically create charged mesons like pions. Because the mesons decay to other particles, such a particle collision leads to a shower of particles. In the decay of pions, muons can be created, but also for example electrons, photons and neutrons. A schematic example of such a shower is shown with figure 4.1a. The muons can be measured in detectors such as ATLAS. For calibration purposes the measurement of a shower of muons is not convenient, as it gives several measured muons with a wide distribution of arrival times. A single muon gives a clearer and cleaner event which allows for more precise time corrections. At sea level, muons are the most numerous charged particles as can be seen in figure 4.1b. The mean energy of muons at sea level is 4 GeV [2], which from this figure shows that the muon flux is relatively high, around 100 m 2 sr 1 s 1. Because of this high rate, cosmic muons are an appropriate candidate for calibration of muon detectors. 4.2 Data set The installed muon chambers have been tested and calibrated using cosmic muon measurements. From analysis of these measurements, hardware problems could be identified and the characteristics of the detectors determined. Not all sections of the muon spectrometer were involved in the cosmic muon testing. The first runs, started in November 2006, used only sector 13 for trigger and cosmic data taking. Later runs used sector 3, 4,5 and 6 and both RPCs and TGCs to trigger the event. 22

(a) (b) Figure 4.1: (a) A typical shower of particles created by a primary cosmic ray. The different types of particles are shown. (b) The vertical flux of different particles at a given altitude. Muons and neutrinos are clearly the most numerous particles at sea level (see scale on top). The data set used for the analysis in this thesis is from the M5 run, taken from October 22nd till November 5th 2007, with run number 29576. The following figures show some properties of this data set. Figure 4.2a shows the number of RPC hits per event in this run, with a mean of about 52 hits per event. The RPC hits can be part of a segment of MDT hits and most hits lie on a segment. Figure 4.2b shows the number of segments per event, with a mean of about 4. The distribution of ϕ and η hits is shown in figure 4.3a, so 55% of the hits are ϕ hits. Figure 4.3b shows the time distribution for all hits in the data set. Figure 4.4 shows the distribution of hits in the x-y plane for several η regions. This shows that almost all of the chambers in sectors 5 and 6 were activated and registered hits. 23

(a) (b) Figure 4.2: (a) The number of RPC hits per event. (b) The number of segments per event. (a) (b) Figure 4.3: (a) The number of ϕ and η hits. (b) The time distribution of the hits. 24

(a) η = 1 (b) η = 2 (c) η = 3 (d) η = 4 (e) η = 5 (f) η = 6 Figure 4.4: Hit distribution of ϕ and η hits in x-y plane for different η regions. The figures show that the hits are distributed along all the chambers in sector 5 and 6. The x and y axis give the positions in mm. 25

4.3 Introduction on timing In the hit data, every RPC hit has an associated time of measurement. To be able to use these time measurements, it is important to understand how they are created and what the associated uncertainties are. The time measurement of a muon hit consists of several elements. Besides the true hit time t 0, one has to take in account contributions which influence the final stored time t m t m = t 0 + t s + t fe + (t c ) i + t bc. The first contribution is t s, the propagation time of the signal on the strip. The strips have been designed in such a way that this delay is always < 11 ns [6]. Because the smallest time bin is 3.125 ns, t s can be an important contribution to the time measurement. It is assumed that all strips have similar conduction properties and the propagation speed on all strips is similar. To prevent double measurements, the strips are on both ends terminated on their characteristic impedance. The second contribution t fe is the timing associated to the processing of the front-end electronics. The front-end is an amplifier which is connected to a comparator. Figure 4.5 shows the simulated input and output to these elements and one can see that there is only a small delay in the return-to-zero time for both elements. (a) Amplifier input and output (b) Comparator input and output Figure 4.5 The third contribution is the cable propagation time t c from the front-end to further electronics. The cabling length can be different for every front-end box. The time t c should be determined by analysis of the hit data. The final contribution is time of the bunch crossing. This is determined by an external clock running at 40 MHz, so a bunch crossing is 25ns. So the hit time in a certain bunch crossing is t m mod 25. Besides the structure of a single time measurement as described in the previous section, there are additional factors when combining several of these measurements. The trigger is based on the majority principle, which means that in both the φ and η strip planes, 3 4 of these planes have to register a hit. To reduce noise, these hits have to be in a certain time window. 26

4.4 Logical division of an RPC To be able to perform a correct analysis, it is necessary to use a logical division of the RPC chamber and analyse the hits in these divisions separately. Otherwise, hits from completely different regions will be compared. The division is based on the software identifier, which is stored together with the hit data. The logical scheme is based on the existing software scheme for the Muon Spectrometer.[9] An important difference is that the numbering in the Muon Spectrometer software scheme begins at 1. In the scheme defined below the numbering begins at 0, because of storage efficiency. The location of a time measurement or hit is stored within a hit identifier and is based on a logical division of the RPCs in substructures. This division has several levels. First of all, this identifier associates the RPC doublet which is hit to an MDT chamber. For middle chambers two RPC doublets are placed on the MDT, while for outer chambers only one is used. This means that the identifier for the RPC value can have the value 1 or 2 for middle chambers and only 1 for outer chambers. The next step is the division of these doublets in gas gaps. Each doublet consists of two gas gaps, numbered 0 and 1. Both the doublets and the gas gaps are numbered with increasing R. By combining the identifier for the doublet and the gas gap, a module can be defined by mod RP C = 2 (db R ) + gg where db R is the identifier for the doublet and gg is the gas gap within the identifier. So, for middle chambers mod RP C can take the values [0, 3] and for outer chambers [1, 2]. These modules can be further subdivided in submodules. A submodule is a region in a module with a certain doublet φ and η value, which increase respectively with φ and η. The submodules are defined in a way similar to the modules as smod RP C = 2 (db φ ) + db Z where db φ [0, 1] is the doublet φ value and db Z [0, 2] the doublet Z. So a submodule can take the values [0, 5]. Figure 4.6 shows a schematic overview of these divisions. 27

Figure 4.6: An overview of the logical division of the RPC chambers. The figure shows the two RPC doublets with an MDT chamber in the middle. Because there are RPC doublets on both sides, this is a middle chamber. The numbering of the doublets and of the modules increases with R. The division of a single module in four submodules is shown on the top module (in some RPCs there are six submodules). The direction of the MDT tubes is shown for reference, but the real MDT chambers consists of two multi-layers of tubes. (not to scale) 28

Chapter 5 Correction of strip times 5.1 Data 5.1.1 Data preparation The RPC data are stored in ROOT [10] CalibrationNtuples. The data in these ntuples are raw data obtained from the byte stream decoding and higher level reconstruction objects such as patterns, segments and tracks. The raw RPC data used in this analysis contains an identifier, a position and a time. From the identifier the chamber, module, submodule, strip number etc. can be obtained. The Moore reconstruction is used here, e.g. to select RPC hits on a segment for the timing studies. For the processing of the data, the Athena framework 12.0.4[11] has been used. 5.1.2 Chamber identification In addition to the naming convention specified in section 2.2.2, the chambers are identified by the number of the module and submodule. The number of the module, which can have the values [0, 3], is independent of the trigger plane, but based on the MDT chamber it is associated with. This is only of importance for the middle chambers, trigger planes 1 and 2, as the outer chambers only have a single trigger plane. So the first module in the second trigger plane is numbered M2, as it is the third module from the interaction point. The submodules are identified by an S followed by the number, which is explained in section 4.4. Therefore, a valid identification of a chamber is for example R.B2L.5A3.M2.S1. 5.2 Time differences Because a single muon is measured by several detector elements, their measurements should give similar timings. A cosmic muon travels with v c, so in 3 ns it travels about 1 m. Detector elements close together therefore measure the hit in the same time bin (which is 3.125 ns), if correctly calibrated. Minimising the time differences between such elements is thus an good method for calibration. Because not every strip will register a hit in a not too large dataset, for the sake of statistics clusters of 8 strips are grouped together in the analysis. Such a cluster is connected to a single 29

front-end electronics box, to time measurements can be assumed to be equivalent. Wherever the word strip is used, a cluster of 8 strips is meant. For strip corrections to be calculated, time differences for a large number of strip combinations have to be acquired, stored and analysed. In general two sets of time differences exist, those resulting from dependent and from (roughly) independent strips. An example of the former are the time differences ( t ) from adjacent strips in a submodule. The most basic example of the latter are orthogonal strips in a submodule. Orthogonal strips combinations, which means strips from the ϕ plane combined with those from the η plane, are a canonical choice for first calculations of t. Nevertheless, the described method can be applied to all combinations of strips. 5.2.1 Acquiring time differences Using the RPC hits from the MuonCalibRawHitCollection in the MuonCalibEvent_E[12], hits were selected on the following criterion: 1. There has to be at least one segment present in the event, and no more than 10. This to exclude events caused by showers and are not useful for calibration purposes (see chapter 4). 2. The RPC hit has to be on such a segment. 3. The timing of the hit has to be positive. Some events contain marked hits with negative timings, which have to be excluded. 4. The hit has to be unique. Off-line, hits with the same timing can be duplicated, and stored (at least) twice in different submodules [8, 13, 14]. Only the first hit in the event is used. 5. There is a cut on the time differences t 15 ns. This to exclude out-of-time hits. The cut is made after the corrections have been applied. For all of these hits, the time differences where calculated. planes, this time difference is If the hits are in different strip t ϕη = t ϕ t η. (5.1) In the case of two hits in the same strip plane, those hits are always in different modules. The time difference is defined as t ϕϕ = t ϕ t ϕ+. (5.2) where t ϕ is the time from the module with the lowest number and t ϕ+ the time from the other module. The same definition is applied to η hits. Every time difference is stored and the mean per event is calculated. In the end, the total mean of all time differences is stored, so t ij = 1 N events N events 1 n δt ij (5.3) n 30

where δt ij is the time difference for a single hit combination, n the number of hits for this combination per event and N event the number of events. To store these values and be able to use them in a convenient way, for each t ij an identifier is created, which is a 64 bit integer containing all information of both hits. The structure of this identifier is explained in appendix B. These identifiers are stored in a text file for analysis. This file contains, besides the identifier, also the number of hits on which the timing has been based and the standard deviation. This also allows analysis of the UIDs with other tools to extract information from it. The hit database contains all the information necessary to calculate the strip times. This will be explained in the next section. 5.3 Time solving 5.3.1 Matrix construction When the time differences have been calculated and stored, the strip times can be obtained by solving a linear system consisting of these time differences. First, a matrix is constructed which contains the equations for the time differences. There are several different matrices which can be constructed, so based on the available values a choice has to be made. If enough values are available, the system can be solved multiple times using different matrices and the mean of the results can be calculated. Because for N time measurements only N 1 time differences are available, an additional constraint on the data is necessary. The most convenient way, is to put the mean of all measurements to zero: t i = 0. (5.4) N Although other values than 0 can be chosen, this will only result in an offset added to the solution. This offset is related to the unknown offset of the complete muon system, which in the end is determined by the beam crossing, and cannot be determined. The matrix has the form of rows with one 1 and one 1 which are the two time measurements which are subtracted. This gives the equation 1 N 1 N............ 1 N 1 0... 1 0...... 1 0... 0 1 0.... where the first row is equivalent with equation 5.3....... t 0 t 1 t 2. = 0 t 00 t 01 This system is then solved with the CLHEP::solve() function [15], which takes the matrix and the t ij values as arguments and returns the vector containing the solutions for the strip times. This process is partly automated. For every submodule, all available strip combinations are retrieved from the hit database. Next, a check is performed to determine if the set is complete. Completeness can be defined in several ways, because not all strip combinations are necessary to solve the system. For all complete systems, one or more matrices are constructed and the system is solved as described.. (5.5) 31

This process is repeated for two additional matrices, resulting in 3 sets of solutions. The means of these are then stored as corrections in the hit database. The corrections can be retrieved and applied to strip times. This is described below. 5.3.2 Correcting strip times The obtained solutions are corrections which have to be applied to the strip times. The question remains whether they are to be subtracted or added to the measures strip times. We have the solutions C t0... C tn and their associated time differences t ij = C ti C tj. We want the corrected time differences t ij = t i t j to be 0, so it is easy to show that So the corrected time measurements are t i t j = C ti C tj = (t i C ti ) (t j C tj ) = 0 (5.6) t i = t i C ti (5.7) The process of correction is quite straightforward. A new loop over all hits is started and for every hit the correction is retrieved from the hit database. If available, the corrections are applied according to equation 5.7 and the time difference is recalculated. 5.4 An example: R.B2L.4A3.M2.S0 As an example of the above method we apply it to a submodule, R.B2L.4A3.M2.S0. For this chamber a full set of time differences is available from a total of 8 ϕ and 5 η strip clusters, resulting from a run over 50k events. To be able to solve this system, N 1 = 12 time differences are selected. There are several possibilities for the set of time differences to use. In this example, t ϕ0 t η0...4 and t ϕ1...7 t η0 are used. The values for t are retrieved from the hit database. This results in the linear system showed in equation 5.8. 1 13 1 13 1 13 1 13 1 13 1 13 1 13 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 13 1 13 1 13 1 13 1 13 1 13 t ϕ0 t ϕ1 t ϕ2 t ϕ3 t ϕ4 t ϕ5 t ϕ6 t ϕ7 t η0 t η1 t η2 t η3 t η4 = 0 1.33962 1.56555 1.48392 1.78442 1.79958 2.13676 2.22175 3.4192 1.73513 1.18266 0.00602491 1.16535 (5.8) The solution is 32