Luminosity Determination

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1 M2 de Physique École Normale Supérieure de Lyon Université Claude Bernard Lyon 1 Master Thesis HAFNER, Andreas M2 Option Physique BABAR Luminosity Determination Abstract: The project consists of a precise luminosity determination of the PEP-II e + e storage ring with the BABAR experiment at SLAC/Stanford. This determination is achieved using the theoretically known cross section σ theo of e + e (Bhabha) scattering. By means of an event generator and a detector simulation the actual visible cross section σ vis can be determined. With σ vis and the number of detected events the luminosity of the e + e beam can finally be calculated. Keywords: BABAR particle physics event generators Laboratory: Supervisors: Institut für Experimentelle Kernphysik Universität Karlsruhe Postfach 3640 D Karlsruhe www-ekp.physik.uni-karlsruhe.de Dr. Denig, Achim Prof. Müller, Thomas September 13, 2006

2 Contents 1 Introduction 3 2 The BABAR Experiment The Asymmetric PEP-II Collider The BABAR Detector Vertex Detector Drift Chamber / Central Tracker Barrel Particle ID: DIRC Electromagnetic Calorimeter Instrumented Flux Return Solenoid Theoretical Background Luminosity Determination Generator Comparison Event Generation Exploration Phase Generation Phase Born Approximation Corrections To Born Approximation Results Total Cross Section Including All Amplitudes Excluding Vacuum Polarization Differential Cross Section Born Approximation Excluding Vacuum Polarization Including All Corrections Total Cross Section In BABAR Production Framework Outlook And Conclusion 23 6 Acknowledgement 25

3 Chapter 1 Introduction The PEP-II B Factory is an asymmetric e + e collider operating at a center of mass (CM) energy of.58 GeV, the mass of the Υ (4S) resonance. This resonance decays almost exclusively to B 0 B 0 and B + B pairs and is thus ideally suited for the study of B meson decays with the BABAR experiment, which is located in the interaction region of the collider. The primary physics goal is the systematic study of CP -violating asymmetries in the decay of neutral B mesons to CP eigenstates. As one of its first results BABAR has measured in the golden decay channel B 0 J/ψ K 0 S the angle β of the CKM unitary triangle and has proven like this for the first time that there are CP -violating effects not only in the kaon-system, but also in the B-system. This measurement is continiously updated with the increasing statistics (sin2β= ±0.040±0.023, ref.[1]) and many other CP -violating asymmetries are measured allowing to extract also the other CKM-angles γ and α. BABAR has also a broad physics program beneath CP -physics, including measurements of decays of τ-leptons and mesons including b and c quarks. The work presented here aims for an improved measurement of the hadronic cross section σ hadr = σ(e + e hadrons), which is performed at BABAR by means of the so called radiative return, using events with initial state radiation. In the following chapters the PEP-II facility and the BABAR detector are described. The method used in this study to improve the PEP-II luminosity measurement is then discussed in detail. Finally the obtained results are presented. 3

4 Chapter 2 The BABAR Experiment 2.1 The Asymmetric PEP-II Collider The PEP-II (Positron Electron Project) facility consists of two independent storage rings. Electrons are stored in the high-energy ring. Each beam electron has an energy of 9 GeV, while the low-energy ring stores 3.1 GeV positrons. The term asymmetric refers to the fact that the electron and positron energies are not equal. This results in a collision CM energy of.58 GeV and a forward boost of the CM frame, which is crucial for a precise measurement 08/21/ :23 of the B decay posi- 400 tion [9]. Injection is achieved BaBar Run 1-5 by extracting electrons and 350 PEP II Delivered Luminosity: /fb positrons at collision energies BaBar Recorded Luminosity: /fb 300 Off Peak Luminosity: 37.43/fb from the Stanford Linear Collider (SLC) and transporting 250 Delivered Luminosity Recorded Luminosity them each in a dedicated bypass Off Peak line. The low-emittance 200 SLC beams is used for the injection 150 process. The collider was completed in July Since then an integrated luminosity L int = L(t)dt of 50 about 400 fb 1 was achieved 0 (figure 2.1) with an instantaneous luminosity L up to cm 2 s 1. A new detector had to be constructed Figure 2.1: Luminosity performance of PEP-II in order to study those highintensity collisions: the BABAR detector. ] -1 Integrated Luminosity [fb

5 2.2. THE BABAR DETECTOR 2.2 The BABAR Detector The tracking system of the experiment consists of a silicon vertex detector and a cylindrical drift chamber. Particle identification is accomplished by means of a newly developed technology called DIRC. Additional detector components are an electromagnetic calorimeter and a muon system it the instrumented flux return. The angular acceptance for the entire experiment is determined by the vertex detector, which is limited by machine components. In the following the subsystems of the BABAR detector, ordered from the inside out are described. Further details can be found in reference [9] Vertex Detector The vertex detector is the only tracking device inside the 20 cm radius of the inner mechanical structure, the so called the support tube. It is used to measure precisely both impact parameters for charged tracks (z with σ z =65 µm and r - φ with σ r =65 µm); these measurements are used to determine the difference in decay times of the two B 0 mesons. The vertex detector also provides the measurements of production angles, given momentum information from the drift chamber. Finally, charged particles with p t between 40 MeV/c and 0 MeV/c are tracked only with the vertex detector, which must therefore provide a good pattern recognition. The vertex detector consists of five layers of double-sided silicon strip detectors. The inner three layers Figure 2.2: Silicon Vertex Tracker are ordered in a barrel geometry with detectors parallel to the beam pipe. The outer two layers combine barrel detectors in the central region with wedge detectors forward and backward. The detector can track particles with a polar angle in the laboratory frame of up to 20.1 in the forward direction and of up to in the backward direction. 5

6 2.2. THE BABAR DETECTOR Drift Chamber / Central Tracker The second component of the tracking system is the drift chamber, which is used primarily to achieve excellent momentum resolution ( σ p t p t =0.47%) and pattern recognition for charged particles with p t > 0 MeV/c. It also supplies information for the charged track trigger and a measurement of de/dx for particle identification. The chamber extends in radius from 22.5 cm, just outside the support tube to 80 cm. For most particles of interest at PEP-II, the optimum momentum resolution is achieved by having a continuous tracking volume with a minimum amount of material to cause multiple scattering. By using a helium-based gas mixture with low mass wires and a magnetic field of 1.5 T, very good momentum resolution can be obtained. The forward edge of Figure 2.3: Drift chamber the chamber is situated 1.66 m from the interaction point, which makes it possible to obtain reasonable momentum resolution down to the limit of forward acceptance of 300 mr (17.2 ). A design of four axial and six stereo superlayers, each consisting of four individual layers, was chosen as the baseline design for the drift chamber. The chamber is constructed to minimize the amount of material in front of the particle identification and calorimeter systems in the heavily populated forward direction. The readout electronics are mounted only on the back end of the chamber and the endplates are designed as truncated cones. Figure 2.4: Drift chamber 6

7 2.2. THE BABAR DETECTOR Barrel Particle ID: DIRC There are two primary goals for the particle identification system. One is to identify kaons beyond the momentum range where the de/dx information can be used. The other one is to identify pions from few body decays. A new detector technology was required to achieve these goals. A Detector of Internally Reflected Cherenkov radiation (DIRC) is used in the barrel region. Cherenkov light is produced in 1.75 x 3.5 cm 2 quartz bars and is transferred by total internal reflection to a large water tank outside the backward end of the magnet. The light is observed by an array of photomultiplier tubes at the outside of the tank, where images governed by the Cherenkov angle are formed. A mirror at the forward end of the bars reflects the forward-going light, preserving the angular information. Figure 2.5: DIRC Electromagnetic Calorimeter The electromagnetic calorimeter has excellent energy resolution ( σe E = 3.0%) down to very low photon energies. This is provided by a fully projective CsI(TI) crystal calorimeter, which has very good energy and angular resolution and retains high detection efficiency at the lowest relevant photon energies. The calorimeter consists of a cylindrical barrel section with an inner radius of 90.5 cm and a conical forward endcap. The barrel calorimeter contains 5880 trapezoidal crystals; the forward endcap calorimeter contains 900 crystals. Each crystal is readout by two independent silicon photodiodes. Electronic noise and beam-related backgrounds dominate the resolution at low photon energies, while shower leakage from the rear of the crystals dominates at higher energies. 7

8 2.2. THE BABAR DETECTOR Instrumented Flux Return The IFR is designed to separate pions from muons for momenta greater than 0.5 GeV/c; it also has the ability to detect and provide coordinate information on neutral hadrons. The magnetic flux return iron is divided into 18 layers whose thickness increases outwards from 2 to cm for a total thickness of cm. The gaps between iron plates are filled with active detectors, originally only consisting of Resistive Plate Chambers (RPCs). The RPCs are now systematically replaced by Limited Sreamer Tubes (LSTs) since a significant efficiency drop of the RPCs with time has been observed. Both RPCs and LSTs provide two dimensional position information in each plane with a resolution of 1-2 cm. Muons produce a track through most if not all of the IFR layers with a 90% µ detection efficiency, while most pions interact in the EMC or IFR steel (6-8% mis-identification) Solenoid To achieve good momentum resolution without increasing the tracking volume and therefore calorimeter cost, it is necessary to have a magnetic field of 1.5 T. The magnet coil is therefore of superconducting design, with an inner radius of 1.40 m for the coil dewar and a cryostat length of 3.85 m. The implementation of nonstandard features like a a special segmentation of the iron was necessary because of the IFR and the Figure 2.6: Solenoid superconductive magnet complications caused by the DIRC readout in the backward direction. 8

9 Chapter 3 Theoretical Background 3.1 Luminosity Determination Luminosity is usually measured in e + e colliders through the relation L int = N ev /σ vis, where the visible cross section σ vis = ɛ σ theo and N ev is the number of events observed for a reference reaction. σ theo is the theoretically calculated cross section and ɛ the efficiency to identify a certain event in the experiment. To determine the value of ɛ a full detector simulation is needed. It is evident that this is only a powerful method, if the theoretical cross section can be predicted with high precision. Also the detector simulation must be very exact and validated by the use of real data. If those two conditions are fulfilled the redundancy offered by the use of many different reactions is a powerful tool in order to minimize systematic errors. In BABAR the luminosity is measured using the following reactions: e + e e + e (γ) e + e µ + µ (γ) e + e γγ where e + e γγ events are only considered in order to reveal time dependent variations of the detector and trigger acceptances. The main challenges for a precise luminosity measurement in BABAR are: Over the last decade the theoretical interest has been focussed on Bhabbha scattering at LEP or even higher energies. The generators used in those studies have not been written for the Υ (4S) energy region. The generators for sub-lep energies have also been not well supported and dated. Recently a new precise event generator, Babayaga@NLO (ref. [2]) was developed. The aim of my project is to replace the old generator, BHWIDE (ref. [3]), currently used in the BABAR framework by this new one. 9

10 3.2. GENERATOR COMPARISON There is no special luminosity detector in BABAR. Therefore large parts of the BABAR detector must be used for the measurements. This demands a good knowledge of detector material in order to make a precise detector simulation over a large volume. 3.2 Generator Comparison The Bhabha event generator currently used for the luminosity measurement in the BABAR environment, BHWIDE, has a theoretical accuracy of 0.5%. The aim of this early work is to precisely compare BHWIDE with the newly developed and more accurate Babayaga@NLO event generator. The theoretical error of this new generator is estimated to be better than 0.1% according to ref. [2]. The next step will be to include Babayaga@NLO in the BABAR production framework. 3.3 Event Generation In order to generate physical events Babayaga@NLO computes decay amplitudes and a probability distribution ρ( x) for each point x in the multi-particle Lorentz invariant phase space. This is the exploration phase. In the generation phase randomly generated points are created according to this distribution Exploration Phase During the exploration phase the entire shape of the distribution ρ( x) is generated and memorized as efficiently as possible. A multidimensional system of cells, called foam, covering entirely the integration space is built up and a uniform distribution in each cell is assumed. The continuous distribution ρ( x) is transformed into a discrete distribution ρ ( x) (see fig. 3.1) Generation Phase Monte Carlo generation in the foam is very simple: a cell is chosen randomly according to the distribution ρ ( x) and then an event x is generated within the cell according to a uniform distribution. Weighted Events The so called weighted events are distributed according to ρ ( x). Unweighted Events Once received a weighted event x, it can be turned into an unweighted event. The actual distribution ρ( x) has to be calculated and only the fraction w=ρ( x)/ρ ( x) is saved as unweighted events. Those events are then redistributed according to

11 3.3. EVENT GENERATION the distribution ρ( x) as desired in order to recover physical events. This process of unweighting, however, takes a lot of computing time ρ (x) ρ (x) point in Lorentz phase space x Figure 3.1: 1-D representation of the weighted probability distribution ρ( x) and unweighted distribution ρ ( x) in the Lorentz phase space x 11

12 3.4. BORN APPROXIMATION 3.4 Born Approximation It is helpful to consider the simplest case for Bhabha scattering: no photon is present in the final state and only the leading order contribution, represented by the following Feynman diagrams, are taken into account: k k k k e e + γ e e + γ e e + p p p p Figure 3.2: t-channel and s-channel leading order Feynman diagrams Using the Feynman rules the following relation 3.1 for the spin average of the invariant amplitude M is obtained. M 2 = e4 + u 2 16πs (s2 t 2 + 2u2 ts + u2 + t 2 s 2 ) (3.1) with the Mandelstam variables: s (k + p) 2, t (k k ) 2 and u (k p ) 2. In the CM frame equation 3.2 relating the differential cross section and the invariant amplitude M for a two body process is found. Neglecting the electron mass, simple relations between the Mandelstam variables and the scattering angle θ according to equations 3.3 and 3.4 can be obtained: dσ dω = 1 p f 64π 2 M s p 2 (3.2) i t 1 (1 cos θ)s (3.3) 2 Now formula 3.2 can be expressed in terms of cos θ: u 1 (1 + cos θ)s (3.4) 2 dσ d cos θ = e4 + (1 + cos θ)2 (1 + cos θ)2 { πs (1 cos θ) 1 cos θ 2 (1 + cos2 θ)} (3.5) The event generator gives us a certain number of events N( cos θ), in a certain interval cos θ, which can be compared to equation 3.5 with the help of equation 3.6. N( cos θ) cos θ = dσ N T ot (3.6) d cos θ σ T ot This is used in chapter 4.2 to give a crude test of the Babayaga@NLO event generator. 12

13 3.5. CORRECTIONS TO BORN APPROXIMATION 3.5 Corrections To Born Approximation To approach the physical cross section of Bhabha scattering, a variety of corrections to the Born approximation have to be taken into account. The most important corrections are the electromagnetic Next to Leading Order NLO corrections. They are Initial State Radiation, Final State Radiation and diagrams containing one loop. They have to be considered in the t-channel as well as in the s-channel. FSR is illustrated in figure 3.3. BHWIDE and Babayaga@NLO include all NLO corrections. k p e e p e + γ e + p Figure 3.3: Final state radiation in t-channel The Next to Next Leading Order corrections NNLO are combinations of the NLO corrections: for example two ISR photons, one loop and one ISR photon, and so on. Those higher order Feynman diagrams have been treated differently in the BHWIDE and Babayaga@NLO generators. BHWIDE uses a Parton Shower method whereas Babayaga@NLO uses in addition the Leading Log method (ref. [4]). Besides the higher order QED effects weak corrections have also to be considered. Figure 3.4 shows the weak Leading Order correction in the t-channel. Other weak corrections are for example the leptonic vacuum polarization. k e e e + Z e + p Figure 3.4: Weak LO correction in t-channel All the effects discussed until now are calculated at high precision using perturbation theory. However the strong interaction effect of the hadronic vacuum polarization cannot be calculated because of the fact that QCD correction cannot be treated in perturbation theory. It is phenomenologically obtained from data by applying the dispersion relation between σ(e + e hadrons) and the hadronic vacuum polarization (ref. [5]). It might be different for the two generators, since the data for the BHWIDE corrections is not up to date. Therefore in this study the event generators have also been compared with each other without the effect of vacuum polarization. k p 13

14 Chapter 4 Results I present in this chapter results of the initial studies performed during my Master Thesis. As a first step a comparison of the total cross section simulated by two event generators for different cuts is established. For the computation a center of mass energy of.576 GeV is used as needed for BABAR. There are neither requirement made on the maximum number of created photons nor on the accolinearity, the angle between outgoing electron and outgoing positron. In a second step the differential cross sections are investigated, before finally the effective cross section in the BABAR production framework is compared to values of ref. [6] (current BABAR luminosity determination). 4.1 Total Cross Section In the following the cross sections of the weighted events of the different event generators are compared with each other. The weighted cross section is more precise than the unweighted one because of higher statistics Including All Amplitudes At first the total cross sections of different event generators are compared with each other. As already mentioned, BHWIDE is the event generator currently used in BABAR and is compared to the newly developed Babayaga@NLO generator. Both are also compared to an older version (3.5) of Babayaga that does not calculate all NLO corrections. 14

15 4.1. TOTAL CROSS SECTION The results for different cuts on the polar angle θ of the outgoing relative to the incoming particles in the CM frame are shown in table 4.1. angular range cross section [nb] (CM) BHWIDE Babayaga (3.5) BHWIDE ref.[1] ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±0.001 Table 4.1: Total cross sections for different event generators There is excellent agreement between the results for and BHWIDE. They coincide within the statistical errors (see figure 4.1). There is however a clear difference in the order of one percent between Babayaga@NLO and Babayaga (3.5), most probably due to the fact that Babayaga (3.5) did not take into account all NLO corrections. rel. difference in percent angular range (from x to 180-x degrees) Figure 4.1: Relative difference of the BHWIDE and Babayaga@NLO cross section 15

16 4.1. TOTAL CROSS SECTION Excluding Vacuum Polarization As discussed before, the hadronic vacuum polarization cannot be calculated by the means of perturbation theory. It is therefore phenomenologically obtained from data that is continiously being updated. Considering the fact that BH- WIDE does not have the up to date hadronic vacuum polarization corrections, the total cross sections are also compared to each other without this effect. This way, one can be sure to only consider the differences of the two generators by the fact, that they handle the higher to leading order corrections differently. However, for the BHWIDE generator it is not a simple task to switch off only the vacuum polarization. It is more convenient to switch off the weakcorrections at the same time. That is not the intended task. Therefore in a first analysis the importance of the weak corrections have to be investigated. When comparing the resulting cross sections with switched off weak interaction to the cross section including all corrections, it is clear that the effect of weak interaction is in the sub-permil range and therefore negligible for this study. This can be seen in table 4.2. angular range cross section [nb] (CM) BHWIDE with EW BHWIDE without EW ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 4.2: Absolute cross sections with and without weak corrections 16

17 4.1. TOTAL CROSS SECTION As a consequence it is now possible to compare the BHWIDE cross section without vacuum polarization and without weak interaction corrections with the cross section of Babayaga@NLO without vacuum polarization. The resulting values for the total cross section and different angular ranges can be seen in table 4.3. angular range cross section [nb] (cms) BHWIDE Babayaga@NLO ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 4.3: Absolute cross sections without vacuum polarization Figure 4.2 shows the relative difference. There is still an excellent agreement of the cross sections of BHWIDE and Babayaga@NLO. To further investigate the small differences of the event generators, the differential cross sections have to be studied. rel. difference in percent angular range (from x to 180-x degrees) Figure 4.2: Relative difference between the BHWIDE and Babayaga@NLO cross sections without vacuum polarization 17

18 4.2. DIFFERENTIAL CROSS SECTION 4.2 Differential Cross Section In order to compare the differential cross sections, it was necessary to save n-tuples with momentum information of the outgoing electron, positron and photons for a non-fixed number of outgoing photons. The physical results distributed according to the probability distribution ρ( x), the unweighted events, have to be saved in these n-tuples Born Approximation As discussed above, the simplest case of e + e scattering is a final state without any photons in Born approximation. In chapter 3.4 the cross section for this process is calculated analytically in dependence of cos θ. Figure 4.3 shows the results for Babayaga@NLO in comparison to the calculated function according to equation 3.6. Babayaga@NLO 4 events/ cosθ Figure 4.3: Differential cross section of Babayaga@NLO in Born approximation The comparison between the distribution of simulated events with the analytically calculated distribution leads to the assumptions that the saved events are the precise unweighted events since the histogram created with Babayaga@NLO data is in perfect agreement with the function calculated in chapter

19 4.2. DIFFERENTIAL CROSS SECTION Excluding Vacuum Polarization In this section vacuum polarization of the generators is switched off in order to exactly investigate the differences between and BHWIDE. As mentioned before the weak corrections do not influence the resulting cross section in a significant way, so again it was possible to run BHWIDE without vacuum polarization and weak corrections and compare it to Babayaga@NLO with only switched off vacuum polarization. The fraction of events in a certain bin is proportional to the differential cross section dσ d cos θ. The results are shown in figure 4.4. BHWIDE Babayaga@NLO relative difference 1 fraction of events / fraction of events / relative difference in % / cosθ cosθ cosθ Figure 4.4: Angular distribution of outgoing positron, left: BHWIDE, center: Babayaga, right: relative difference with zoom Since only a small fraction of events is in the angular region cos θ < 0.75 a zoom is used in the right histogram of figure 4.4 to show the relative difference of the two generators in the most important region more precise. The relative difference is always smaller than one percent. However the two generators angular distributions do not coincide within the statistical errors. There is a small but noticeable difference between the two generators, which compensates in the total cross section. In figure 4.5 the probability distribution to receive a certain number of photons N γ in one e + e scattering process is shown. The distributions for BHWIDE and Babayaga@NLO coincide on a level of one percent. 19

20 4.2. DIFFERENTIAL CROSS SECTION percentage of events with Nγ BHWIDE Number of photons Nγ Figure 4.5: Fraction of events for a given number of photons N γ in the final state The θ distribution of the most energetic, the so called hardest photon, is pictured on figure 4.6. There is large relative difference from up to 14 percent in regions with few events, however a nice agreement in the small but strongly populated regions. BHWIDE Babayaga@NLO relative difference fraction of events / 3degrees -2 fraction of events / 3degrees -2 difference in % / 3degrees θ / degree θ / degree θ / degree Figure 4.6: Angular distribution of hardest photon, left: BHWIDE, center: Babayaga, right: relative difference with zoom 20

21 4.2. DIFFERENTIAL CROSS SECTION Including All Corrections The most important comparison of the differential cross section is the one including all corrections. The results for the percentage of events that have a certain scattering angle θ are displayed in figure 4.7. BHWIDE Babayaga@NLO relative difference 1.5 fraction of events / fraction of events / relative difference in % / cosθ cosθ cosθ Figure 4.7: Angular distribution of outgoing positron, left: BHWIDE, center: Babayaga, right: rel. difference with zoom The zoom used in the right histogram of figure 4.4 shows a similar result as the results without vacuum polarization. The relative difference of the two generators is again up to around one percent. In figure 4.8 the distribution of number of photons N γ is shown. As 35 BHWIDE in the production without vacuum polarization, Babayaga@NLO 30 the two generators coincide within a level of two percent. 15 The θ distribution for the hardest photon in a e + e scattering event is pictured in figure 4.9. There is large relative difference from up to 15 percent in regions with few events. It is the same effect as seen in the γ percentage of events with N Number of photons N γ Figure 4.8: Probability of a certain Number of photons N γ in the final state 21

22 4.3. TOTAL CROSS SECTION IN BABAR PRODUCTION FRAMEWORK production without vacuum polarization 4.6. There seems to be a systematic effect, in which the most energetic photon of BHWIDE has a distribution tending to a larger polar angle θ than the Babayaga@NLO photon. This cannot be clearly seen on figure 4.6, because of the superposition of the distribution of events where the hardest photon is being emitted from the forward-going electron and the backward-going positron. BHWIDE Babayaga@NLO relative difference fraction of events / 3degrees -2 fraction of events / 3degrees -2 difference in % / 3degrees θ / degree θ / degree θ / degree Figure 4.9: Angular distribution of hardest photon, left: BHWIDE, center: Babayaga, right: rel. difference 4.3 Total Cross Section In BABAR Production Framework Up to now the values for the absolute cross section of the BHWIDE generator are compared in the stand-alone-version of the generator. The next task was to work through the BABAR workbook (ref. [7]) and understand correctly how to work with the BABAR environment. When BHWIDE is run in the BABAR production framework, the reported cross section by the Monte Carlo jobs are lower than for the BHWIDE stand-alone version. This difference is already mentioned in ref. [6]. It is due to the effect of a trigger routine which applies cuts in the CM and LAB frames. The reported value in ref.[6] for the absolute cross section in the BABAR production framework is ± nb which agrees to the value of my production ± 5.56 nb. 22

23 Chapter 5 Outlook And Conclusion BHWIDE and Babayaga@NLO give very similar results for the total cross section. However there are also differences in order of one percent concerning the angular distributions of the differential cross sections. Since the Babayaga@NLO event generator has a theoretical accuracy of less then 0.1% and BHWIDE has an accuracy of around 0.5%, it is worthwhile to implement the Babayaga@NLO generator in the BABAR framework. The next step is to make this inclusion. However, more things have to be taken into account, for example special requirements for the random number generator. The given detector simulation has to be understood and it must be clear which parameters of the generated events are needed in order to achieve a correct event simulation. I will continue this work for my German diploma thesis. After having included Babayaga@NLO into the BABAR framework a better accuracy in the measurement of the luminosity of the PEP-II collider will be achieved, since the error associated to the theoretical accuracy will drop from 0.5% to 0.1%. I will continue with a BABAR analysis as soon as the precise luminosity determination is achieved. A large flux of photons with the energy of the electron mass is observed coming from the center of our galaxy. The large number of these photons is not yet understood. One possible explanation is that dark matter particles annihilate to e + e pairs that later annihilate to photons. If this is true, it could be possible to measure this cross-section with the BABAR detector. It is, however, not the energy region PEP-II is running on. Looking for events with ISR allows us to scan lower energy regions and to perform the search for these Dark Matter particles (ref.[]). 23

24 BIBLIOGRAPHY Bibliography [1] The BABAR collaboration, PRL 94, , (2005). [2] Matching perturbative and Parton Shower corrections to Bhabha process at flavour factories, FNT/T-2006/05 (2006). [3] Jadach, S.,Placzek, W. Ward, B.F.L., Bhwide: YFS exponentiated Monte Carlo for Bhabha scattering at wide angles [4] Matrix elements and Parton Shower in the event generator BABAYAGA, (2006). [5] Jegerlehner, F., Hadronic vacuum polarization effects in α em, (2003). [6] BaBar Collaboration, Touramis, C. and Want, P., BaBar Analysis Document 229, Version 1, (2001). [7] The BABAR Collaboration, workbook/workbook.html, (2006). [8] Halzen, F., Martin, A.D., Quarks & Leptons, Wiley, (1984). [9] The BABAR Collaboration, The BABAR Detector, hep-ex/05044, (2001). [] Borodatchenkova, N., Debajyoti, C., Drees,M., Probing MeV Dark Matter at Low-Energy e + e -Colliders, (2006). 24

25 Chapter 6 Acknowledgement Finally, I would like to take this opportunity to thank my supervisors Dr. Achim Denig and Dr. Grégory Schott for always taking the time to help me out and answering my questions and Prof. Thomas Müller for the wonderful time I spent and will spend in his institute. 25