Analysis of Prompt Diphoton Production at the Large Hadron Collider.

Transcription

1 Analysis of Prompt Diphoton Production at the Large Hadron Collider. Andy Yen Mentor: Harvey Newman Co-Mentors: Marat Gataullin, Vladimir Litvin California Institute of Technology, Pasadena, CA, Abstract One of the primary objectives of the Large Hadron Collider is the discovery of the elusive Higgs boson thought to be responsible for mass in the Universe. For the most probable Higgs masses, the leading discovery mode is production through gluon-gluon fusion followed by decay into two photons (H γγ). In this paper, I present a strategy for analyzing diphotons produced through quarkantiquark collisions ( qq γγ ) and gluon-gluon collisions (gg γγ) as these are the most important backgrounds for this process. An optimized event selection is used to isolate the prompt diphoton events. The obtained sample is then analyzed with statistical techniques that utilize the characteristics of the electromagnetic shower profile. The results from the analysis show that it is possible to perform a precise measurement of the prompt diphoton production rates and invariant mass distribution using the CMS detector at the LHC. This information will allow us to increase the sensitivity of Higgs searches (and therefore reduce the integrated luminosity needed before discovery) while simultaneously testing whether the LHC diphoton data is consistent with perturbative QCD predictions.

2 1 Introduction One of the primary motivations for the construction of the LHC and a main goal of the CMS experiment is the discovery for the Higgs boson. It is expected that when running at its maximum 14 TeV center of mass energy, the LHC will produce the elusive Higgs boson at a high enough rate to be detected in the relatively early phases of LHC operation. The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. One of the crowning achievements of high energy particle physics in the second half of the twentieth century, the Standard Model (SM) is one of the most accurate physical models ever developed and has successfully predicted a host of elementary particles and their interactions with extraordinary precision. It predicted the existence of the W and Z bosons, the gluon, the top quark, and the charm quark. All of these particles have been successfully observed in collider experiments. The Higgs boson is the last Standard Model particle still not yet observed. Its discovery would be a resounding verification of the SM, while failure to discover the Higgs would indicate that the best current theory is incorrect 1. Recent precision measurements of electroweak observables at the CDF experiment at the Tevatron collider in Fermilab have established a new upper limit for the mass of the Higgs boson at 144 GeV with 95 percent probability [1]. Thus, if it exists, it is highly likely that the Higgs boson will be discovered at the LHC. The Higgs boson plays a key role in the mechanism by which elementary particles are expected to acquire mass in the Standard Model. The Higgs boson is the particle associated with the hypothetical Higgs field which permeates all of space at all times. The Higgs field has a non-zero vacuum expectation value which allows for the spontaneous breaking of electroweak gauge symmetry, a phenomenon known as the Higgs mechanism. In the Standard Model, the masses for the W and Z bosons, quarks, charged leptons, and the Higgs boson itself, are all generated by the Higgs mechanism. The Higgs, if it exists, can also offer an explanation for the huge differences between the electroweak force carriers - the massless photon and the relatively massive W and Z bosons. The Higgs boson is also often predicted by extensions of the Standard Model. For instance, in the Minimal Supersymmetric Standard Model, the lightest Higgs boson is predicted to have a mass of around 135 GeV [2]. Thus, discovery of the Higgs and characterization of its properties can have profound impacts on physics and our understanding of the world around us. 1 An initial failure to find the SM Higgs would intensify the search for alternative theories, such as supersymmetry (SUSY). SUSY still explains the existence of spontaneous symmetry breaking but depending on the parameters of the theory, the Higgs couplings and branching ratios could be very different from those predicted by the SM. 2

3 The Higgs is expected to be produced at the LHC through two main processes, gluongluon fusion and vector boson fusion (Figure 1). The Higgs can then be detected from its decay through a variety of different possible channels. For Higgs mass less than 140 GeV, the most promising discovery mode is production through gluon-gluon fusion followed by decay into two photons (H γγ). As we can see in Table 1, the H γγ decay is quite rare as it has a very low branching ratio [3]. Figure 1: Gluon-Gluon Fusion (Left) and Vector Boson Fusion (Right) Higgs production. Table 1: Cross sections for various Higgs production processes and H γγ branching ratios 2. Despite this, the excellent mass resolution of the CMS detector should allow the narrow Higgs resonance signal to be detected. However, the Higgs resonance signal can only be seen and experimentally verified if enough data is taken so that the Higgs can be measured as a statistically significant resonance signal above the non-resonant SM backgrounds. This poses a significant problem because the gg H γγ resonant cross section is small compared to the much larger continuum diphoton (γγ) background from the SM processes gg γγ and qq γγ. This problem will also be relevant for many other searches involving a γγ final state. For instance, an excess of γγ production at high invariant mass could be a signature for large extra spatial dimensions or heavy graviton decays [4]. Thus, in order to perform an effective Higgs search in the H γγ channel and numerous other channels, it is necessary to have a good understanding of the diphoton background. 2 The LHC and CMS Detector 2 In the region of interest, the theoretical uncertainty for the H γγ branching ratio is at the 5% level (dominated by the uncertainty on the H bb width; see Djouadi, Abdelhak. The Anatomy of Electroweak Symmetry Breaking. 2005). 3

4 The LHC, which began operation in September 2008, is the most powerful particle accelerator ever built. Measuring twenty-seven kilometers in circumference and situated 100 meters underground, the LHC with its 14 TeV center of mass energy proton-proton collisions will considerably extend the range of Higgs masses that can be probed, reaching well beyond the exclusion limits set by the earlier colliders such as Tevatron. One of the two general purpose detectors at the LHC which is collecting and analyzing data from the produced collisions is the Compact Muon Solenoid (CMS). The CMS consists of an all-silicon tracker, a high precision electromagnetic calorimeter (ECAL) composed of lead tungstate crystals, a hadron calorimeter (HCAL), a four Tesla superconducting solenoid, and arrays of muon chambers (Figure 2). Figure 2: Cutaway view of the CMS detector showing its main components. The most important detector components needed for this study are the tracker, the ECAL, and the HCAL. A brief overview of these subdetectors is given below. 2.1 Tracker The CMS tracker is 5.5 meters in length and 1.1 meters in radius. Its innermost layer consists of silicon pixel detectors capable of precise three dimensional measurements while its outer layers consist of silicon strip detectors capable of two dimensional measurements. In terms of pseudorapidity 3, the CMS tracker extends in the region η < 3 In particle physics, pseudorapidity (η) is used instead of the polar angle θ because a Lorentz boosts leads to the addition to η of a constant that is angle-independent. As a result, the difference in η between two particles is independent of the Lorentz boosts along the beam axis. η = corresponds to the beamline while η = 0 corresponds to θ = 90. 4

5 2.5 where η = θ ln tan and θ is the polar angle relative to the beam axis. Only 2 charged particles leave tracks in the tracker. These tracks are reconstructed using the method described in detail in [5]. Here, a brief overview of the reconstruction method is given. The first step in track reconstruction is seed generation using the cluster-driven pixel-seed finding strategy. Seed generation starts with a supercluster in the ECAL (covered in Section 2.2) which is then propagated backwards through the magnetic field to the innermost layers of the tracker. There, within a loose ΔR window, the pixel detectors are scanned for a hit. If a hit is found, it is then propagated outwards to the next pixel layer where another hit is searched for. A seed is created when two compatible hits are found within the pixel detectors. From that point onwards, subsequent hits are looked for in the next innermost layers of the tracker and so on until the last layer of the tracker is reached. The number of hits required to constitute a track can be varied but in general, a larger number of hits will lead to better track reconstruction. The final step in track reconstruction is performing a fit of the track to estimate the key parameters of the particle such as the location of its interaction vertex and its momentum. Normally, this fit is performed using the Kalman Filter 4, but for electrons, due to the non-gaussian fluctuations induced by bremsstrahlung emission (See Section 2.2), a Gaussian Sum Filter (GSF) is used [6]. 2.2 ECAL The CMS ECAL is composed of 75,848 lead tungstate crystals completely surrounding the tracker. The ECAL is divided up into two sections, the barrel region ( η < 1.5) and the endcap region (1.5 < η < 3). Due to initial miscalibration, the ECAL is expected to have a precision of around 1.5% at LHC startup; however within a month of data taking, the ECAL is expected to be calibrated to its design energy resolution of approximately 0.5% for electrons and photons with transverse momentum (P t ) > 100 GeV [7]. Here and in the following, the transverse direction is defined with respect to the collision axis. At energies above 100 MeV, electrons and positrons traveling through dense material lose energy through the bremsstrahlung process, radiating photons as a result of the Coulomb interaction with the electric fields of the atomic nuclei [8]. Similarly, photons interact with matter by converting through the process of electron-positron pair production. Both pair production and bremsstrahlung processes produce secondary photons and electrons which can also interact with matter leading to a chain reaction called an electromagnetic shower. The electromagnetic showers are reconstructed using superclustering algorithms. The superclustering algorithms start by identifying a seed which is a crystal that has an energy above a certain threshold. Starting from the seed crystal, the algorithm moves in all directions and collects all crystal energies until it sees a rise in crystal energies or until crystal energies drop below a certain threshold. This collected energy is combined together to form a supercluster. Through use of the superclustering algorithms, almost all the energy from photons and electrons can be collected in ECAL superclusters, with the relative energy resolution increasing at higher energies. This is true even for photons which convert early or electrons which shower extensively in the material in the 4 The Kalman and Gaussian Sum Filters are recursive filters that are used to estimate the state of a dynamic system from a series of incomplete or noisy measurements. More details can be found in [5] and [6]. 5

6 tracker. The only exceptions are very low energy electrons (or converted photons) which become caught in the magnetic field and thus never fully reach the ECAL. 2.3 HCAL The CMS HCAL consists of four sections. The barrel HCAL (HB) surrounds the barrel region of the ECAL and the endcap HCAL (HE) surrounds the endcap region of the ECAL, providing combined coverage over the region η < 3. In addition, there are two forward calorimeters (HF) extending out to η = 5, and an outer hadron calorimeter (HO) located outside the solenoid which provides extra containment to keep very high energy jets from reaching the muon chambers. Electrons and photons deposit almost all of their energy in the ECAL while hadrons deposit most of their energy in the HCAL. Thus, the hadronic jets are measured using both the HCAL and ECAL subdetectors. 3 Diphoton Production at the LHC The two main sources of diphoton production come from the prompt processes qq γγ (quark annihilation) and gg γγ (gluon annihilation). The qq γγ process, 2 also known as the born process, is a leading order process on the order of α em (see Figure 3a). In the gg γγ process, also known as the box process, the gluon-gluon initial state is coupled to the γγ final state via a quark loop (see Figure 3b). This process is actually beyond next-to-leading-order (NLO) as it is suppressed by α ; however, its rate is very large in the lower M γγ kinematic region where the gluon density is high. Thus, these two QCD processes contribute a large irreducible background for Higgs searches because the final state consists of two real photons, just like the H γγ signal. 2 s (a) qq γγ (b) gg γγ Figure 3: Born and Box prompt diphoton production. While there are existing Standard Model predictions for these prompt diphoton cross sections, they must be experimentally verified at LHC energies, especially since it is difficult to calculate and account for all NLO processes. Measuring these cross sections 6

7 is important because without precise knowledge of the prompt diphoton cross section, it becomes difficult to formulate an accurate prediction of the level of prompt diphoton background to expect and the amount of luminosity need to extract an unambiguous, statistically significant signal at a particular Higgs mass point. The measurement of the prompt diphoton cross section is also complicated by the presence of a very large background from photons which are faked by individual hadrons. For instance, a sufficiently high energy π, η or other neutral meson could be misidentified in the CMS ECAL as a photon because the Lorentz boost causes the two photons from their decay to be nearly collinear and their energies collected in a single fairly isolated supercluster. Thus, it is possible for one or both photons to be produced via this fragmentation. This background is large because nearly every jet will contain at least one or more neutral meson. Events where one of the two photons in the final state are produced at fragmentation are referred to as Brem events while events where both final state photons are produced at fragmentation are called QCD events. In Brem events, a photon is typically balanced against a jet containing an isolated π carrying most of the jet energy (Figure 4) while QCD events contain two such jets with isolated π s which resemble real photons. The Feynman diagrams for some of these processes are shown in Figure 5. Figure 4: Brem event where one photon comes from fragmentation and is embedded in a jet. 7

8 (a) Brem (b) QCD Figure 5: Diagrams for Brem and QCD photon pair production 4 Simulated Data Samples As the actual experimental data will not be available until Spring 2009, simulated data produced with various Monte Carlo (MC) tools was used to develop the tools to select and reconstruct prompt diphoton events. Because the LHC will initially start up at the 10 TeV center of mass energy, the data samples for this study were generated with 10 TeV collision energies. PYTHIA version [9] was used to simulate the Born and Box events. A generator level cut of M γγ >60 GeV was used to restrict our sample to the area of interest for Higgs searches. PYTHIA was also used to generate the Brem and QCD background samples. For these events, a generator level cut of M γγ >60 GeV was used along with a filter designed to only keep events with clean jet fakes. This filter requires that the Pt of the photon candidates be at least 10 GeV and that each photon candidate has 2 2 at most one charged particle within a 0.2 ΔR cone (ΔR is defined as Δ η +Δ φ ). Events not passing this filter would almost certainly be rejected by the photon track isolation cuts utilized in the selection (see Section 6). Table 2 summarizes the MC simulated data used in this analysis. Sample σ (fb) Filter Efficiency σ (after filter) # Gen Events Born 9.33x10 4 NA NA 100k Box 5.24x10 4 NA NA 100k Brem 1.47x % 1.68x k QCD 1.88x % 3.38x k Table 2: Summary of data samples used in this analysis. The generated signal and background events were fully simulated using CMSSW (version 2.1.0) [10], an analysis and simulation software framework used by the CMS 8

9 Collaboration to fully simulate the propagation of produced particles through the CMS detector. 5 High Level Trigger Studies The LHC will deliver proton-proton collisions at a rate of 40 MHz, far exceeding the computational resources available to process and analyze all the data. The triggering system is implemented to reduce the accepted event rate to approximately 100 Hz [11]. The high level triggers are used to preselect with high efficiency, events which may be of interest for physics studies. For an event to be recorded, it must pass both the low level and the High Level Triggers (HLT). In the prompt diphoton channel studies, the photon object HLTs are the most important because they have very specific constraints designed to only pick up events with photons. Table 3 shows the efficiencies of the available photon HLT subtriggers. Trigger Born Box Brem QCD IsoPhoton30_L1I IsoPhoton10_L1R IsoPhoton15_L1R IsoPhoton20_L1R IsoPhoton25_L1R IsoPhoton40_L1R Photon15_L1R Photon25_L1R DoubleIsoPhoton20_L1I DoubleIsoPhoton20_L1R DoublePhoton10_Exclusive Overall Table 3: Efficiencies for different photon high level trigger paths (algorithms). 6 Photon Candidate Identification and Event Selection For my analysis, a cut based selection is used to isolate the signal (Born/Box) events from the background (Brem/QCD). The photon candidates are first identified as energetic showers in the ECAL (superclusters). As the background contains many jet fakes, the first goal of the selection is to separate the superclusters associated with real photons from the superclusters associated with jet fakes. To do this, a series of supercluster isolation cuts are utilized. The supercluster (SC) cuts utilized and their descriptions are given below: Minimum SC Pt In my selection, superclusters are required to have a transverse momentum (Pt) of at least 10 GeV in both the barrel and endcap regions of the detector. This cut is important for rejecting soft EM objects from pileup events or initial/final state radiation. 9

10 Minimum track Pt Tracks are required to have a Pt of at least 1 GeV or they are not used in the selection. This removes a large number of tracks from soft charged particles unrelated to the signal and background being analyzed. Number of tracks per SC Since photons do not leave tracks unless they convert early in the tracker, most photon superclusters should have zero associated tracks. On the other hand, jets often contain charged particles which can leave tracks in the vicinity of the π or η faking a photon. H/E H/E is calculated by summing up the energies deposited in the HB and HE regions of the HCAL within a ΔR < 0.25 cone around the reconstructed position of an ECAL supercluster, and then dividing by the total energy of the supercluster. The HCAL isolation is implemented to reject showers with leakage into the HCAL and prevent jets from being misidentified as photons because jets deposit most of their energy in the HCAL rather than the ECAL. R9 - The R9 showershape variable is defined as the sum of the energies collected in a central 3x3 ECAL crystal matrix around the center of a SC divided by the total energy of the supercluster. For a supercluster created by a single photon, almost all of the photon energy will be collected in the 3x3 matrix. On the other hand, superclusters produced by π jet fakes will typically have a lower percentage of their total energy collected within the central 3x3 crystal matrix as other components of the jet may leave energy outside of the central 3x3 but still within the supercluster. ECAL isolation The ECAL isolation variable is calculated by summing up the energies deposited in individual crystals within a dr<0.4 cone around the center of a supercluster and then subtracting out the raw energy of the supercluster. Photons produced from the born and box processes should be well isolated while jets fakes will have other associated particles which will lead to more energy deposited that is not picked up by the supercluster (leading to a higher value of the ECAL isolation variable). In an event, any superclusters which pass the above series of cuts are selected as photon candidates. After the photon candidates are selected from an event, a second series of cuts are utilized to determine whether a particular event contains the signature from prompt diphoton production. First, at least two photon candidates are required. If there are more than two photon candidates, the two most energetic photon candidates are used. The two photon candidate requirement almost completely suppresses the QCD background. Next, a cut is applied on the vector sum Pt of the two photon candidates. The motivation for this cut is two-fold. First, as quark annihilation and gluon annihilation typically occur through a head-on interaction between the particles; conservation of momentum dictates that the majority of photon pairs should be produced back to back leading to a small vector sum Pt. Secondly, as seen in Figure 4, the second photon in Brem events is usually embedded in a jet. As other parts of the jet carry away some of the transverse momentum, the faked photon within the jet has a smaller Pt. Thus, the vector sum Pt for the Brem photon and jet fake photon will be significantly greater than for the two real photons from Born and Box events. 10

11 7 Selection Optimization and Results Because many of the cut variables used do not have a clear differentiation between signal and background, both the signal and background acceptances are sensitive to small fluctuations in the cut value used. Thus, a cut optimization routine can significantly improve the selection. The two primary goals of the selection algorithm are to give the best signal over background ratio while simultaneously minimizing systematic uncertainty in the cross section calculations. As can be shown relatively easily, maximizing the quantity ερ minimizes error in cross section calculation while maximizing signal over background. Here, ε is defined as the signal selection efficiency while ρ is defined as the number of signal events over the total number of events (signal + background). The cut values are optimized separately for barrel and endcap regions of the detector. This is a necessary step because factors such as multiplicity, material budget, transverse momentum, etc can vary significantly as a function of η. Due to limitations in time and processing power, the cut optimization is currently carried out one cut at a time. Ideally, the optimization should be done over an n-dimensional parameter space where n gives the total number of cuts (barrel and endcaps regions counted separately); however, this simplified optimization routine is found to be already very effective. Table 4 summarizes the final cut values after optimization. Supercluster Cuts Barrel Endcap Supercluster Pt >10 GeV >10 GeV Track isolation dr <0.25 <0.2 Number of tracks per SC <1 <1 H/E <0.09 <0.07 R9 >0.6 >0.84 ECAL Isolation <5 GeV <10 GeV Event Topology Cut Cut value Number of photon candidates per event >=2 Vector sum Pt of photon candidates <24 GeV Table 4: Optimized selection cut values. The track isolation ΔR refers to the size of the cone used to match superclusters to tracks. The value for this cut is closely correlated with the cut on the number of tracks per supercluster. Appendix A contains n-1 plots for each cut utilized to demonstrate the effectiveness of each cut (keep in mind that the MC Brem and QCD samples used are already filtered in the generator level). The efficiencies listed in Table 5 were obtained using the cut values specified above. For an event to be considered in the detector on the generator level, both photon candidates comprising the diphoton pair are required to have η < 2.5. An event is defined as reconstructed if there are superclusters matching both generator level photons within a ΔR <0.15 window. An event passes the SC cuts if at least two photon candidates survive the SC cuts. 11

12 Process In detector (based on MC) Pass Pt cuts (based on MC) Reconstructed Pass SC cuts 5 Pass topology cuts Born Box Brem NA NA NA QCD NA NA NA ~0.0 Table 5: Selection efficiencies. These efficiencies are not cumulative; to obtain cumulative efficiencies, one would have to multiply the efficiencies together as the table gives relative efficiencies. Figure 6 shows the resulting M γγ distribution for background and signal+background and Table 6 lists the number of events expected after 1fb -1 of integrated luminosity. As we can see, significant activity in the diphoton channel is expected within the first year of LHC running (which should total at least 100 pb -1 of data). Figure 6: Invariant mass distributions for signal and signal+background. Born Box Brem QCD 2700 ± ± ± 0.13 <3.0 (at 95% CL) Table 6: Number of accepted events expected for 1fb -1 of integrated luminosity. The statistical errors are due to the limited MC statistics. 8 Monte Carlo Studies of Brem Background The selection algorithm succeeds in nearly completely supressing the QCD background but the contribution from the Brem background is still significant. Monte Carlo generator level information was used to analyze the Brem events passing the selection cuts. This is done by matching the two photon candidates from passing Brem events with MC 5 For Brem and QCD events, this percentage is calculated out of the number of events passing the photon Pt cuts on the reconstruction level. 12

13 particles. The MC particles are required to be within a ΔR<0.15 cone of the photon candidates and further required to have energies within 60% of the photon candidates. Then, the most energetic matching MC particle is selected. For a reconstructed real photon, this procedure allows us to pick out the corresponding MC photon. For jet fakes, this procedure allows us to select on the generator level, the neutral meson whose decay gives rise to the second reconstructed photon candidate in the event. When this MC matching procedure is applied to the passing Brem events, it is found that 73% of the events have one photon candidate matched to a MC photon and another photon candidate matched to a MC particle which is not a photon. Figure 7 shows the distributions of the particle ID s of the MC particles which are not photons. Figure 7: Around 60% of the jet fakes are π s (pid = 111) and 25% are η s (pid = 221) As we can see, almost all of these particles are neutral mesons as we would expect for jet fakes. A more surprising result is that ~27% of the accepted Brem events have both photon candidates matched to real MC photons. This indicates that a quarter of the passing Brem events are actually composed of two real photons where the second real photon is likely radiated from a quark. These two real photon Brem events are experimentally indistinguishable from the Born and Box events. The implications of this are further explained in Section Method of templates As prompt diphoton production through the Born and Box processes does not result in resonance in the invariant mass distribution, a bump hunting approach cannot be used to estimate cross sections. Instead, the template method is utilized. The templates consist of the distributions of a variable plotted for the signal and the background. A linear combination of the signal and background templates is fitted to the distribution of the same variable plotted for the obtained data sample. The coefficients from this fit will determine the signal to background ratio in the data. For this method to be effective, the signal and background templates need to be substantially different. The variable σ ηη (covetaeta) is found to be the best discriminator between photons and jet fakes (primarily π s) in the barrel [13]. Covetaeta is defined as 13

14 25 2 c= 1 σ ηη = 2 ( η < η > ) w wcη c c= 1 where w M (0.,4.2 log( / and and the sum is over all c = AX + Ec S25)) < η > = 25 w c 25 c= 1 crystals in a 5x5 array centered at the supercluster seed. As covetaeta is only effective in the barrel region of the detector, the analysis will have to be limited to the barrel regions. Thus, the data distribution we are fitting will consist of the covetaeta of the two superclusters from accepted events where both superclusters lie within the barrel region of the detector. Two templates are needed for this analysis, a pure photon template and a pure jet fake template. The prompt diphoton signal covetaeta distribution should match the pure photon template while the Brem background should ideally closely match a 1:1 superposition of the photon and jet templates. The above statement must be justified by checking that the photon covetaeta distributions from prompt diphotons and the Brem photon are similar. The prompt diphoton covetaeta distribution is created by plotting the covetaeta of barrel superclusters from passing Born/Box signal events while the Brem photon covetaeta distribution is created by taking all Brem events which pass the selection and then applying MC level truth matching to select out the photon. The MC level truth matching works by requiring that the most energetic MC particle within a ΔR<0.15 cone of the supercluster is a photon. As we can see from Figure 8, the similarity of the distributions indicates that the photon template can be applied universally to Born/Box events as well as Brem events. w c c 25 c= 1 c Figure 8: A comparison between photon templates derived from prompt diphoton events and Brem events. Both samples were checked with MC information. A second issue that must be addressed is the generation of photon and jet templates from actual experimental data. For photon templates, possible methods involve utilizing Z μμγ or Z e + e - events. Using cuts on the reconstructed Z mass should allow for very pure photon or electron samples. As electrons and photons appear identical in the ECAL, 14

15 they should have nearly identical convetaeta distributions. Using Z e + e - events is the favored approach as the Z e + e - decay mode has a higher branching ratio. We require events where two superclusters pass all supercluster isolation cuts (with the exception of the track cut which is reversed) and have a reconstructed invariant mass near the Z mass (the 85 to 95 GeV window is used). This exercise was performed using simulated Z e + e - events and the resulting covetaeta distribution in the barrel was found to be very similar to covetaeta distributions from Born/Box and Brem events (Figure 9). Thus, we see that Z e + e - events can be used to create the photon template. Figure 9: Comparison between photon templates derived using photons from Born/Box events and electrons from Z e + e - decays. The jet templates can be constructed from experimental data using a jet triggered sample filtered to include at least one loose photon object. The supercluster isolation cuts will be applied with the exception that the cut on the number of tracks is reversed. For this study, we use the Brem sample to form the jet template as it contains a mix of photons and jets similar to what we expect from real data. As we can see from Figure 10, the photon and jet templates are indeed significantly different. Figure 10: Photon (blue) and Jet (Red) Templates derived from Brem events. 15

16 Using generator level information we find that the purity of the photon template is 97.32% and the purity of the jet template is 93.97%. This result demonstrates that reversing the track isolation cut to differentiate between jet and photon candidates is effective. 10 Statistical Analysis A linear combination of jet and photon templates is fitted to the data template through a likelihood fit using Poisson statistics. This method works by maximizing the log likelihood with respect to the jet and photon fractions we wish to determine subject to the constraint that the fractions sum to unity. This fitter is implemented in the ROOT class TFractionFitter [12] which treats the case where the probability density functions are not specified analytically, but sampled by a MC calculation. As no real data is available yet, the effectiveness of the template method was tested using MC. A data template was generated by running the selection over Born, Box, and Brem events, normalizing the remaining events to the known cross section values (calculated by PYTHIA), and then adding the resulting histograms. Then, the template method is applied using the photon and jet templates described in Section 9. The results are given below: Figure 11: Comparison between the data covetaeta distribution and the distribution obtained from the fitted linear superposition of the jet and photon templates. Template Fraction Error Photon Jet Table 7: Photon and Jet fractions derived from the fit. As discussed in Section 8, 27% of the Brem events are experimentally indistinguishable from the Born and Box signal. Hence, we can only calculate an inclusive diphoton cross section that consists of this two real photon Brem contribution in addition to the Born and Box contributions. We will define the remaining 73% of Brem events as a photon+jet background. Using this new characterization, our known data changes as shown in Table 16

17 8. The photon and jet fractions are obtained by assigning two photons for each Born/Box/Inclusive γγ event and one photon one jet for each Brem/γ+Jet event. # of events pass Photon Fraction Jet Fraction selection Born/Box 2962 ± ± ± Brem 3208 ± 57 Inclusive γγ 3825 ± ± ± γ+jet 2345 ± 42 Table 8: Number of events expected based on PYTHIA cross sections before and after compensating for the 27% of Brem events consisting of two real photons. The errors are calculated based on Poisson statistical uncertainties in the number of events which pass the selection. The number of events does not match Table 6 because for the covetaeta template analysis, we can only use the barrel region of the detector. Comparing Table 7 with Table 8, we see that the photon/jet fractions obtained from the fit are very close to what we expect after compensating for Brem events containing two real photons. Using this information, we can calculate the inclusive γγ cross section with the equation Nevt = σ ε L (10.1) where Nevt is the number of events, ε is the selection efficiency, σ is the cross section and L is the integrated luminosity. We wish to calculate the cross section within the acceptance region, passing the Pt cuts and with invariant mass greater than 80 GeV. The accepted region is limited to η <1.479 as we are using covetaeta as our template method discriminator. The value of efficiency must account for the selection efficiency of Brem events containing two real photons. The total number of Brem events which constitute part of the inclusive γγ signal is determined using generator level information by counting the number of events where there are two isolated (i.e. not matched to η, π ) MC photons in the barrel, passing the Pt cuts, and having invariant mass greater than 80 GeV. The number of passing and number of total γγ events for Born, Box and Brem are normalized for 1fb -1 of integrated luminosity and then used to calculate the overall inclusive γγ efficiency. This is done in Table 9. Born Box Brem Total # Passing Total Number Table 9: Born, Box and Brem γγ efficiencies in barrel with photon Pt>10 GeV and invariant mass >80 GeV. Thus, we see that the overall inclusive γγ efficiency is 50.33%. Our data template contains 6170 events total and a photon content of 84% yields an inclusive γγ content of 68%. Thus, based on the template analysis, we find 4195 inclusive γγ events. Using the calculated efficiency along with equation 10.1, we find that the inclusive γγ cross section in the barrel for invariant mass > 80 GeV and photon Pt>10 GeV is 8335 fb. 17

18 11 Conclusion In this paper, a method for calculating the inclusive diphoton cross section using the template method has been developed. These results represent the first diphoton cross section studies done at CMS. The selection algorithm presented above has been demonstrated to be effective at selecting out events containing two real photons and rejecting a vast majority of the jet fakes. The template method has been shown to be a viable procedure for determining the γγ and γ+jet content of a sample passing the selection. Furthermore, methods for generating photon and jet templates from first experimental data have been developed. While the current method works well in the barrel, more studies will need to be done before this template method analysis can be extended to the endcap regions of the detector. 12 Acknowledgements First of all, I would like to thank Professor Harvey B. Newman for providing me with the opportunity to do this study. Without your support and encouragement, this research would not have been possible. Secondly, I would like to thank Marat Gataullin for being there daily to answer questions and provide helpful suggestions; I could not have done this without all your help. I would also like to thank Vladimir Litvin for generating the Monte Carlo data samples used in this analysis and Alexey Atramentov and Abe DeBendetti for many useful discussions about the template method and making available their template fitting code which I was able to successfully adapt. Lastly, I would like to thank the Caltech Student-Faculty Programs Office for coordinating the SURF program and the Rose Hills Foundation for generously providing funding for this project. 18

19 Appendix A: Selection Cut Plots Figure A1: Number of tracks per supercluster. Figure A2: H/E distributions for Barrel (left) and Endcap (right). 19

20 Figure A3: ECAL isolation distributions for Barrel (left) and Endcap (right). Figure A4: R9 distributions for Barrel (left) and Endcap (right). Figure A5: Photon candidates vector sum Pt distributions. 20

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