Search for Randall-Sundrum Gravitons and Intermediate-Mass Diphoton Resonances

Search for Randall-Sundrum Gravitons and Intermediate-Mass Diphoton Resonances (CMS Draft Analysis Note) V. Litvin, H. Newman, T. Orimoto, E. Schneider California Institute of Technology, Pasadena, CA, 91125, USA Abstract We investigate the potential for the discovery of Randall-Sundrum gravitons through the diphoton decay channel using the Compact Muon Solenoid detector at the Large Hadron Collider. Simulated data for the G γγ process were generated and analyzed. Additional data were produced for the irreducible Standard Model backgrounds q q γγ and gg γγ, as well as for reducible processes leading to the production of one or two hadronic jets. At an integrated luminosity of 200 pb 1, 10 TeV center-of-mass energy scale, and luminosity 1 10 31 cm 2 s 1, we find the diphoton resonance events are visible at a 5σ significance level for graviton masses up to 1.4 TeV/c 2 in the case of strong coupling between graviton excitations and Standard Model particles (c = 0.1). In the case of weak coupling (c = 0.01), the same discovery level may be achieved up to 500 GeV/c 2. We also consider the discovery potential for an intermediate-mass diphoton resonance between the Higgs region and the unitary limit. Amidst the Standard Model backgrounds, we determine the minimal cross section necessary to claim a discovery at S = 5σ as a function of the width and position of the invariant mass window containing the resonance. By fitting this distribution, we offer a data driven approach to searching for an intermediate-mass diphoton resonance. 1 Introduction Several recent theories proposed to solve the hierarchy problem have claimed the existence of additional spatial dimensions beyond the known three [3, 4]. In particular, the Randall-Sundrum model consists of a 5-dimensional non-factorizable geometry based on a slice of AdS 5 space with length πr c, where r c is the compactification radius. Two 3-branes, with equal and opposite tensions, rigidly reside at S 1 /Z 2 orbifold fixed points at the boundaries of the AdS 5 slice. Einstein s equations in five dimensions permit a solution which preserves 4-dimensional Poincare invariance with the metric: ds 2 = e 2σ(φ) η µν dx µ dx ν r 2 cdφ 2 where the greek indices extend over ordinary 4-dimensional space, σ(φ) = kr c φ, and k is the AdS 5 curvature scale. The latter is of the order of the Planck scale, determined by the bulk cosmological constant Λ = 24M5 3 k 2, where M 5 is the 5-dimensional Planck scale. The 5-dimensional curvature scalar is given by R 5 = 20k 2. The reduced 4-dimensional Planck scale is given by M P 2 l = M 3 5 k (1 e 2krcπ ). The scale of physics phenomena as realized by the 4-dimensional flat metric transverse to the fifth dimension y = r c φ is specified by the exponential warp factor. TeV scales can naturally be obtained on the 3-brane at φ = π if gravity is localized on the Planck brane at φ = 0 and kr c 11-12. The scale of physical processes on this TeV-brane is then Λ π = M P l e krcπ. The observed hierarchy is thus generated by a geometric exponential factor. The Randall- Sundrum model requires that Λ π 10 TeV/c 2 as discussed in Ref. [5]. The theory suggests the existence of heavy graviton particles with masses between 1 and several TeV/c 2, detectable via the decay G γγ. No known Standard Model process would lead to such a massive diphoton resonance. Therefore, the observation of a diphoton resonance in the neighborhood of 1 TeV/c 2 at the LHC could offer significant evidence for the existence of the graviton particle, and consequently for the existence of an extra dimension. The present paper investigates the potential for observing such diphoton decays amidst the Standard Model backgrounds using the CMS detector. 1

We also consider the discovery potential for diphoton resonances in the intermediate mass range 250 GeV/c 2 to 1 TeV/c 2, to which little study has previously been devoted. The observation of any unanticipated resonance in this range could point to new physics be it an intermediate mass Randall-Sundrum graviton or any beyond the Standard Model process not yet hypothesized. The present search therefore intends to offer a model independent analysis of the diphoton final state in this region. 2 Event generation and kinematics pre-selection The proton-proton collisions under investigation were generated using CMSSW 3.1.0 and PYTHIA 6.416 [6] with L1 and HLT triggers corresponding to luminosity 1 10 31 cm 2 s 1. Signal data was produced for graviton masses 250, 500, 750, 1000, 1250, 1500, and 2000 GeV/c 2. The data sets include coupling constants c = 0.01, 0.025, 0.05, 0.075, and 0.1, all for center-of-mass energy 10 TeV/c 2. To simulate the effects of anticipated background events at the LHC, data representing Standard Model processes were also generated. There are four primary background processes interfering with the desired diphoton resonance signal: The prompt diphoton production from the quark annihilation ( born ) and gluon fusion ( box ) subprocesses, which provides an intrinsic or irreducible background (see Tables 2 and 2). The γ + jets production ( bremsstrahlung ) consisting of two parts: 1. One prompt photon produced by a hard interaction and a second photon produced by the outgoing quark due to final state radiation. 2. One prompt photon produced by a hard interaction and a jet produced by the decay of a neutral hadron (primarily an isolated π 0 ), which could fake a real high energy photon (see Table 2). The background from QCD hadronic jets, where electromagnetic energy deposits result from the decay of neutral hadrons (especially isolated π 0 s) in both jets (see Table 2). The Drell Yan process with e + e pairs in the final state could mimic photon production if the corresponding electron tracks were not assigned to the superclusters during the event reconstruction. This background was studied previously [2] and is negligible. Dataset CKIN(3)-CKIN(4) (GeV) σ PYTHIA (pb) Rejection Rate σ sel (pb) N events Born 80-120 0.71 1. 0.71 10500 Born 120-250 0.23 1. 0.23 1000 Born 250-500 0.015 1. 0.015 1000 Born 500-1000 8.33 10 4 1. 8.33 10 4 1000 Born 1000-1500 1.47 10 5 1. 1.47 10 5 1000 Born 1500-2000 5.5 10 7 1. 5.5 10 7 1000 Born 2000-inf 5.5 10 8 1. 5.5 10 8 1000 Table 1: Quark annihilation ( born ) background datasets for the RS graviton diphoton decay study. σ PYTHIA denotes the nominal PYTHIA subprocess cross section without preselection. The rejection rate r is the ratio of the numbers of generated and preselected PYTHIA events, σ sel = σ PYTHIA /r. N events denotes the number of preselected events produced. The electromagnetic component of a hadronic jet could be misinterpreted as a photon signal in the Electromagnetic Calorimeter (ECAL) if there are few additional particles surrounding the electromagnetic component in the ECAL, Hadronic Calorimeter (HCAL), and tracker. At this stage, we can usually identify these fake photons using our knowledge of the generated Monte Carlo particles. With real data from the LHC, however, it will not possible to distinguish the two. As such, one of the goals of our analysis is to make our selection sufficiently robust so as to suppress the fake photon signal, while preserving the true photon signal as much as possible. The QCD and bremsstrahlung processes are termed reducible as they do not contain two true high energy photons, but rather zero and one photons along with two and one hadronic jets, respectively. These two backgrounds will be 2

Dataset CKIN(3)-CKIN(4) (GeV) σ PYTHIA (pb) Rejection Rate σ sel (pb) N events Box 80-120 0.16 1. 0.16 1000 Box 120-250 0.03 1. 0.03 1000 Box 250-500 6.5 10 4 1. 6.5 10 4 1000 Box 500-1000 9.3 10 6 1. 9.3 10 6 1000 Box 1000-1500 5.0 10 8 1. 5.0 10 8 1000 Box 1500-2000 7.0 10 10 1. 7.0 10 10 1000 Box 2000-inf 1.6 10 11 1. 1.6 10 11 1000 Table 2: Gluon fusion ( box ) background datasets for the RS graviton diphoton decay study. σ PYTHIA denotes the nominal PYTHIA subprocess cross section without preselection. The rejection rate r is the ratio of the numbers of generated and preselected PYTHIA events, σ sel = σ PYTHIA /r. N events denotes the number of preselected events produced. Dataset CKIN(3)-CKIN(4) (GeV) σ PYTHIA (pb) Rejection Rate σ sel (pb) N events Brem 60-80 1900 370. 5.135 20k Brem 80-120 790 72. 11. 20k Brem 120-250 205. 14.5 14.1 20k Brem 250-500 9.4 8.1 1.16 20k Brem 500-1000 0.32 10.1 0.03 20k Brem 1000-1500 4.1 10 3 10.5 4.1 10 4 20k Brem 1500-2000 1.33 10 4 10.1 1.33 10 5 20k Brem 2000-inf 5.8 10 6 10.1 5.8 10 7 20k Table 3: γ + jets ( bremsstrahlung ) background datasets for the RS graviton diphoton decay study. σ PYTHIA denotes the nominal PYTHIA subprocess cross section without preselection. The rejection rate r is the ratio of the numbers of generated and preselected PYTHIA events, σ sel = σ PYTHIA /r. N events denotes the number of preselected events produced. Dataset CKIN(3)-CKIN(4) (GeV) σ PYTHIA (pb) Rejection Rate σ sel (pb) N events QCD 60-80 4.67 10 6 8400 556.0 200k QCD 80-120 1.61 10 6 1420 1133.8 1M QCD 120-250 3.05 10 5 340 897.0 500k QCD 250-500 9.1 10 3 301 30.23 20k QCD 500-1000 218 410 0.53 20k QCD 1000-1500 2.42 340 0.007 20k QCD 1500-2000 0.088 400 2.2 10 4 20k QCD 2000-inf 4.67 10 3 490 9.5 10 6 20k Table 4: QCD hadronic jets background datasets for the RS graviton diphoton decay study. σ PYTHIA denotes the nominal PYTHIA subprocess cross section without preselection. The rejection rate r is the ratio of the numbers of generated and preselected PYTHIA events, σ sel = σ PYTHIA /r. N events denotes the number of preselected events produced. 3

Mass (TeV/c 2 ) c σ tot (pb) N events 0.25 0.1 365.0 1000 0.5 0.1 17.1 1000 0.75 0.1 2.07 1000 1.0 0.1 0.389 1000 1.25 0.1 0.116 1000 1.5 0.1 0.04 1000 2.0 0.1 0.006 1000 0.25 0.075 207 1000 0.5 0.075 8.95 1000 0.75 0.075 1.21 1000 1.0 0.075 0.23 1000 1.25 0.075 0.068 1000 1.5 0.075 0.022 1000 2.0 0.075 3.25 10 3 1000 0.25 0.05 101 1000 0.5 0.05 3.81 1000 0.75 0.05 0.5 1000 1.0 0.05 0.1 1000 1.25 0.05 0.032 1000 1.5 0.05 0.01 1000 2.0 0.05 1.55 10 3 1000 Mass (TeV/c 2 ) c σ tot (pb) N events 0.25 0.025 23.5 1000 0.5 0.025 1.05 1000 0.75 0.025 0.125 1000 1.0 0.025 0.0265 1000 1.25 0.025 7.7 10 3 1000 1.5 0.025 2.55 10 3 1000 2.0 0.025 3.9 10 4 1000 0.25 0.01 3.8 1000 0.5 0.01 0.155 1000 0.75 0.01 0.02 1000 1.0 0.01 4.25 10 3 1000 1.25 0.01 1.18 10 3 1000 1.5 0.01 4.1 10 4 1000 2.0 0.01 6.5 10 5 1000 Table 5: Signal datasets for the RS graviton diphoton decay study. Mass and c are the model parameters described above. σ tot denotes the total RS graviton production cross section. N events denotes the total number of events produced. minimized using isolation cuts and additional selection tools. The born and box processes, however, constitute an irreducible background because they result in the production of genuine γγ final states where both photons are highly energetic. 3 QCD hadronic jets and γ+jet generator level pre-selection In order to limit the quantity of data to be processed, generator level pre-selection was first applied to eliminate events that were certain to be rejected by later selection criteria. The pre-selection is intended to identify events that may produce reasonably energetic and isolated showers in the ECAL. Only events with diphoton signals carrying invariant mass between 200 and 14000 GeV/c 2, and momenta p T > 40 and 30 GeV/c for the first and second leading photons, respectively, were accepted. Moreover, loose isolation was applied in the tracker, where we require that at most three tracks exist in a cone of R = ( η) 2 + ( φ) 2 = 0.2 surrounding the photon. For potentially isolated and energetic superclusters, transverse momentum p T cuts were then applied: p T > 100 GeV/c and p T > 80 GeV/c for the first and second most energetic superclusters. 4 Event selection The two superclusters with the highest E T were selected as photon candidates. The selection cuts, listed below, are based on the reconstruction of two very energetic and isolated photons in the final state. Only superclusters passing at least one of the HLT electromagnetic trigger bits are selected. In order to reduce the background produced by jets, the two superclusters must be isolated in the ECAL. The isolation criterion is based on the sum of the transverse energies deposited in clusters within a cone of opening radius R centered around and excluding the photon candidate. The photon candidate is isolated if, in a cone of R < 0.5, the energy sum is less than 2% of the transverse energy of the supercluster (see Figure 1a). 4

In addition to the above, the so-called Jurassic isolation has been studied in the ECAL. This algorithm constructs an annulus of inner-radius 0.06 and outer-radius 0.3 centered on the supercluster in η-φ space. Moreover, a band of width 0.04 is set along the diameter of the annulus in the η direction. Only additional superclusters outside the η-band but within the boundaries of the annulus are then considered in computing the isolation (see Figure 1b). The background from hadrons is eliminated with a cut on the hadronic energy fraction H/E, the ratio of energy deposited in the HCAL to that deposited in the ECAL (see Figure 1c). For each signal, only supercluster pairs with invariant mass in a set range around the graviton mass are admitted. In the tracker, only superclusters surrounded by a fixed number of tracks are selected (see Figure 1d). To further reduce the backgrounds, tracker isolation may be required: the sum of the transverse energies of the charged particle tracks deposited in a cone R = 0.5 around the supercluster should be less than 1% of the transverse energy of the supercluster (see Figure 1e). This cut is optional, and has not been applied in the below analysis. Table 6 lists the cut-values on the above parameters employed to produce the results given below. Figure 1: Isolation variables for the leading supercluster photon candidate from a 1 TeV/c 2 graviton decay signal (c = 0.1) and all backgrounds (normalized to 200 pb 1 ). Plot (a) shows the standard ECAL isolation followed by the Jurassic modification of the ECAL isolation in (b). Plot (c) shows the H/E ratio, the ratio of energy deposited in the HCAL to that deposited in the ECAL, (d) shows the number of tracks, and (e) shows the track transverse momentum p T. 5

Cut Value γ p T 100 GeV/c ECAL iso 0.02 H/E 0.05 N tracks 3 Track p T 0.01 Table 6: Cut-values on the isolation variables. These cuts have been applied to the data samples in the analysis below, with the exception of track p T. Bit Name 250 GeV 500 GeV 750 GeV 1000 GeV 1250 GeV 1500 GeV 2000 GeV 40 L1 SingleIsoEG5 98.2 ± 1.0 97.2 ± 1.0 95.9 ± 1.0 93.3 ± 1.0 91.3 ± 1.0 87.8 ± 0.9 82.5 ± 0.9 41 L1 SingleIsoEG8 97.4 ± 1.0 96.5 ± 1.0 94.5 ± 1.0 90.9 ± 1.0 87.9 ± 0.9 83.4 ± 0.9 76.3 ± 0.9 42 L1 SingleIsoEG10 97.1 ± 1.0 96.2 ± 1.0 94.1 ± 1.0 90.2 ± 1.0 86.9 ± 0.9 82.0 ± 0.9 74.5 ± 0.9 43 L1 SingleIsoEG12 96.9 ± 1.0 96.1 ± 1.0 93.9 ± 1.0 89.8 ± 1.0 86.3 ± 0.9 81.2 ± 0.9 73.2 ± 0.9 44 L1 SingleIsoEG15 96.5 ± 1.0 95.9 ± 1.0 93.6 ± 1.0 89.4 ± 1.0 85.6 ± 0.9 80.4 ± 0.9 72.3 ± 0.9 45 L1 SingleEG1 100.0 ± 1.0 100.0 ± 1.0 100.0 ± 1.0 100.0 ± 1.0 100.0 ± 1.0 100.0 ± 1.0 100.0 ± 1.0 46 L1 SingleEG2 99.9 ± 1.0 99.9 ± 1.0 100.0 ± 1.0 99.9 ± 1.0 100.0 ± 1.0 99.9 ± 1.0 100.0 ± 1.0 47 L1 SingleEG5 99.6 ± 1.0 99.7 ± 1.0 99.8 ± 1.0 99.8 ± 1.0 99.8 ± 1.0 99.8 ± 1.0 99.8 ± 1.0 48 L1 SingleEG8 99.3 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.8 ± 1.0 99.8 ± 1.0 99.7 ± 1.0 49 L1 SingleEG10 99.1 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 50 L1 SingleEG12 98.9 ± 1.0 99.6 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.6 ± 1.0 51 L1 SingleEG15 98.6 ± 1.0 99.6 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.6 ± 1.0 52 L1 SingleEG20 97.9 ± 1.0 99.5 ± 1.0 99.6 ± 1.0 99.6 ± 1.0 99.7 ± 1.0 99.7 ± 1.0 99.6 ± 1.0 103 L1 DoubleEG1 99.4 ± 1.0 99.7 ± 1.0 99.8 ± 1.0 99.9 ± 1.0 99.9 ± 1.0 99.9 ± 1.0 99.9 ± 1.0 104 L1 DoubleEG5 89.6 ± 1.0 93.7 ± 1.0 95.8 ± 1.0 96.5 ± 1.0 96.8 ± 1.0 97.1 ± 1.0 96.5 ± 1.0 Bit Name 250 GeV 500 GeV 750 GeV 1000 GeV 1250 GeV 1500 GeV 2000 GeV 56 HLT Photon10 L1R 99.0 ± 1.0 99.5 ± 1.0 99.5 ± 1.0 99.6 ± 1.0 99.6 ± 1.0 99.6 ± 1.0 99.6 ± 1.0 57 HLT Photon10 LooseEcalIso TrackIso L1R 98.5 ± 1.0 99.3 ± 1.0 99.2 ± 1.0 99.3 ± 1.0 99.5 ± 1.0 99.4 ± 1.0 99.4 ± 1.0 58 HLT Photon15 L1R 98.5 ± 1.0 99.4 ± 1.0 99.3 ± 1.0 99.4 ± 1.0 99.5 ± 1.0 99.4 ± 1.0 99.3 ± 1.0 59 HLT Photon20 LooseEcalIso TrackIso L1R 97.3 ± 1.0 99.2 ± 1.0 99.1 ± 1.0 99.3 ± 1.0 99.3 ± 1.0 99.2 ± 1.0 99.2 ± 1.0 60 HLT Photon25 L1R 96.9 ± 1.0 99.2 ± 1.0 99.2 ± 1.0 99.4 ± 1.0 99.4 ± 1.0 99.3 ± 1.0 99.3 ± 1.0 61 HLT Photon25 LooseEcalIso TrackIso L1R 96.5 ± 1.0 99.1 ± 1.0 99.1 ± 1.0 99.3 ± 1.0 99.3 ± 1.0 99.2 ± 1.0 99.2 ± 1.0 62 HLT Photon30 L1R 1E31 95.8 ± 1.0 99.0 ± 1.0 99.1 ± 1.0 99.4 ± 1.0 99.4 ± 1.0 99.3 ± 1.0 99.3 ± 1.0 63 HLT Photon70 L1R 78.5 ± 0.9 94.8 ± 1.0 97.6 ± 1.0 98.5 ± 1.0 99.1 ± 1.0 99.2 ± 1.0 99.2 ± 1.0 64 HLT DoublePhoton10 L1R 80.2 ± 0.9 87.5 ± 0.9 90.9 ± 1.0 92.5 ± 1.0 93.4 ± 1.0 94.3 ± 1.0 93.7 ± 1.0 65 HLT DoublePhoton15 L1R 78.8 ± 0.9 86.4 ± 0.9 89.7 ± 1.0 91.6 ± 1.0 92.6 ± 1.0 93.6 ± 1.0 93.1 ± 1.0 66 HLT DoublePhoton15 VeryLooseEcalIso L1R 77.3 ± 0.9 84.5 ± 0.9 87.9 ± 0.9 90.1 ± 1.0 91.2 ± 1.0 92.2 ± 1.0 91.4 ± 1.0 Table 7: L1 and HLT electromagnetic bit efficiency tables for c = 0.1 (in percent). 5 Randall-Sundrum Gravitons Efficiency tables for the L1 and HLT triggers have been produced for all signals and backgrounds (see Table 7). Further, for all coupling constants listed above, the significance S = 2( N s + N b N b ) was calculated as a function of the graviton mass (see Figure 2). For c = 0.1, Table 8 shows the number of signal and background events in each invariant mass window from which the significance was calculated. From these plots, we determined the exclusion limit for a discovery claim at the S = 5 level (see Figure 3). For the cuts listed in Table 6, we calculated the signal efficiencies for each graviton mass after applying each cut (see Table 9). Tables 10, 11, 12, and 13 show the efficiencies after applying the selection to the backgrounds. See Figure 4 for an example comparison of the signal and backgrounds after applying the selection. 6 Uncertainties Inaccuracies in the generation of data, errors in the simulation of the detector, uncertainties in the cross sections for the processes under investigation among many other potential sources of error must be taken into consideration. For the present purposes, it suffices to assign errors of ±10% to N s and N b. These values were used to assign the appropriate errors to the significance and exclusion limit calculations (see Figures 2 and 3). 6

Figure 2: Significance plots for all coupling constants studied in this analysis. The significance S = 2( N s + N b Nb ) is plotted as a function of invariant mass. The horizontal green lines indicate S = 5. The first row shows c = 0.01 and 0.025 from left to right, the second shows c = 0.05 and 0.075, and the third shows 0.1. The error bars assume ± 10% errors in N s and N b. 7

Mass Window (GeV/c 2 ): 250 500 750 1000 1250 1500 2000 N s 9385.8196 1374.4248 197.6964 38.8804 12.0956 4.4230 0.6912 N b 13.3747 3.5687 0.9654 0.1885 0.0690 0.0319 0.0064 Significance 186.5850 70.4645 26.2244 11.6327 6.4502 3.8641 1.5105 Minimal Significance 186.5850 70.4645 26.1919 10.6302 5.2376 2.6575 0.6009 Table 8: Significance calculations (c = 0.1). For invariant mass windows surrounding each graviton mass, we count the number of signal and background events surviving the cuts (normalized to 200 pb 1 ). The significance S = 2( N s + N b N b ) is then calculated. The last row shows the same significance calculation where N b has been rounded to one for mass windows where N b < 1. Selection 250 GeV 500 GeV 750 GeV 1000 GeV 1250 GeV 1500 GeV 2000 GeV HLT 100.0 ± 1.3 100.0 ± 1.0 100.0 ± 0.9 100.0 ± 0.9 100.0 ± 0.9 100.0 ± 0.9 100.0 ± 0.9 + γ p t 36.9 ± 0.8 76.8 ± 0.9 83.1 ± 0.9 85.3 ± 0.8 85.0 ± 0.8 85.8 ± 0.8 85.1 ± 0.8 + ECAL iso 27.6 ± 0.7 56.7 ± 0.8 60.4 ± 0.7 61.5 ± 0.7 61.8 ± 0.7 63.6 ± 0.7 64.4 ± 0.7 + H/E 26.1 ± 0.6 53.0 ± 0.7 55.7 ± 0.7 55.8 ± 0.7 56.5 ± 0.7 57.8 ± 0.7 58.9 ± 0.7 + inv mass 23.4 ± 0.6 48.6 ± 0.7 51.4 ± 0.7 50.5 ± 0.6 50.1 ± 0.6 52.1 ± 0.6 51.9 ± 0.6 + N trks 20.3 ± 0.6 40.3 ± 0.6 42.3 ± 0.6 41.3 ± 0.6 41.6 ± 0.6 43.1 ± 0.6 43.9 ± 0.6 Table 9: Selection efficiencies (in percent) for signals with c = 0.1. For each signal, the efficiency is shown after applying each cut. The cuts are cumulative, meaning each successive efficiency includes all prior cuts. Figure 3: S = 5 exclusion limit. For each coupling constant c, the corresponding mass value gives the maximal mass at which the S = 5 discovery level can be reached. In the left plot, the significance was calculated without adjusting N b, even if N b < 1. In the right plot, for mass windows containing less than one background event N b was rounded up to one, giving a more conservative estimate of the exclusion limit. The error bars assume ± 10% errors in N s and N b. Selection Born: 120-250 GeV/c 250-500 500-1000 1000-1500 1500-2000 2000-inf HLT 100.0 ± 3.7 100.0 ± 3.2 100.0 ± 3.0 99.9 ± 3.0 100.0 ± 2.9 99.8 ± 2.9 + γ p t 93.8 ± 3.6 95.6 ± 3.1 92.8 ± 2.9 91.3 ± 2.8 91.2 ± 2.8 91.5 ± 2.8 + ECAL iso 74.6 ± 3.2 78.4 ± 2.8 81.7 ± 2.7 82.8 ± 2.7 78.2 ± 2.6 59.8 ± 2.3 + H/E 71.4 ± 3.1 73.0 ± 2.7 76.1 ± 2.6 76.8 ± 2.6 73.2 ± 2.5 52.4 ± 2.1 + N trks 60.9 ± 2.9 61.3 ± 2.5 63.5 ± 2.4 68.4 ± 2.4 64.6 ± 2.3 47.1 ± 2.0 Table 10: Selection efficiencies for Born backgrounds. For each range of p T values considered in generating the Born background, we calculate the selection efficiency after applying each cut. The cuts are cumulative, meaning each successive efficiency includes all prior cuts. 8

Selection Box: 120-250 GeV/c 250-500 500-1000 1000-1500 1500-2000 2000-inf HLT 100.0 ± 3.3 100.0 ± 3.0 100.0 ± 2.7 100.0 ± 2.5 100.0 ± 2.3 99.8 ± 2.3 + γ p t 88.6 ± 3.1 92.9 ± 2.9 82.0 ± 2.5 81.6 ± 2.3 78.2 ± 2.0 76.3 ± 2.0 + ECAL iso 73.2 ± 2.8 78.3 ± 2.7 66.4 ± 2.2 57.1 ± 1.9 50.3 ± 1.6 42.3 ± 1.5 + H/E 69.1 ± 2.7 73.0 ± 2.6 61.0 ± 2.1 52.1 ± 1.8 43.3 ± 1.5 34.4 ± 1.4 + N trks 60.6 ± 2.6 61.1 ± 2.4 51.3 ± 1.9 44.1 ± 1.7 37.9 ± 1.4 30.7 ± 1.3 Table 11: Selection efficiencies for Box backgrounds. For each range of p T values considered in generating the Box background, we calculate the selection efficiency after applying each cut. The cuts are cumulative, meaning each successive efficiency includes all prior cuts. Selection Bremsstrahlung: 60-80 GeV/c 80-120 120-250 250-500 500-1000 1000-1500 1500-2000 2000-inf HLT 100.0 ± 2.8 100.0 ± 1.2 99.9 ± 0.9 99.9 ± 0.7 99.9 ± 0.5 99.9 ± 0.4 99.8 ± 0.4 99.8 ± 0.4 + γ p t 0.1 ± 0.1 3.3 ± 0.2 33.3 ± 0.5 56.7 ± 0.5 60.9 ± 0.4 63.9 ± 0.3 65.2 ± 0.3 65.3 ± 0.3 + ECAL iso 0.1 ± 0.1 1.7 ± 0.2 8.9 ± 0.3 11.5 ± 0.2 10.4 ± 0.2 8.3 ± 0.1 7.3 ± 0.1 6.2 ± 0.1 + H/E 0.1 ± 0.1 1.2 ± 0.1 2.3 ± 0.1 1.5 ± 0.1 1.6 ± 0.1 1.5 ± 0.1 1.3 ± 0.0 1.1 ± 0.0 + N trks 0.1 ± 0.1 0.8 ± 0.1 1.2 ± 0.1 0.9 ± 0.1 1.1 ± 0.1 1.1 ± 0.0 1.0 ± 0.0 0.8 ± 0.0 Table 12: Selection efficiencies for Bremsstrahlung backgrounds. For each range of p T values considered in generating the Bremsstrahlung background, we calculate the selection efficiency after applying each cut. The cuts are cumulative, meaning each successive efficiency includes all prior cuts. Selection QCD: 60-80 GeV/c 80-120 120-250 250-500 500-1000 1000-1500 1500-2000 2000-inf HLT 98.2 ± 2.9 97.3 ± 0.5 95.6 ± 0.3 97.6 ± 0.8 99.2 ± 0.4 99.8 ± 0.4 99.9 ± 0.3 99.9 ± 0.3 + γ p t 0.2 ± 0.1 0.7 ± 0.0 10.8 ± 0.1 31.6 ± 0.4 44.9 ± 0.3 54.4 ± 0.3 59.3 ± 0.2 61.9 ± 0.2 + ECAL iso 0.1 ± 0.1 0.1 ± 0.0 0.6 ± 0.0 1.0 ± 0.1 1.6 ± 0.1 2.3 ± 0.1 2.6 ± 0.0 2.9 ± 0.0 + H/E 0.1 ± 0.1 0.0 ± 0.0 0.0 ± 0.0 0.1 ± 0.0 0.1 ± 0.0 0.1 ± 0.0 0.2 ± 0.0 0.2 ± 0.0 + N trks 0.0 ± 0.0 0.0 ± 0.0 0.0 ± 0.0 0.0 ± 0.0 0.0 ± 0.0 0.1 ± 0.0 0.1 ± 0.0 0.1 ± 0.0 Table 13: Selection efficiencies for QCD backgrounds. For each range of p T values considered in generating the QCD background, we calculate the selection efficiency after applying each cut. The cuts are cumulative, meaning each successive efficiency includes all prior cuts. Figure 4: Signal versus background after selection. The 1 and 1.25 TeV/c 2 signals with c = 0.1 are plotted in red above the stacked Standard Model backgrounds (normalized to 200 pb 1 ). 9

7 Intermediate-Mass Diphoton Resonances We also investigated the discovery potential for diphoton resonance events in the intermediate-mass range 250 GeV/c 2 to 1 TeV/c 2. The above selection was re-applied to the simulated background data with the photon momentum threshold reduced from 100 GeV/c to 60 GeV/c. After applying the selection, the number of background events in a variety of invariant mass windows were counted. The windows were centered at invariant masses between 250 and 600 GeV/c 2 in steps of 5 GeV/c 2 (250, 255,..., 595, 600 GeV/c 2 ). Around each such central mass, windows with total width from 6 to 30 GeV/c 2, in integer steps, were imposed (see Figure 5). For each invariant mass window, the minimal number of signal events necessary to claim a discovery at S = 5 = 2( N s + N b N b ) was calculated (see Figure 5). The distribution of the minimal cross section for a particular process necessary to claim a discovery was then produced by normalizing the signal events to the integrated luminosity 200 pb 1 and the signal selection efficiency (see Figure 6). The selection efficiency was estimated at 40% based on the results of the Randall-Sundrum graviton signal selection (see Figure: 7). For each window width m, the cross section was then fit as a function of the central mass value M according to σ(m m) = (A + BM + CM 2 ) exp(d + EM) (see Figure 8). Both 10 and 20% errors were considered in assigning error to the number of background events counted in each mass window. The propagated errors were then calculated by determining the corresponding upper and lower bounds on the number of signal events in each window, subsequently giving the bounds on the cross section distribution. As functions of the window width, the parameters A( m), B( m), C( m), D( m), and E( m) were then fit to lines. Figures 9 and 10 show the fits on the five parameters with 10 and 20% errors on N b, and Table 14 shows the fits. Figure 5: Distribution of background and signal events for various invariant mass windows. Left: For invariant mass windows specified by a central value M and total width m, the number of background events therein were counted (normalized to 200 pb 1 ). Right: For the number of background events in each invariant mass window shown on the left, the minimal number of signal events necessary to claim a discovery at S = 5 = 2( N s + N b N b ) is shown. 8 Conclusions We investigate the potential for the discovery of a massive diphoton resonance signal corresponding to the Randall- Sundrum graviton diphoton decay channel using the CMS detector at the LHC. At an integrated luminosity of 200 pb 1, 10 TeV center-of-mass energy scale, and luminosity 1 10 31 cm 2 s 1, we find the diphoton resonance events are visible at a 5σ significance level for graviton masses up to 1.4 TeV/c 2 in the case of strong coupling between graviton excitations and Standard Model particles (c = 0.1). In the case of weak coupling (c = 0.01), the same discovery level may be achieved up to 500 GeV/c 2. We also calculate the distribution of Standard Model background events as a function of invariant mass window position and width in the intermediate-mass region 250 GeV/c 2 to 1 TeV/c 2. By imposing S = 2( N s + N b N b ) = 5, we determine the minimal number of signal events necessary to claim the discovery of a diphoton resonance in each window. We subsequently determine and fit the distribution of the minimal cross section as a function of the invariant 10

Figure 6: Distribution of minimal cross section for various invariant mass windows. The distribution of the minimal number of signal events necessary to claim an S = 5 discovery (Figure 5) was normalized to 200 pb 1 and signal selection efficiency 40% to obtain the minimal cross section needed for such a discovery. Figure 7: Randall-Sundrum signal selection efficiencies. For each coupling constant c considered in the above Randall- Sundrum analysis, the signal selection efficiency (in percent) is plotted versus the graviton mass. All errors in the efficiencies are less than 2%. 11

Figure 8: Fitting σ(m m). For invariant mass window widths 15 and 25 GeV/c 2, the minimal cross section (Figure 6) is fit according to σ(m m) = (A + BM + CM 2 ) exp(d + EM). Both 10 and 20% errors on N b (Figure 5) were considered. The top row shows the fits for m = 15 and 25 GeV/c 2, from left to right, using 10% errors. The bottom row shows the same with 20% errors. Parameter p 0 σ p0 p 1 σ p1 A (pb) 2.938 0.022 4.390 10 3 1.255 10 3 B (pb GeV 1 ) 1.541 10 2 0.016 10 2 2.947 10 5 0.902 10 5 C (pb GeV 2 ) 3.074 10 5 0.014 10 7 1.277 10 7 0.084 10 7 D () 1.958 10 2 5.977 10 2 4.379 10 2 0.299 10 2 E (GeV 1 ) 6.825 10 3 0.083 10 3 5.746 10 5 0.418 10 5 Parameter p 0 σ p0 p 1 σ p1 A (pb) 6.392 10 1 0.096 10 1 1.017 10 3 0.545 10 3 B (pb GeV 1 ) 3.351 10 3 0.069 10 3 6.405 10 6 3.601 10 6 C (pb GeV 2 ) 6.655 10 6 0.064 10 6 2.851 10 8 0.383 10 8 D () 1.687 0.103 3.761 10 2 0.493 10 2 E (GeV 1 ) 7.026 10 3 0.145 10 3 4.819 10 5 0.696 10 5 Table 14: Fitting the parameters A, B, C, D, and E as functions of the invariant mass window width. The parameters A, B, C, D, and E, used to fit the minimal cross section for fixed window widths m according to σ(m m) = (A + BM + CM 2 ) exp(d + EM), are fit as functions of m to lines: (p 0 ± σ p0 ) + (p 1 ± σ p1 ) m. The top table accounts for 10% error in N b, while the bottom accounts for 20%. mass window parameters. Comparison of the observed LHC background with the simulated data offers a data driven approach to searching for intermediate-mass diphoton resonance events. 12

Figure 9: Fitting the parameters A, B, C, D, and E as functions of the invariant mass window width. The parameters A, B, C, D, and E, used to fit the minimal cross section for fixed window widths m according to σ(m m) = (A + BM + CM 2 ) exp(d + EM), are fit as functions of m to lines. The plots account for 10% error in N b. 13

Figure 10: Fitting the parameters A, B, C, D, and E as functions of the invariant mass window width. The parameters A, B, C, D, and E, used to fit the minimal cross section for fixed window widths m according to σ(m m) = (A + BM + CM 2 ) exp(d + EM), are fit as functions of m to lines. The plots account for 20% error in N b. 14

9 Acknowledgments The authors would like to thank the entire Caltech CMS group. This work was made possible thanks to the generous financial support of Ms. Linda Blinkenberg. References [1] M. Pieri et al. Inclusive Search for the Standard Model Higgs Boson in the H γγ Channel. CMS Note 2006/112 (2006). [2] M.-C. Lemaire, V. Litvin, H. Newman, Search for Randall-Sundrum excitations of gravitons decaying into two photons for CMS at LHC. CMS Note 2006/051 (2006). [3] L. Randall, R. Sundrum, Phys. Rev. Lett. 83 (1999) 3370 and ibid (1999) 4690. [4] N. Arkani-Hamed, S. Dimopoulos, G.Dvali, Phys. Lett. B249 (1998) 263 I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, G.Dvali, Phys. Lett. B436 (1998) 257 [5] H.Davoudiasl, J.L. Hewett and T.G. Rizzo, Experimental Probes of Localized Gravity: On and Off the Wall, Phys. Rev. D63 (2001) 075004. [6] T. Sjöstrand, Comput. Phys. Commun. 82 (1994) 74; T. Sjöstrand et al., Comput. Phys. Commun. 135 (2001) 238, LU TP 00-30, hep-ph/0010017. [7] CMS Collaboration, CERN/LHCC 2000-038, CMS TDR 6.1, CMS The Tridas Project Design Report, Volume 1: The Trigger Systems. [8] CMS Collaboration, CERN/LHCC 2002-02, CMS TDR 6.2, CMS The Tridas Project Technical Design Report, Volume 2: Data Acquisition and High-Level Trigger. [9] CMS Collaboration, Object oriented Simulation for CMS Analysis and Reconstruction, http://cmsdoc.cern.ch/oscar/. [10] P. Bartalini, R.Chierici, A De Roeck, Guidelines for the estimation of theoretical uncertainties at the LHC, CMS Note 2005/013, 2005. [11] D. Acosta et al., CDF Collaboration, PRL 95 (2005) 022003, 2005. 15