The ability of the CMS experiment to detect massive Kaluza-Klein excitations
of gravitons, predicted by the Randall-Sundrum model, is studied. The search
reach is estimated for the channel with the graviton, produced in proton-proton
collision, decaying into a pair of electrons or muons.Comment: 13 pages, 13 figure

Traczyk, Piotr

Wrochna, Grzegorz

English

arXiv

The ability of the CMS experiment to detect massive Kaluza-Klein excitations of gravitons, predicted by the Randall-Sundrum model, is studied. The search reach is estimated for the channel with the graviton, produced in proton-proton collision, decaying into a pair of electrons or muons.The ability of the CMS experiment to detect massive Kaluza-Klein excitations of gravitons, predicted by the Randall-Sundrum model, is studied. The search reach is estimated for the channel with the graviton, produced in proton-proton collision, decaying into a pair of electrons or muons

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The Compact Muon Solenoid ExperimentMailing address: CMS CERN, CH-1211 GENEVA 23, SwitzerlandCMS NoteAvailable on CMS information server CMS NOTE 2002/003Search for Randall-Sundrum GravitonExcitations in the CMS ExperimentP. Traczyka), G. Wrochnaa)Soltan Institute for Nuclear Studies, Warsaw, Poland.AbstractThe ability of the CMS experiment to detect massive Kaluza-Klein excitations, predicted bythe Randall-Sundrum model, is studied. The search reach is estimated for the channel withthe graviton, produced in the proton-proton collision, decays into a pair of electrons ormuons.a. Partially supported by the Polish Committee for Scientific Research under grant KBN 621/E-78/SPUB/P-03/DZ 5/99.22 January 200221 IntroductionIn 1999 Arkani-Hamed, Dimopoulos and Dvali (ADD) proposed a framework for solving the gauge hierarchyproblem by introducing n large extra dimensions [1]. In this model, the Standard Model fields remain confined toour 4-dimensional world - new dimensions are only felt by gravity. The observed Planck scale MPl ~ 1019 GeV isan effective scale, related to the fundamental scale MS through the volume of the compactified dimensions,. The hierarchy problem is radically solved without fine-tuning the hierarchy, but simply byremoving it, setting MS equal or close to the electroweak scale MEW ~ 103 GeV. Experimental consequencesinclude possible deviations from Newtons law at small distances, and production of Kaluza-Klein excitations ofthe graviton in future particle colliders. Unfortunately a closer look reveals, that, while removing the original hier-archy, this model introduces a new hierarchy between the electroweak scale and the compactification scale, the latter ranging from around and eV to ~MeV, depending on the number of extra dimensions n.Another scenario, but this time without a large compactification volume, was proposed by Randall and Sundrum(RS) [2]. Here, only one extra dimension φ is introduced, with a non-factorizable geometry based on a slice ofAdS5 spacetime. The extra dimension is compactified on an S1/Z2 orbifold, with fixed points φ = 0 , π holdingtwo 3-branes. A solution to 5-dimensional Einstein’s equations, preserving 4-dimensional Poincare invariance, isgiven by the metric(1)where k ~ MPL is the AdS5 curvature, xµ are ordinary 4-dimensional coordinates, and rc is the compactificationradius. In this set-up, a fundamental 5-dimensional mass scale m0, appears in a 4-dimensional theory at φ = π, as(2)The hierarchy between the Planck and electroweak scales is removed by the exponential warp factor, whenkrc ~ 11-12. The compactification scale µc = 1/rc is of the order of the Planck scale, and no new hierarchiesappear. Because of the small compactification radius, there are no deviations from Newton’s law at experimen-tally accessible distances. On the other hand, massive graviton excitations appear, with masses given by [3](3)where xn is the nth root of the Bessel function J1. These masses are of order of a TeV, and Kaluza-Klein gravitonscan be detected as massive resonances in collider experiments. Coupling of an excited graviton to matter isdescribed by(4)where Tµν is the energy-momentum tensor of the matter field, hµν(n) is the nth excitation of the graviton, and Λπ isthe scale parameter of the theory, given by(5)Two parameters control the properties of the RS model: the mass of the first Kaluza-Klein graviton excitationmG = m1, and the constant c = k / MPl, determining graviton couplings (see eq. (4) and (5)) and widths:(6)where ρ is a constant depending on the number of open decay channels. Fig. 1, taken from [6], shows experimen-tal and theoretical constraints no these two parameters. The limit is a higher-dimensional curvaturebound, originally formulated in [2] as k < M, where M ~ MPl is the fundamental, five-dimensional Planck scale.The constraint Λπ < 10 TeV assures no new hierarchy appears between mEW and Λπ. The remaining two curvesrepresent experimental bounds, obtained from lepton and jet pair production analysis at the Tevatron, and from aglobal fit to the electroweak oblique parameters S and T. The allowed region, enclosed by the four curves, can,according to [6] be completely covered by the LHC. This, however, is based on an analysis assuming an idealdetector. The purpose of this paper will be to obtain the search reach for the CMS experiment and verify the abovestatement taking into account detector effects.MSn 2+ Vn MPl2=µc Vn1 n/–=ds2 e 2krcϕ– ηµνdxµdxν rc2dϕ2+=m ekrcπ– m0=mn kxnekrcπ–=L 1Λπ------Tµν hµνn( )n 1=∞∑–=Λπ MPlekrcπ–=Γn ρmnxn2 k MPl⁄( )2=R5 M52<3Figure 1: Experimental and theoretical constraints on the RS model parameters c = k / MPl and mG = m1 [6].2 Monte Carlo simulations2.1. Signal and background simulationThe process chosen to be the “signal from the extra dimension” is the production of the first excited KK gravitonstate, and it’s decay into a pair of leptonsa). A clear signature of this process are high-pt leptons, easy to identifyand trigger. The Standard Model background in this channel consists mostly of the Drell-Yan process. Simulations were done independently with two event generators, PYTHIA 6.157 [4] andHERWIG 6.201 [5]. Both have production and decay of RS graviton resonances implemented in the originalcode.The Monte Carlo generators were set to produce gravitons in proton-proton collisions at 14 TeV centre-of-massenergy. Leptons were identified among the final state particles, and an initial detector acceptance cut (|η| < 2.4 formuons, and |η| < 3.0 for electrons) was applied. Simulations were done for 20 sets of model parameters, coveringthe range suggested in [6].Fig. 2 shows a comparison between results from the two event generators. The numbers of events shown corre-spond to one year of LHC running at the design luminosity of 1034 cm-2s-1, giving an integrated luminosity of100 fb-1. The graviton can be seen as a peak in the invariant mass distribution of leptons. The graviton decays intoall SM particles, with leptonic decays being only about 4% of all decays. Low energy secondary leptons, comingfrom tau, W and Z decays, are responsible for most of the peak’s asymmetry. Dotted histogram shows leptonscoming directly from graviton decay (for data from Herwig).Results from Pythia and Herwig are not identical, the shape and height of the resonance are different in the twocases. The origin of these differences is show in Fig. 3, showing the mass distribution of generated gravitons. Thegraviton generated with Herwig is symmetric, whereas the shape generated by Pythia resembles more the oneseen in Fig. 2. The reason is simple: Herwig calculates graviton production cross section in the maximum, andsmears the particle’s mass according to the Breit-Wigner distribution, while Pythia works the other way around -the cross section is calculated as a function of the graviton mass. In proton-proton collisions, the probability offinding a pair of partons with a given centre-of-mass energy is a rapidly falling function of that energy, hence theasymmetry. The approximation used in Herwig is good for narrow resonances, but not in the case of a 20 GeV-wide graviton. Calculated cross sections are shown in Tab. 1. Background simulation results from both generatorsa. Throughout this paper the term “lepton” refers to electrons and muons only.pp Z0 γ⁄ ll→ →4are consistent with each other, as shown in Fig. 4.Figure 2: Invariant mass distribution of lepton pairs from a 2 TeV graviton simulation (with c = 0.1). Solid lineshows results from Pythia, dashed line from Herwig. Dotted histogram shows what the distribution wouldlook like if only leptons coming directly from graviton decay were taken into account (for Herwig data).Figure 3: Distribution of graviton mass for Pythia (solid line), and Herwig (dashed line), normalized for 100 fb-1of integrated luminosity.events/bin5Figure 4: Background simulation results. Invariant mass distribution of lepton pairs from Pythia (solid line) andHerwig (dashed line).Table 1: Cross sections (in mb) for the simulated graviton production and decay process.GeneratormG[GeV] 0.01 0.02c0.05 0.07 0.10 0.20PYTHIA 1000 3.93 10-10 1.58 10-09 1.00 10-08 4.14 10-081500 4.53 10-11 1.16 10-09 4.99 10-092000 8.44 10-12 2.20 10-10 9.90 10-103000 5.69 10-13 1.59 10-11 3.48 10-11 8.57 10-114000 1.95 10-12 1.46 10-11 1.67 10-105000 4.27 10-12 6.09 10-116000 2.80 10-11HERIWG 1000 5.77 10-10 2.31 10-09 1.44 10-08 5.73 10-081500 6.50 10-11 1.62 10-09 6.44 10-092000 1.14 10-11 2.86 10-10 1.13 10-093000 6.84 10-13 1.71 10-11 3.34 10-11 6.78 10-114000 1.56 10-12 6.23 10-12 2.48 10-115000 6.75 10-13 2.84 10-126000 3.56 10-13× × × ×× × ×× × ×× × × ×× × ×× ××× × × ×× × ×× × ×× × × ×× × ×× ××62.2. Detector simulationDetector response was simulated by passing generated signal and background leptons through CMSJET 4.703program [7]. Fig. 5 shows the impact of detector effects on the signal. Some of the signal is lost, and the peak issmeared, especially in the case of muons. This is natural, since muon momentum measurement is based on theparticle track’s curvature in magnetic field, momentum resolution of the muon system can be approximated by([8])(7)where the muon momentum p is measured in TeV. Electron energy is measured in a calorimeter, with resolutionparametrized by(8)where E is measured in GeV. The a, b, and c parameter values used in CMSJET are of order of, respectively, 5%,20% and 0,5%.Figure 5: Electron and muon pair invariant mass distributions for mG = 3 TeV and c = 0.1. The upper two plotsshow results directly from the Herwig generator, the lower two show data after detector simulation.3 Data analysisFor every set of model parameters an invariant mass window around the graviton mass was chosen, and the num-ber of signal and background events inside was calculated. Muons and electrons were treated independently,because of the difference in observed resonance widths induced by the detector. Tab. 2 shows the graviton widths,as calculated by Herwig. The total observed width can be approximated by(9)where Γ1 is the graviton width, and ∆E is the electron or muon energy measurement uncertainty (equations (7)and (8)) for a particle with momentum mG.∆pp------% 4% p=∆EE-------aE-------bE--- c⊕ ⊕=events/binevents/binevents/binevents/binΓobs Γ12 2 ∆E( )2+≈7Width of the mass window was set to . Expected number of signal and background events (NS and NB)inside the window was calculated for 100 fb-1 integrated luminosity. The number of actually observed back-ground leptons fluctuates according to the Poisson distribution, with a dispersion of . The total number ofsignal and background events is also described by the Poisson distribution. The probabil-ity P, that it will be less than is given by:(10)and when 1 - P = 0.05, the hypothesis can be excluded at 95% confidence level when no signal is observed.The figures below show examples of signal and background distributions (from Pythia) for a few sets of modelparameters. Numbers of events from both generators are shown in Tab. 3 and Tab. 4. There is a significant differ-ence in electron and muon signal in the data from Pythia. This effect arises from the difference in window widthsand from the asymmetric shape of the graviton resonance. The muon window is wider, and more particles fromthe peak’s left slope fall into the window. In the data from Herwig, where the resonance is symmetric, no sucheffect is observed.Figure 6: Signal distribution for mG = 1000 GeV and c = 0.1. Background, shown with the hatched histogram, ispractically invisible.Table 2: Widths of simulated gravitons.mG[GeV] 0.01 0.02c0.05 0.07 0.10 0.201000 0.1 0.6 3.5 14.11500 0.2 5.3 21.32000 0.3 7.1 28.43000 0.4 10.6 20.9 42.64000 14.2 56.8 227.25000 71.0 284.06000 340.82Γobs±NB±Nobs NSobs NBobs+=NB 2 NB+P Nobs NB 2 NB+<( )NS NB+( )kk!------------------------- eNS NB+( )–k 0=NB 2 NB+∑=8Figure 7: Signal and background distribution for mG = 1000 GeV and c = 0.01.The most optimistic case is shown in Fig. 6. A light, strongly coupled graviton is impossible to miss. Backgroundis negligible, totally overwhelmed by the signal. Event numbers drop by a factor of 10 after reducing the couplingten times (Fig. 7). Fig. 8 shows a more difficult case, with graviton mass of 2 TeV, and c = 0.01. This is a rare par-ticle, with expected 11 signal electron events over 3 events in background, giving a 3.3% chance of accidentallyexcluding the model. The muon background is higher, due to a wider mass window, and with 15 signal and 44background events the probability of loosing the signal is 48%. Increasing the coupling to a value of 0.2 allows a4 TeV graviton to be observed (Fig. 10). Increasing the mass further causes the signal to drop, the heaviest case isshown in Fig. 11. A 5 TeV graviton is practically out of reach at this luminosity.Figure 8: Signal and background distribution for mG = 2000 GeV and c = 0.01.9Figure 9: Signal and background distribution for mG = 3000 GeV and c = 0.05.Figure 10: Signal and background distribution for mG = 4000 GeV and c = 0.2.Figure 11: Signal and background distribution for mG = 5000 GeV and c = 0.2.10Table 3: Signal/background events from Pythia.SignalmG[GeV] 0.01 0.02c0.05 0.07 0.10 0.20e+e− 1000 490/65 2028/65 11770/72 45953/1481500 56/13.8 1361/15.4 5244/302000 10.8/3.1 255/3.6 1042/7.23000 0.7/0.3 15.4/0.4 31/0.4 69/0.74000 1.5/0.04 6.7/0.1 33/0.35000 0.8/0.01 3.2/0.046000 0.3/0.01µ+µ− 1000 716/540 2861/540 16120/541 65370/5571500 80/138 2039/139 8234/1412000 15/44 379/44 1477/453000 1.1/6.2 25/6.2 50/6.2 102/6.24000 2.7/1.3 10.2/1.3 42/1.65000 1.2/0.4 5.2/0.36000 0.8/0.1Table 4: Signal/background events from Herwig.SignalmG[GeV] 0.01 0.02c=0.05 0.07 0.10 0.20e+e− 1000 1128/71 4543/71 26640/79 91564/1601500 772/12.6 3313/14.0 11174/302000 22/3.5 521/3.9 1958/8.13000 1.3/0.4 32/0.4 56/0.5 115/0.84000 2.8/0.05 10.3/0.1 40.9/0.45000 1.2/0.01 4.4/0.16000 0.5/0.01µ+µ− 1000 1095/590 4747/590 28253/591 108123/6101500 774/151 3213/151 12809/1542000 22/48 574/48 2178/493000 1.3/7.3 34/7.3 66/7.3 134/7.44000 3.0/1.4 12.0/1.5 47.3/1.95000 1.3/0.3 5.1/0.46000 0.6/0.111The above results had to be interpolated, in order to allow plotting the 95% excluded region in (c, mG) parameterspace. Background was described by(11)and signal by(12)The functions’ parameters were tuned with the χ2 method to reproduce simulated event numbers. The valuesobtained are shown in Tab. 5.4 ResultsThe search reach of the CMS experiment is shown in Fig. 12 for Pythia, and in Fig. 13 for Herwig. The plotsshow 95% confidence level exclusion limits for electrons and muons. The results show that LHC should probe thewhole theoretically allowed region. The contour from Herwig reaches masses ~100-200 GeV higher than Pythia,because of a higher number of selected events.For masses under 4 TeV, the electron channel gives a higher search reach. Because of better energy resolution forelectrons, the observed resonance width is smaller, resulting in a smaller mass window and a better ratio of signalto background. For higher graviton masses the background is negligible, and the effect vanishes. Because the sig-nal in Pythia is higher for muons, this channel has a higher reach for large masses.Table 5: Signal and background parametrization.PYTHIA HERWIGSignal Electrons Muons Electrons MuonsF 129.1 79.7 130.1 86.2G 0.36 0.15 0.34 0.09H 3.04 10-7 3.27 10-7 3.14 10-7 3.12 10-7I -0.0046 -0.0047 -0.0047 -0.0047J 14.57 15.59 15.57 16.05χ2 / NDF 2.30 / 3 3.08 / 3 2.91 / 3 3.17 / 3BackgroundA 1.42 0.49 1.43 0.50B 102.9 187.8 103.2 187.1C 2.54 10-7 2.46 10-7 3.09 10-7 2.49 10-7D -0.0038 -0.0033 -0.0041 -0.0033E 12.18 10.99 12.49 11.08χ2 / NDF 1.95 / 14 1.29 / 14 2.77 / 14 1.96 / 14NB c mG,( ) A c2 B+⋅( ) e C mG2 D mG E+⋅+⋅( )⋅=NS c mG,( ) F c2 G c⋅+⋅( ) e H mG2 I mG J+⋅+⋅( )⋅=× × × ×× × × ×12Figure 12: Search reach of the CMS experiment, based on results from Pythia. The 95% exclusion region liesabove the curves.Figure 13: Search reach based on results from Herwig.PYTHIA0,010,101,001000 1500 2000 2500 3000 3500 4000 4500 5000m G [GeV]cΛπ = 10 TeVElektronyMiony|R5| < M52MuonsElectronsRegion of interestHERWIG0,010,101,001000,00 1500,00 2000,00 2500,00 3000,00 3500,00 4000,00 4500,00 5000,00m G [GeV]cΛπ = 10 TeVElektronyMiony|R5| < M52MuonsElectronsRegion of interest135 Summary and outlookThe analysis presented in this paper shows that the CMS experiment should be able to test the Randall-Sundrummodel at 95% confidence level, after a year of CMS data taking at the design luminosity. Still, the graviton has tobe distinguished from other exotic heavy particles, which requires analyzing angular distributions of the decayproducts. Such an analysis for the ATLAS detector is presented in [9]. According to the authors, spin-2 hypothesisis favored over spin-1 at 90% confidence level for masses up to 1440 GeV (with c = 0.01). The mass reach for thepp → GKK → e+e− channel is 1830 GeV.References[1] N. Arkani-Hamed, S. Dimopoulos, G. Dvali: The Hierarchy Problem and New Dimensions at a Millimeter,Phys. Lett. B429, 263 (1998), hep-ph/9803315[2] L. Randall, R. Sundrum: A Large Mass Hierarchy from a Small Extra Dimension, Phys. Rev. Lett. 83, 3370(1999), hep-ph/9905221[3] H. Davoudiasl, J. L. Hewett, T. G. Rizzo: Warped Phenomenology, Phys. Rev. Lett. 84, 2080 (2000), hep-ph/9909255[4] T. Sjöstrand, Computer Physics Commun. 82 (1994) 74[5] G. Marchesini, B. R. Webber, G. Abbiendi, I. G. Knowles, M. H. Seymour, L. Stanco: HERWIG: A MonteCarlo event generator for simulating hadron emission reactions with interfering gluons. Version 5.1 - April1991, Comput. Phys. Commun. 67, (1992) 465; G. Corcella et al., HERWIG 6: an event generator for HadronEmission Reactions With Interfering Gluons (including supersymmetric processes), hep-ph/0011363[6] H. Davoudiasl, J. L. Hewett, T. G. Rizzo: Experimental Probes of Localized Gravity: On and Off the Wall,hep-ph/0006041[7] S. Adbullin, A. Khanov, N. Stepanov: CMSJET, CMS-TN/94-180[8] G. Wrochna: Muon Trigger of the CMS detector for LHC, CMS NOTE 1997/096, CMS Collaboration: TheMuon Project Technical Design Report, CERN/LHCC 97-32[9] B. C. Allanach, K. Odagiri, M. A. Parker, B. R. Webber: Searching for Narrow Graviton Resonances with theATLAS Detector at the Large Hadron Collider, hep-ph/0006114[10]W. D. Goldgerger, M. B. Wise: Modulus Stabilization with Bulk Fields, Phys. Rev. Lett. 83, 4922 (1999), hep-ph/9907447[11]L. Randall, R. Sundrum: An Alternative to Compactification, Phys. Rev. Lett. 83, 4690 (1999), hep-th/9906064

Search for Randall-Sundrum Graviton Excitations in the CMS Experiment

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