Available on the CERN CDS information server CMS PAS EXO-11-009 CMS Physics Analysis Summary Contact: cms-pag-conveners-exotica@cern.ch 01/05/06 Search for Contact Interactions in µ + µ Events in pp Collisions at s = 7 TeV The CMS Collaboration Abstract We report the results of a search for contact interactions in events with two isolated muons collected in proton-proton collisions at s =7 TeV with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 5.3 fb 1. The observed dimuon mass spectrum is consistent with that expected from the standard model. The data are interpreted in the context of a quark and muon compositeness model with a left-left isoscalar contact interaction described by an energy scale parameter Λ. We set 95% confidence level lower limits on Λ of 9.5 TeV for destructive interference and 13.0 TeV for constructive interference, which are the most stringent limits to date.
1 1 Quark-lepton compositeness and contact interactions The variety of observed quark and lepton flavors suggests that they may in fact be composed of more fundamental constituents. In order to confine the constituents (often referred to as preons ) and to account for the properties of quarks and leptons, a new strong gauge interaction, metacolor, is introduced. Below a given interaction scale Λ the effect of the metacolor interaction is to bind the preons into metacolor-singlet states. For parton interaction ŝ values that are much less than the Λ scale the metacolor force will manifest itself in the form of a flavor-diagonal contact interaction [1, ] (CI). In the case where both quarks and leptons share common constituents it is possible to write the Lagrangian density for CI leading to dimuon final states L ql = (g0 /Λ ){η LL ( q L γ µ q L )( µ L γ µ µ L ) + η LR ( q L γ µ q L )( µ R γ µ µ R ) +η RL (ū R γ µ u R )( µ L γ µ µ L ) + η RL ( d R γ µ d R )( µ L γ µ µ L ) (1) +η RR (ū R γ µ u R )( µ R γ µ µ R ) + η RR ( d R γ µ d R )( µ R γ µ µ R )} where q L = (u, d) L is a left-handed quark doublet, u R and d R are right-handed quark singlets, and µ L and µ R are the left- and right-handed muons. By convention, g0 /4π = 1 and the η values are taken to have a magnitude of one. The parameter Λ, which represents the compositeness scale, is potentially different for each of the individual terms in the Lagrangian density, so lower limits on Λ are set separately for the individual currents in Eq. 1. Figure 1: Interference between DY and CI amplitudes resulting in dimuon final states. As illustrated in Fig. 1, standard model Drell-Yan [3] (DY) dimuon production and CI dimuon production have the same final state, so their scattering amplitudes are summed. The observed cross section can be described as dσ dσ (Λ) = dm dm (DY) η I Λ + C η Λ 4 () where I corresponds to the product of DY and contact amplitudes and C corresponds to a pure contact term. Note that η = +1 corresponds to destructive interference and η = 1 to constructive interference. The processes contributing to the cross section in Eqn. are denoted collectively by CI/DY. 1.1 Compositeness implementation in PYTHIA PYTHIA (version 6.4 [4]) implements two compositeness models where the final states are equivalent to those resulting from γ /Z 0 exchange in the standard model (SM). These are the left-left isoscalar model (LLIM) and the helicity non-conserving model. Both of these models
1 Quark-lepton compositeness and contact interactions include DY production in addition to CI, and the LLIM allows for interference between the two amplitudes. This analysis is restricted to the LLIM where all of the initial state quarks are assumed to be composite and the final state is taken to be µ + µ. This model corresponds to the first term of L ql in Eqn. 1 and is the conventional benchmark for CI in the dilepton channel [5]. In the LLIM, the basic features of the dimuon mass spectra expected in the CMS detector are demonstrated using PYTHIA with appropriate kinematic cuts. The polar angle θ is measured from the beam axis and pseudorapidity η = -ln[ tan(θ/)]. Transverse momentum p T is the component of momentum in the plane transverse to the beam axis. For this example, both muons in the dimuon pair are subject to the requirements η <.1 and p T > 40 GeV/c. Figures a and b show the LLIM dimuon event yields at different values of Λ for destructive and constructive interference, respectively. The curves corresponding to different Λ values in Fig. illustrate that the CI leads to a less steeply falling cross section relative to DY production, with the effect steadily increasing with decreasing Λ. Events/30 GeV/c 5 CMS Simulation Λ = 3 TeV Λ = 5 TeV Λ = 7 TeV 4 Λ = 9 TeV Λ = 13 TeV SM DY 3 Events/30 GeV/c 5 CMS Simulation Λ = 3 TeV Λ = 5 TeV Λ = 7 TeV 4 Λ = 9 TeV Λ = 13 TeV SM DY 3 0 500 00 1500 000 500 3000 (GeV/c ) M µµ 0 500 00 1500 000 500 3000 (GeV/c ) M µµ (a) Figure : Dimuon event yields for different values of Λ for (a) destructive interference and (b) constructive interference. Values are shown for M >10 GeV/c since the CI contribution below this value is much smaller than that due to DY. As Λ increases the differential cross section tends toward pure DY. (b) A comparison of the constructive and destructive differential cross sections (dσ/dm) is shown in Fig. 3. The fits to cross-section points are based on Eqn. and differ only in the sign of the second term. For Λ values larger than TeV it is clear that the two cross sections asymptotically approach the DY limit (7.9 µb for M µ + µ >10 GeV/c ) as suggested by Eqn.. One can also observe the effect of negative interference in the destructive case, where the cross section achieves a minimum at around Λ = 6 7 TeV. 1. Previous results Previous searches for CI have all resulted in limits on the compositeness scale Λ. These include studies from LEP [6 ], HERA [11, 1], the Tevatron [13 18], and recently from the ATLAS [19 1] and CMS [] experiments at the CERN Large Hadron Collider. The best limits in the LLIM
3 ) >10 GeV/c µµ σ [pb] (M.5 9.5 9 8.5 CMS Simulation Destructive Constructive 8 7.5 0 5 15 0 5 30 35 40 Λ (TeV) Figure 3: Constructive and destructive LLIM cross sections for M µ + µ >10 GeV/c. The red circles correspond to constructive interference and the inverted blue triangles to destructive interference. The functional fits differ only in the sign of the interference term in Eq.. dimuon channel are currently Λ > 4.9 TeV for constructive interference and Λ > 4.5 TeV for destructive interference at the 95% confidence level (CL) [0]. CMS Detector A detailed description of the CMS detector can be found in Ref. [3]. The main subsystems used in this analysis include the tracker, which is located inside the 3.8 T superconducting solenoid, and the muon detector, which has detection elements interspersed in the return yoke of the solenoid. The tracker measures charged particle trajectories within the range η <.5 and provides a p T resolution of about 1% at a few tens of GeV/c to % at several hundred GeV/c [4]. Tracker elements include 1440 silicon pixel modules, located close to the beamline, and 15 148 silicon microstrip modules, which surround the pixel system. Tracker detectors are distributed in both barrel and endcap geometries. The muon detector includes a combination of drift tubes and resistive plate chambers in the barrel region and a combination of cathode strip chambers and resistive plate chambers in the endcap regions. Muons can be reconstructed in the range η <.4 although the coverage of the trigger elements extends only up to about η =.1. For the trigger path used in this analysis, the first level (L1) selects events based on a sub-set of information from the muon detector. The High Level Trigger (HLT) processor farm then filters L1 triggers using full information from both the tracker and muon systems. 3 Dimuon selection criteria This analysis uses the same event selection as the search for new heavy resonances in the dimuon channel, discussed in Ref. [5]. Muons must be reconstructed in both the tracker and the muon detector. Each muon track is required to have a signal ( hit ) in at least one pixel layer, hits in at least nine strip layers, and hits in at least two muon detector stations. Both
4 4 Simulation of SM and CI dimuon production muons are required to have p T > 45 GeV/c. To reduce the cosmic ray background, the transverse impact parameter of the muon with respect to the beamspot is required to be < 0. cm. In order to suppress muons coming from hadronic decays, a tracker-based isolation requirement is imposed such that the sum of p T of all tracks, excluding the muon, within a cone of radius R = ( η) + ( φ) = 0.3 is less than % of the p T of the muon. The two muons are required to have opposite charge and must be consistent with originating from a common vertex. A constrained fit of the muon tracks to a common vertex must satisfy χ <. To suppress cosmic ray muons that are in time with the collision event, the 3- dimensional angle between the two muons must be smaller than π 0.0 radians. At least one of the reconstructed muons must be matched (within R < 0. and p T /p T < 1) to the HLT muon candidate, which is restricted to η <.1. If an event has more than two reconstructed muons passing all of the above requirements, the two highest p T muons are selected, and the event is retained only if these muons are oppositely charged. Events with more than two reconstructed muons surviving the cuts are very rare; only 14 events are found in the dataset. 4 Simulation of SM and CI dimuon production 4.1 Overview To interpret the observed dimuon mass distribution in the context of the CI model, it is necessary to predict the contributions from SM and CI sources. However, there is no event generator that incorporates all of the required elements: generation of both DY and CI amplitudes, and inclusion of QCD and QED Feynman graphs beyond leading order. For this reason a combination of methods is employed. The predicted number of CI/DY events is determined using PYTHIA for event generation. The effect of the detector is determined using a high-statistics sample of SM DY events that undergo a simulation of the detector, including the effects of the trigger, acceptance, event reconstruction, and mass resolution. The predicted number of CI/DY events is the product of the generated number, a QCD k-factor, a QED k-factor, and a factor denoted as acceptance times migration, determined from simulation. The analysis of CI events is limited to a dimuon mass range from 00 to 000 GeV/c. The lower limit is enough above the Z-peak so that a deviation from DY production is observable, while the upper limit is chosen large enough to include all events that could be produced for values of Λ accessible with this dataset and not excluded by previous measurements. The minimum mass Mµµ Low required in the analysis is varied between the lower and upper limits to optimize the limit on Λ, as described in section 5. A summary of the event samples used for simulation of the detector response to various physics processes is presented in Table 1. The event generators are PYTHIA, POWHEG [6 8], and MADGRAPH [9]. Since PYTHIA is a leading order (LO) generator, k-factors are applied. For the PYTHIA DY µµ samples, the k-factor takes into account the dependence on M µµ, as described in section 4.4. For the other processes simulated by PYTHIA, each k-factor is determined from the ratio of the cross section determined using the next-to-leading-order (NLO) generator MC@NLO [30] to the cross section determined from PYTHIA. 4. Detector acceptance times mass migration For a given value of M Low µµ, the acceptance times migration is given by the ratio of the number of DY events reconstructed with mass above M Low µµ to the number of DY events generated with
4.3 Event pileup 5 Process Generator Events σ(pb) L( pb 1 ) Order Z/γ µ µ PYTHIA0 148 35 1 300 1 653 LO Z/γ µ µ PYTHIA10 54 550 7.9 6 905 LO Z/γ µ µ PYTHIA00 55 000 0.97 56 701 LO Z/γ µ µ PYTHIA500 55 000 0.07 037 037 LO Z/γ µ µ PYTHIA800 55 000 0.0031 17 741 936 LO Z/γ µ µ PYTHIA00 55 000 9.70E-04 56 701 031 LO Z/γ τ τ PYTHIA 03 000 1 300 1 564 LO t t MADGRAPH 4 000 000 1.57E+0 154 140 NLO tw POWHEG 795 379 7.9 0 681 NLO tw POWHEG 801 984 7.9 1 517 NLO WW PYTHIA 4 5 916 43 98 77 LO WZ PYTHIA 4 65 43 18 36 958 LO ZZ PYTHIA 4 191 045 5.9 7 347 LO W + jets MADGRAPH 4 50 000 3.E+04 78 NLO QCD PYTHIA 1 083 09 84 679.3 17.9 LO Table 1: Description of event samples with detector simulation. For the DY process Z/γ µµ, the minimum dimuon mass is indicated as part of the PYTHIA sample name. mass above Mµµ Low. Some of the reconstructed events have generated mass below Mµµ Low due to the mass resolution. The acceptance times migration as a function of Mµµ Low is plotted in Fig. 4 and values are given in Table. Migration Acceptance 1 0.95 0.9 CMS Simulation 0.85 0.8 00 400 600 800 00 100 Low M 1400 (GeV/c 1600 ) Figure 4: Acceptance times migration for M > M Low µµ. µµ To validate the event yields predicted by the combination of the CI/DY generator and the acceptance times migration factor determined from DY events simulated in the detector, we employ an alternate, direct (but computationally intensive) method for determining the yields using only CI/DY events that are simulated in the detector. This study is performed for the cases of constructive interference with Λ = 5 and TeV, which represent a wide range of possible CI/DY cross sections. The results differ by at most 3%, consistent with the statistical precision of the study. The systematic uncertainty on acceptance times migration is conservatively assigned this value. 4.3 Event pileup During the course of the 011 data taking period, the luminosity increased with time, resulting in an increasing event pileup. In principle, the reconstruction efficiency could depend on the
6 4 Simulation of SM and CI dimuon production Mµµ Low ( GeV/c ) Accep. migr. QCD k-factor EW k-factor 00 0.80±0.01 1.59± 0.004 1.01 300 0.8±0.01 1.96± 0.003 0.99 400 0.83±0.01 1.31± 0.003 0.97 500 0.86±0.0 1.334± 0.003 0.95 600 0.86±0.01 1.339± 0.003 0.94 700 0.87±0.01 1.343± 0.003 0.9 800 0.88±0.01 1.343± 0.003 0.91 900 0.89±0.01 1.339± 0.00 0.90 00 0.89±0.01 1.334± 0.00 0.89 10 0.89±0.01 1.34± 0.00 0.88 100 0.91±0.01 1.31± 0.00 0.88 1300 0.9±0.01 1.91± 0.003 0.87 1400 0.94±0.01 1.64± 0.003 0.87 1500 0.97±0.01 1.0± 0.004 0.86 Table : Multiplicative factors used in the prediction of the expected number of events from the CI/DY process. The uncertainties in the EW k-factors are 8%. number of primary vertices per bunch crossing. This effect is taken into account by weighting simulated events so that the distribution of the number of reconstructed primary vertices per event matches that in data. The data taking period was divided into two sections, 011A and 011B, in which the pileup conditions were quite different, as shown in Fig. 5. The weighting factors are determined separately for the two data sets. Simulated event yields for the combined data set are determined from a luminosity-weighted average. # Events 8 6 4 3-1 011A L dt =.41 fb -1 011B L dt =.86 fb 011A 011B CMS Preliminary s = 7 TeV 0 0 5 15 0 5 30 35 # Primary vertices Figure 5: Number of events with a given number of reconstructed primary vertices from data for the 011A and 011B time periods. 4.4 Higher-order strong and electroweak corrections Since we use the LO generator PYTHIA to simulate CI/DY events, we determine a QCD k- factor from the ratio of MC@NLO to PYTHIA event yields, at the generator level. The resulting k-values as a function of Mµµ Low are given in Table. The large samples of simulated events result in statistical uncertainties less than 0.5%. The effect of higher-order electroweak (EW) processes on DY production is quantified by a
4.5 Non-DY SM backgrounds 7 mass-dependent EW k-factor reported in Ref. [31]. The values of the EW k-factor, as a function of M Low µµ, are given in Table. 4.5 Non-DY SM backgrounds Using the simulation samples listed in Table 1, event yields are predicted for various non-dy SM background processes, as shown in Table 3. The yields are given as a function of Mµµ Low and the yields are scaled to the integrated luminosity of the data, 577±116 pb 1 [3]. For comparison, the expected yields are also shown for DY events. The non-zero backgrounds, in decreasing order of importance, are t t, diboson (WW/WZ/ZZ), W (including W+jets, tw, and tw), and Z ττ. The QCD background is negligible. For Mµµ Low > 00 GeV/c the statistical uncertainty in the non-dy background is large, but the absolute yield is much smaller than that for DY. M Low µµ ( GeV/c ) Z ττ W+Jets+ tw+tw t t Diboson sum non-dy DY 00 5.57 44.88 49.51 114.66 594.6 ± 5.75 330.03 ± 40.75 300 0.00 11.87 98.77 35.99 146.63 ± 1.98 844.30 ± 8.14 400 0.00 3.00 4.53 11.8 39.34 ± 1.03 91.5 ± 4.49 500 0.00 0.90 7.70 4.69 13.9 ± 0.60 16.71 ±.47 600 0.00 0.3.74. 5.19 ± 0.38 57.69 ± 0.35 700 0.00 0.06 1.05 0.81 1.9 ± 0. 9.7 ± 0.4 800 0.00 0.06 0.31 0.49 0.87 ± 0.15 15.40 ± 0.16 900 0.00 0.06 0.04 0.4 0.35 ± 0. 8.47 ± 0. 00 0.00 0.06 0.04 0. 0.0 ± 0.07 4.76 ± 0.03 10 0.00 0.06 0.04 0.09 0.19 ± 0.07.78 ± 0.0 100 0.00 0.06 0.00 0.01 0.07 ± 0.05 1.65 ± 0.01 1300 0.00 0.06 0.00 0.01 0.07 ± 0.05 0.98 ± 0.01 1400 0.00 0.06 0.00 0.01 0.07 ± 0.05 0.59 ± 0.01 1500 0.00 0.06 0.00 0.00 0.06 ± 0.05 0.35 ± 0.01 Table 3: Expected event yields for non-dy SM backgrounds. DY event yields are shown for comparison. 4.6 Predicted event yields Event yields corresponding to the integrated luminosity of the data are predicted as a function of Λ and Mµµ Low, including the contributions from the CI/DY process and non-dy SM backgrounds. The predictions for destructive and constructive interference are given in Tables 4 and 5. For destructive interference, there are regions of the M Low µµ Λ parameter space where the predicted number of CI/DY events is less than the predicted number of DY events. An example is M Low µµ = 00 GeV/c, and Λ 8 TeV. The limit-setting procedure, described below in section 5, cannot accommodate this situation. However, for the region of parameter space M Low µµ > 600 GeV/c and Λ > 7 TeV of interest in limit setting, the expected number of CI/DY events is always greater than the expected number of DY events. For constructive interference, the expected number of CI/DY events exceeds the expected number of DY events for all values of Λ and M Low µµ. 5 Expected and observed lower limits on Λ 5.1 Dimuon mass distribution from data The observed number of events versus M Low µµ are given in Table 4. The distribution of M µµ is plotted in Fig. 6. There are 145 71 µ + µ pairs passing the analysis cuts and out of these 1 860 pairs have invariant mass > 10 GeV/c.
8 5 Expected and observed lower limits on Λ -0.5cm Mµµ Low 00 300 400 500 600 700 800 900 00 10 100 1300 1400 1500 (GeV/c ) data 430.0 13.0 338.0 141.0 57.0 8.0 14.0 13.0 8.0 3.0.0 1.0 0.0 0.0 DY 4140.9 19.0 348.8 140.8 58.7 7.8 14. 7.7 3.6. 1. 1.0 0.6 0.6 Λ (TeV) 18 4091.7 05.8 334.3 136.8 58. 7.7 14.9 7.4 4.0.3 1.7 1. 0.9 0.7 17 45.0 19.4 338.5 137.1 57.9 6.5 14.3 6.0.9 1.8 1.0 0.7 0.5 0.3 16 41.4 14.7 337.8 137.5 59.7 8.9 15.0 7.7 4.1.6 1.7 1.1 0.8 0.4 15 40.9 1.1 338.1 138. 60.3 9.1 15. 8.1 4.8 3.0.0 1. 0.9 0.5 14 4079. 05.4 333.7 136.3 60.5 8.7 14.9 8.4 4.5.9 1.8 1. 0.9 0.4 13 4089.4 14.3 336. 136.7 59.8 9. 16.0 9. 5.1 3.1 1.9 1.1 0.6 0.3 1 4078.0 06.8 337.9 141.3 63.5 3.1 16.8 9.4 5.6 3.5.3 1.5 0.9 0.4 11 4059. 01.6 331.9 138.3 63.3 3.1 18..8 6.1 4.6 3.1. 1.4 1.0 4073.0 05.8 34. 143.8 66.7 37. 3.1 15.3 9.3 6. 4.5.9.6 1.7 9 4063.9 17.0 353.4 151.4 75.3 44.7 7.7 17.5 1.0 8. 6.0 4.7 3..3 8 4076.6 31.5 366.6 168.0 87.9 56.0 37. 5.5 18.5 13.6 9.6 7.0 4.8 3.7 7 415.5 81.3 407.8 0.1 10.9 8.0 60.0 45.3 3.9 4.9 18.1 13.4 9.0 6.0 6 4194.9 1164.9 494.5 83.9 187.6 136. 4.4 80. 60.4 46.9 34.1 3. 17.0 11.0 5 4450.4 140.8 713.0 479.1 348.8 70.6 13. 165.9 18.5 0.5 77. 58.1 41.6 8.3 4 555.9 169.6 1381.8 47.5 807.6 641.4 515.6 401.9 315.6 41.8 180.6 130. 94.8 66.3 3 8663.8 553. 4016.6 368. 59.8 081.3 1668.4 198.7 17.8 773.5 595. 447.9 31.1 4.0 Table 4: Number of events observed, expected for DY production, and expected for CI/DY production for destructive interference with given Λ. -0.5cm Mµµ Low 00 300 400 500 600 700 800 900 00 10 100 1300 1400 1500 (GeV/c ) data 430.0 13.0 338.0 141.0 57.0 8.0 14.0 13.0 8.0 3.0.0 1.0 0.0 0.0 DY 4140.9 19.0 348.8 140.8 58.7 7.8 14. 7.7 3.6. 1. 1.0 0.6 0.6 Λ (TeV) 18 4151.1 5.5 364.6 150.6 66.9 34.1 18.4 11.9 6. 3.7.5 1.7 1. 0.8 17 4155.5 55.9 364.4 15. 69. 35. 18.8 11.7 6.4 4.3 3.1 1.9 1.4 1.0 16 4193.6 69.9 370.8 156.7 71.0 36.1 0.4 1.5 7.3 4.3.6 1.6 1. 0.9 15 418.0 6.0 371. 159.4 73.0 37.0.8 14.7 8.4 5.1 3.6.4 1.8 1.3 14 419.6 68.3 374.1 158.0 74.6 37.5 1.4 14.0 8.9 5.5 3.4.4 1.9 1. 13 4188.5 94.4 383.6 167.6 79.7 41. 5.0 16.4.3 6.5 4.0.7 1.9 1.6 1 447.3 96. 385.0 173.9 84.9 45.6 7. 17.7.9 7.1 4.4.8 1.8 1.3 11 455.4 111.9 394.9 178.1 91.5 51.3 30.7 18.5 1.3 8.6 5.6 4.1.6 1.9 488.3 1137.0 41.3 188. 98.8 55.9 34..0 15.8.9 7.5 4.9 3.8.7 9 4350.9 1175.3 447. 19. 11.3 73.1 47.1 31.0 1.7 15.1.6 7.6 4.7 3.1 8 4397.7 18.6 477.4 41.9 138.3 90.3 60. 41.7 30.5.1 16. 11.4 7.4 4.8 7 4550.6 1341.5 57.9 313.7 186.3 14.4 90.4 65.0 46.8 3.7 4.1 17. 1.4 8.5 6 4784.8 151.9 708.1 43.7 77.1 193.7 14.8 6.4 78.6 59.6 43. 31.5 3.3 15.4 5 566.0 1905.3 4.1 689.4 481.8 357.6 79.6 11.5 159.9 11.4 90.3 66.1 47.1 33.1 4 6550.5 946. 1869.5 1374.8 7.3 791.4 61.0 471.8 364.7 77. 07. 151.3 9.8 75.0 3 966.9 6639.3 488.1 3843.6 947.3 38.0 1830.0 140.5 86. 81.5 617.7 464. 339.5 34.4 Table 5: Number of events observed, expected for DY production, and expected for CI/DY production for constructive interference with given Λ.
5.1 Dimuon mass distribution from data 9 - Events / GeV c 6 5 3 CMS Preliminary s = 7 TeV -1 L dt = 5.3 fb Data Λ = 4 TeV (destr.) Λ = 4 TeV (const.) Λ = 5 TeV (destr.) Λ = 5 TeV (const.) DY Diboson Z ττ tw + t W W+Jets QCD tt -1-3 500 00 1500 000 (GeV/c ) M µµ Figure 6: Observed spectrum of M µ + µ and predictions from the SM and LLIM CY/DY model for Λ = 4 and 5 TeV, for constructive and destructive interference. These Λ values correspond approximately to the best limits previous to this analysis.
5 Expected and observed lower limits on Λ 5. Limit setting procedure The expected and observed 95% confidence level lower limits on Λ are determined using the CL s modified frequentist procedure described in Ref. [33], taking the profile likelihood ratio as a test statistic. The expected mean for the number of signal events is the total number of events expected using a given Λ less the total number of events expected using the DY process. The expected mean for the number of background events is the total number of events using the DY process. The observed and expected numbers of events are given in Tables 4 and 5. Systematic uncertainties are estimated from a variety of sources, summarized in Table 6. The systematic uncertainties on integrated luminosity, acceptance, and expected background are included as nuisance parameters in the limit setting procedure. The determination of the uncertainty in integrated luminosity is described in Ref. [3]. The acceptance uncertainty is dominated by the difference between acceptances determined using DY and CI/DY simulations, as discussed in section 4.. The uncertainty in background is dominated by the effect of PDF variations which are evaluated using the PDF4LHC procedure [34]. The larger of the + or - variation is chosen to set a conservative limit. The PDF variation is added in quadrature with the statistical uncertainties on the DY background, non-dy backgrounds, and QCD k-factor. Source Uncertainty (%) Integrated luminosity. Acceptance 3.0 Background estimate 14.7 PDF set variation (+) 1.3 PDF set variation (-) 9.9 DY event yield 0.8 non-dy event yield 15.0 QCD k-factor 0. Table 6: Sources of systematic uncertainty. Where appropriate, the values are quoted for M µµ > 700 GeV/c, Λ = 13 TeV, and for constructive interference. 5.3 Results for limits on Λ The observed and expected lower limits on Λ at 95% confidence level (CL) as a function of Mµµ Low for destructive and constructive interference are shown in Figs. 7a and 7b. The 1- and -σ uncertainties in the expected limits are indicated by the shaded bands. For both types of interference, the sensitivity to Λ is maximal for Mµµ Low in the middle of the range studied. In both cases we select minimum mass of 700 GeV/c, resulting in an observed (expected) limit of 9.5 TeV (9.8 TeV) for destructive interference and 13.0 TeV (13.0 TeV) for constructive interference. The effects of individual systematic uncertainties are studied by finding the change in limit for an explicit change in each uncertainty, or central value to which it corresponds. The PDF uncertainty of approximately 1% has the largest influence on the limits. For example, if the PDF uncertainty is set to zero, the constructive limit is about 6% higher. Since the EW k-factor may or may not apply to the new physics associated with CI, we study the effect of removing this correction, which results in an increase in the constructive limit of about 4%. Including the EW k-factor for CI gives the more conservative limit.
11 95% C.L. Λ [TeV] 1 11 9 8 7 6 5 4 3 CMS Preliminary -1 s = 7 TeV, L dt = 5.3 fb Expected limit Expected limit 1σ Expected limit σ Observed limit 500 00 1500 (GeV/c ) Low M µµ Λ [TeV] 95% C.L. 18 16 14 1 8 6 4 CMS Preliminary -1 s = 7 TeV, L dt = 5.3 fb Expected limit Expected limit 1σ Expected limit σ Observed limit 500 00 1500 (GeV/c ) Low M µµ (a) Figure 7: Observed and expected limits as a function of M Low µµ for (a) destructive interference and (b) constructive interference. (b) 6 Conclusions Using the CMS detector, we measure the invariant mass distribution of µ + µ pairs produced in pp collisions at a center-of-mass energy of 7 TeV, based on an integrated luminosity of 5.3 fb 1. The invariant mass distribution in the range 00 to 000 GeV/c is consistent with Drell-Yan and other standard model sources of dimuons. We analyze the data in the context of a leftleft isoscalar contact interaction model of quark and muon compositeness, with energy scale parameter Λ. We set lower limits on Λ at the 95% CL of 9.5 TeV for destructive interference and 13.0 TeV for constructive interference. These limits represent significant improvements on the current published values of 4.5 TeV and 4.9 TeV. References [1] E. Eichten, K. Lane, and M. Peskin, New Tests for Quark and Lepton Substructure, Phys. Rev. Lett. 50 (1983) 811 814. [] E. Eichten, I. Hinchliffe, K. Lane et al., Supercollider Physics, Rev. Modern Phys. 56 (1984) 579 707. [3] S. Drell and T. Yan, Massive Lepton-Pair Production in Hadron-Hadron Collisions at High Energy, Phys. Rev. Lett. 5 (1970) 316 30. [4] T. Sjostrand, S. Mrenna, and P. Skands, Pythia 6.4 Physics and Manual, JHEP 05 (006). [5] K. Nakamura et al., Particle Data Group, J. Phys. G37 (0). [6] ALEPH Collaboration, Measurement of the High-Mass Drell-Yan Cross Section and Limits on Quark-Electron Compositeness Scales, Eur. Phys. J. C 49 (007) 411 437. [7] DELPHI Collaboration, Measurement and interpretation of fermion-pair production at LEP energies above the Z resonance, Eur. Phys. J. C 45 (004) 589 63.
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