Search for contact interactions in opposite-sign dimuon events in pp collisions at sqrt(s) = 7 TeV

Results are reported from a search for the effects of contact interactions using events with a high-mass, oppositely charged muon pair. The events are collected in proton-proton collisions at sqrt(s) = 7 TeV using the Compact Muon Solenoid detector at the Large Hadron Collider. The data sample corresponds to an integrated luminosity of 5.3 inverse femtobarns. 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-handed isoscalar current and an energy scale parameter Lambda. The 95% confidence level lower limit on Lambda is 9.5 TeV under the assumption of destructive interference between the standard model and contact-interaction amplitudes. For constructive interference, the limit is 13.1 TeV. These limits are comparable to the most stringent ones reported to date.


Introduction
The existence of three families of quarks and leptons might be explained if these particles are composed of more fundamental constituents.In order to confine the constituents (often referred to as "preons" [1,2]) and to account for the properties of quarks and leptons, a new strong gauge interaction, metacolor, is introduced.Below a given interaction energy scale Λ, the effect of the metacolor interaction is to bind the preons into metacolor-singlet states.For parton-parton center-of-mass energy less than Λ, the metacolor force will manifest itself in the form of a flavor-diagonal contact interaction (CI) [3,4].In the case where both quarks and leptons share common constituents, the Lagrangian density for a CI leading to dimuon final states can be written as 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 left-and right-handed muons.By convention, g 2 0 /4π = 1.The parameter Λ characterizes the compositeness energy scale.The parameters η ij allow for differences in magnitude and phase among the individual terms.Lower limits on Λ are set separately for each term with η ij taken, by convention, to have a magnitude of one.
The dimuons from the subprocesses for standard model (SM) Drell-Yan (DY) [5] production and from CI production can have the same helicity state.In this case, the scattering amplitudes are summed, resulting in an interference term in the cross section for pp → X + µ + µ − , as illustrated schematically in Fig. 1.
The differential cross section corresponding to the combination of a single term in Eq. 1 with DY production can be written as where M µµ is the invariant dimuon mass, I is due to interference, and C is purely due to the CI.Note that η ij = +1 corresponds to destructive interference and η ij = −1 to constructive interference.The processes contributing to the cross section in Eq. ( 2) are denoted collectively by "CI/DY".The difference dσ CI/DY /dM µµ − dσ DY /dM µµ is the signal we are searching for in this paper.
Figure 1: Schematic representation of the addition of DY (left) and CI (right) amplitudes, for common helicity states, contributing to the total cross section for pp → X + µ + µ − .For the results presented in this paper, the analysis is limited to a dimuon mass range from 200 to 2000 GeV/c 2 .The lower mass is sufficiently above the Z-peak so that a deviation from DY production would be observable.The highest dimuon mass observed is between 1300 and 1400 GeV/c 2 and, for the values of Λ where the limits are set, less than one event is expected for dimuon masses above 2000 GeV/c 2 .In order to limit the mass range in which the detector acceptance has to be evaluated, we therefore choose an upper mass cutoff of 2000 GeV/c 2 .To optimize the limit on Λ, a minimum mass M min µµ is varied between the lower and upper mass values, as described in Section 6.

CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the field volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass/scintillator hadron calorimeter.Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke.Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors.A detailed description of the CMS detector can be found in Ref. [27].
The tracker and muon detector are important sub-systems for this measurement.The tracker measures charged particle trajectories within the range |η| < 2.5, where pseudorapidity η = − ln[tan(θ/2)], and polar angle θ is measured from the beam axis.The tracker provides a transverse momentum (p T ) resolution of about 1% at a few tens of GeV/c to 10% at several hundred GeV/c [28], where p T is the component of momentum in the plane perpendicular to the beam axis.Tracker elements include about 1400 silicon pixel modules, located close to the beamline, and about 15 000 silicon microstrip modules, which surround the pixel system.Tracker detectors are arranged in both barrel and endcap geometries.The muon detector comprises 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| < 2.4.
For the trigger path used in this analysis, the first level (L1) selects events with a muon candidate based on a sub-set of information from the muon detector.The trigger muon is required to have |η| < 2.1 and p T above a threshold that was raised to 40 GeV/c by the end of the datataking period.This cut has little effect on the acceptance for muon pairs with masses above 200 GeV/c 2 .The small effect is included in the simulation.The high level trigger (HLT) refines the L1 selection using the full information from both the tracker and muon systems.

Event selection criteria
This analysis uses the same event selection as the search for new heavy resonances in the dimuon channel, discussed in Ref. [29].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 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 less than 0.2 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 and within a cone surrounding the muon, is less than 10% of the p T of the muon.The cone is defined by the condition ∆R = (∆η) 2 + (∆φ) 2 = 0.3, where φ is the azimuthal angle of a track, and the differences ∆η and ∆φ are determined with respect to the muon's direction.
The two muons are required to have opposite charge and to be consistent with originating from a common vertex.To suppress cosmic ray muons that are in time with the collision event, the angle between the two muons must be smaller than π − 0.02 radians.At least one of the reconstructed muons must be matched (within ∆R < 0.2 and ∆p T /p T < 1) to the HLT muon candidate.
If an event has more than two muons passing the above requirements, then the two highest-p T muons are selected, and the event is retained only if these muons are oppositely charged.Only three such events are observed with selected dimuon mass above 200 GeV/c 2 , and in all three cases, the dimuon mass is less than 300 GeV/c 2 .Thus, events with multiple dimuon candidates play essentially no role in the analysis.

Simulation of SM and CI dimuon production
This section describes the method used to simulate the mass distribution from the CI/DY process of Eq. ( 2), including the leading-order (LO) contributions from DY and CI amplitudes, their interference, the effects of next-to-leading-order (NLO) QCD and QED corrections, and the response of the detector.The predicted number of CI/DY events is the product of the generated number of CI/DY events, a QCD K-factor, a QED K-factor, and a factor denoted as "acceptance times migration" (A × M).The factor A × M is determined from the detector simulation of DY events, as explained below in Section 5.2.The simulation of background due to non-DY SM processes is also described.

Event samples with detector simulation
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 used are PYTHIA, with the CTEQ6.6Mimplementation [30] of parton distribution functions (PDF), POWHEG [31][32][33], and MADGRAPH5 [34].The detector simulation is based on GEANT4 [35].

Detector acceptance times mass migration
To simplify the analysis, we use the detector simulation for DY events to determine the detector response for CI/DY events, which have a behavior similar to that for DY events for the large values of Λ of interest in this analysis.For a given value of M min µµ , the product of acceptance  2. The error bars indicate statistical uncertainties based on simulation of the DY process.The systematic uncertainty is 3% as explained in the text.The increase of A × M at lower mass is due to the increase in acceptance, while at higher mass, it is dominated by the growth in mass resolution.Since the cross section falls steeply with mass, events tend to migrate from lower to higher mass over a range determined by the mass resolution.times migration (A × M) is given by the ratio of the number of DY events reconstructed with mass above M min µµ to the number of DY events generated with mass above M min µµ .Some of the reconstructed events have been generated with mass below M min µµ because of the smearing due to the mass reconstruction, which has a resolution of 6.5% at masses around 1000 GeV/c 2 , rising to 12% at 2000 GeV/c 2 .The dependence of A × M on M min µµ is plotted in Fig. 3 and values are given in Table 2.The increase of A × M at lower mass is due to the increase in acceptance, while at higher mass, it is dominated by the growth in mass resolution.Since the cross section falls steeply with mass, events tend to migrate from lower to higher mass over a range determined by the mass resolution.
To validate that the A × M factor based on DY production is applicable to CI/DY production, we compare event yields predicted using the A × M factor with those predicted using a simulation of CI/DY production.The study is performed for the cases of constructive interference with Λ = 5 and 10 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 in A × M is conservatively assigned this value.

Event pileup
During the course of the 2011 data taking period, the luminosity increased with time, resulting in an increasing "event pileup", the occurrence of multiple pp interactions recorded by the detector as a single event.The dependence of reconstruction efficiency on event pileup is studied by weighting simulated events so that the distribution of the number of reconstructed primary vertices per event matches that in data.The reconstruction efficiency is found to be insensitive to the variations in event pileup encountered during the data taking period.
Table 2: Multiplicative factors used in the prediction of the expected number of events from the CI/DY process.The uncertainties shown are statistical.The systematic uncertainty is 3% for A × M and 3% for the QCD K-factor, as explained in the text.The uncertainty in the QED Kfactor is dominated by the systematic uncertainty that is assigned as the size of the correction, |(QED K-factor) − 1|, to allow for systematic uncertainty in the generator.

Higher-order strong and electromagnetic corrections
Since we use the leading-order generator PYTHIA to simulate the CI/DY production, we must determine a QCD K-factor which takes into account higher-order initial-state diagrams.Under the assumption that the QCD K-factor is the same for DY and CI/DY events, we determine the QCD K-factor as the ratio of DY events generated using the next-to-leading-order generator MC@NLO [36] to those generated using PYTHIA.The MC@NLO generator is used with the same PDF set as used with PYTHIA.The resulting QCD K-factor as a function of M min µµ is given in Table 2.The large sizes of the simulated event samples result in statistical uncertainties less than 0.5%.The systematic uncertainty is assigned the value 3%, the size of the correction [37] between next-to-next-to-leading order (NNLO) and NLO DY cross sections.For SM processes other than DY production, the QCD K-factor is found, independent of dimuon mass, from the ratio of the cross section determined using MC@NLO to the cross section determined from PYTHIA.
The effect of higher-order electromagnetic processes on CI/DY production is quantified by a mass-dependent QED K-factor determined using the HORACE generator [38].The values of the QED K-factor, as a function of M min µµ , are given in Table 2.The systematic uncertainty is assigned as the size of the correction, |(QED K-factor) − 1|, since the effect of higher-order QED corrections on the new physics of CI is unknown.

Non-DY SM backgrounds
Using the samples of simulated events 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 M min µµ and they are scaled to the integrated luminosity of the data, 5.28 ± 0.12 fb −1 [39].For comparison, the expected yields are also shown for DY events.The relevant backgrounds, in decreasing order of importance, are tt, diboson (WW/WZ/ZZ), W (including W+jets and tW), and Z → ττ production.The background from multi-jet events is studied using both the simulation sample listed in Table 1 and control samples from data, as reported in Ref. [29].The results of either method indicate that no multi-jet background events are expected for M min µµ > 200 GeV/c 2 .For M min µµ > 1000 GeV/c 2 the fractional statistical uncertainty in the non- DY background is large, but the absolute yield is much smaller than that for DY background.

Predicted event yields
Using the methods described above, the sum of the event yields for the CI/DY process and the non-DY SM backgrounds, for the integrated luminosity of the data sample, are predicted as a function of M min µµ and Λ.The predicted event yields for destructive and constructive interference are given in Tables 4 and 5.
For destructive interference, there is a region of the M min µµ -Λ parameter space where the predicted number of events is less than for SM production.This "reduced-yield" region is indicated in Table 4.The region of parameter space, M min µµ > 600 GeV/c 2 and Λ ≤ 12 TeV, where our expected limit is most stringent (see Fig. 5(a)), lies outside the reduced-yield region.For constructive interference, the predicted number of events is always larger than for SM production.

Dimuon mass distribution from data
The observed numbers of events versus M min µµ are given in Table 4.The observed distribution of M µµ is plotted in Fig. 4 along with the expected distributions from the SM and for CI/DY plus non-DY SM processes, for three illustrative values of Λ.The data are consistent with the predictions from the SM, dominated by DY production.

Limit-setting procedure
Since the data are consistent with the SM, we set lower limits on Λ in the context of the LLIM.The expected and observed 95% CL lower limits on Λ are determined using the CL S modifiedfrequentist procedure described in [40,41], taking the profile likelihood ratio as a test statistic [42].The expected mean number of events for a signal from CI is the difference of the number of CI/DY events expected for a given Λ, and the number of DY events.The expected mean number of background events is the sum of events from the DY process and the non-DY SM backgrounds.The observed and expected numbers of events are given in Tables 4 and 5.
Table 4: Observed and expected number of events for illustrative values of M min µµ .The expected yields are shown for SM production and for the sum of CI/DY production (for destructive interference and for a given Λ) and non-DY SM backgrounds.For each column of M min µµ , the expected yield for CI/DY + non-DY SM production that is just above that expected for SM production is highlighted in red.Entries above the highlighted ones correspond to values of Λ for which the expected yield is less than that for SM production, because of the destructive interference term in the cross section.As discussed in Section 6.3, the best expected limit is obtained for M min µµ = 1100 GeV/c 2 .For this choice, the expected event yield is highlighted in gray that corresponds to the value of Λ closest to the observed 95% CL lower limit on Λ of 9.5 TeV (9.7 TeV expected).Systematic uncertainties in the predicted signal and background event yields are estimated from a variety of sources and included as nuisance parameters in the limit-setting procedure.Significant sources of systematic uncertainty are given in Table 6.The uncertainty in the integrated luminosity is described in Ref. [39].The uncertainty in the CI/DY acceptance is explained in Section 5.2.The uncertainties in the prediction of backgrounds depend on the value of M min µµ .These uncertainties are given in Table 6 for the values of M min µµ chosen for limits on Λ with destructive and constructive interference.The PDF uncertainty in the expected yield of DY events is evaluated using the PDF4LHC procedure [43].The uncertainties in the QED and QCD K-factors are explained in Sec.5.3.The uncertainty from non-DY backgrounds is due to the statistical uncertainty associated with the simulated event samples.The systematic uncertainties which decrease the limit on Λ by the largest amounts are the uncertainties on the PDF and QED K-factor.When both these uncertainties are set to zero, the limit for destructive interference is increased by 0.4% and the limit for constructive interference is increased by 3.0%.Thus, the systematic uncertainties degrade the limits by only small amounts.
We considered possible systematic uncertainties in modeling the detector response by comparing kinematic distributions between data and simulation of DY and non-DY SM processes.There are no differences in these distributions that could lead to significant systematic uncertainties through their effect on selection efficiency and mass resolution.

Results for limits on Λ
The observed and expected lower limits on Λ at 95% CL as a function of M min µµ for destructive and constructive interference are shown in Figs.5(a) and 5(b).The value of M min µµ , chosen to maximize the expected sensitivity, is 1100 GeV/c 2 for destructive interference, and 800 GeV/c 2 for constructive interference.The observed (expected) limit is 9.5 TeV (9.7 TeV) for destructive interference and 13.1 TeV (12.9 TeV) for constructive interference.The variations in the observed limits lie almost entirely within the 1-σ (standard deviation) uncertainty bands in the expected limits, consistent with statistical fluctuations.The number of expected events corresponding to the observed limits on Λ are highlighted in Tables 4 and 5.

Summary
The CMS detector is used to 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 200 to 2000 GeV/c 2 is found to be consistent with standard model sources of dimuons, which are dominated by Drell-Yan production.The data are interpreted in the context of a quark-and muon-compositeness model with a left-handed isoscalar current and an energy scale parameter Λ.The 95% confidence level lower limit on Λ is 9.5 TeV under the assumption of destructive interference between the standard model and contact-interaction amplitudes.For constructive interference, the limit is 13.1 TeV.These limits are comparable to the most stringent ones reported to date.µµ , chosen to maximize the expected sensitivity, is 1100 GeV/c 2 for destructive interference, and 800 GeV/c 2 for constructive interference.The observed (expected) limit is 9.5 TeV (9.7 TeV) for destructive interference and 13.1 TeV (12.9 TeV) for constructive interference.The observed limit at the value chosen for M min µµ is indicated with a red plus sign.The variations in the observed limits lie almost entirely within the 1-σ bands, consistent with statistical fluctuations.search Council (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of Czech Republic; the Council of Science and Industrial Research, India; the Compagnia di San Paolo (Torino); and the HOMING PLUS programme of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund.

Figure 2 :
Figure 2: Simulated dimuon mass spectra using the left-left isoscalar model for different values of Λ for (a) destructive interference and (b) constructive interference.The events are generated using the PYTHIA Monte Carlo program with kinematic selection requirements that approximate the acceptance of the detector.As Λ increases, the effects of the CI are reduced, and the event yield approaches that for DY production.The model predictions are shown over the full mass range, although the model is not valid as M µµ c 2 approaches Λ.The integrated luminosity corresponds to 63 fb −1 .

Figure 3 :
Figure 3: Acceptance times migration, A × M, versus M min µµ .Corresponding values and uncertainties are given in Table2.The error bars indicate statistical uncertainties based on simulation of the DY process.The systematic uncertainty is 3% as explained in the text.The increase of A × M at lower mass is due to the increase in acceptance, while at higher mass, it is dominated by the growth in mass resolution.Since the cross section falls steeply with mass, events tend to migrate from lower to higher mass over a range determined by the mass resolution.

Figure 4 :
Figure 4: Observed spectrum of M µµ and predictions for SM and CI/DY plus non-DY SM production.Predictions are shown for three illustrative values of Λ, for constructive and destructive interference.The error bars for data are 68% Poisson confidence intervals.

Figure 5 :
Figure 5: Observed and expected limits as a function of M min µµ for (a) destructive interference and (b) constructive interference.The value of M minµµ , chosen to maximize the expected sensitivity, is 1100 GeV/c 2 for destructive interference, and 800 GeV/c 2 for constructive interference.The observed (expected) limit is 9.5 TeV (9.7 TeV) for destructive interference and 13.1 TeV (12.9 TeV) for constructive interference.The observed limit at the value chosen for M min µµ is indicated with a red plus sign.The variations in the observed limits lie almost entirely within the 1-σ bands, consistent with statistical fluctuations.

Table 1 :
Description of event samples with detector simulation.The cross section σ and integrated luminosity L are given for each sample generated.

Table 3 :
[39]cted event yields for DY and non-DY SM backgrounds.The uncertainties shown are statistical.A systematic uncertainty of 2.2% arises from the determination of integrated luminosity[39].

Table 5 :
Observed and expected number of events as in Table4.Here CI/DY predictions are for constructive interference.Shown with gray highlighting is the expected event yield corresponding to the value of Λ closest to the observed 95% CL lower limit on Λ of 13.1 TeV (12.9 TeV expected) for M min µµ selected to be 800 GeV/c 2 .

Table 6 :
Systematic uncertainties affecting the limit on Λ, evaluated for the values of M min µµ that provide the best expected limits for constructive and destructive interference.