Search for contact interactions using the inclusive jet p
Tspectrum in pp collisions at
p
ffiffiffi
s
¼ 7 TeV
S. Chatrchyan et al.*(CMS Collaboration)
(Received 21 January 2013; published 26 March 2013)
Results are reported of a search for a deviation in the jet production cross section from the prediction of perturbative quantum chromodynamics at next-to-leading order. The search is conducted using a 7 TeV proton-proton data sample corresponding to an integrated luminosity of 5:0 fb1, collected with the Compact Muon Solenoid detector at the Large Hadron Collider. A deviation could arise from interactions characterized by a mass scale too high to be probed directly at the LHC. Such phenomena can be modeled as contact interactions. No evidence of a deviation is found. Using theCLscriterion, lower limits are set on of 9.9 TeVand 14.3 TeV at 95% confidence level for models with destructive and constructive interference, respectively. Limits obtained with a Bayesian method are also reported.
DOI:10.1103/PhysRevD.87.052017 PACS numbers: 13.85.Rm
I. INTRODUCTION
Interactions at an energy scale much lower than the mass of the mediating particle can be modeled by contact inter-actions (CI) [1–4] governed by a single mass scale conven-tionally denoted by. A search for contact interactions is therefore a search for interactions whose detailed charac-teristics become manifest only at higher energies. Contact interactions can affect the jet angular distributions as well as the jet transverse momentum (pT) spectra, particularly for low-rapidity jets. Lower limits on have been set by the CDF [5], D0 [6], and ATLAS [7] collaborations. The Compact Muon Solenoid (CMS) collaboration has previ-ously measured the dijet angular distribution [8] using a data set of pffiffiffis¼ 7 TeV proton-proton collisions corre-sponding to an integrated luminosity of 2:2 fb1, and found > 8:4 TeV and > 11:7 TeV at 95% confidence level (C.L.), for models with destructively and construc-tively interfering amplitudes, respecconstruc-tively.
The inclusive jet pTspectrum, i.e., the spectrum of jets in pþ p ! jet þ X events, where X can be any collection of particles, is generally considered to be less sensitive to the presence of contact interactions than the jet angular distribution. This perception is due to the jet pTspectrum’s greater dependence on the jet energy scale (JES) and on the parton distribution functions (PDF), which are difficult to determine accurately. However, considerable progress has been made by the CMS collaboration in understanding the JES [9]. The understanding of PDFs has also improved greatly at high parton momentum fraction [10–12], in part because of the important constraints on the gluon PDF provided by measurements at the Tevatron [13,14]. These developments have made the jet pTspectrum a competitive
observable to search for phenomena described by contact interactions, reprising the method that was used in searches by CDF [15] and D0 [16].
In this paper, we report the results of a search for a deviation in the jet production cross section from the next-to-leading-order (NLO) quantum chromodynamics (QCD) prediction of jets produced at low-rapidity with transverse momenta >500 GeV. The analysis is based on a 7 TeV proton-proton data sample corresponding to an integrated luminosity of5:0 fb1, collected with the CMS detector at the Large Hadron Collider (LHC).
II. THEORETICAL MODELS
The experimental results are interpreted in terms of a CI model described by the effective Lagrangian [3,17]
L¼ 2
2ð qLqLÞð qLqLÞ; (1) where qL denotes a left-handed quark field and ¼ þ1 or 1 denote destructively or constructively interfering amplitudes, respectively. The amplitude for jet production can be written as
a¼ aSMþ aCI;
where aSM and aCI are the standard model (SM) and contact interaction amplitudes, respectively. Since the am-plitude is linear in ¼ 1=2, the cross section k in the kth jet pTbin is given by
k¼ ckþ bkþ ak2; (2) where ck, bk, and ak are jet-pT-dependent coefficients.
We use models characterized by the cross section QCDNLOþ CIðÞ, where QCDNLO¼ ck is the inclusive jet cross section computed at next-to-leading order, and CIðÞ ¼ bkþ ak2 parametrizes the deviation of the inclusive jet cross section from the QCD prediction arising from the hypothesized contact interactions. The QCDNLO cross section is calculated with version 2.1.0-1062 of the *Full author list given at the end of the article.
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attridistri-bution to the author(s) and the published article’s title, journal citation, and DOI.
fastNLO program with scenario table fnl2332y0.tab [18] using the NLO CTEQ6.6 PDFs [19]. We do not unfold the observed inclusive jet pTspectrum. Instead, the NLO QCD jet pT spectrum is convolved with the CMS jet response function, where the jet energy resolution (JER) pT for low-rapidity jets is given by
PT ¼ PT ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 p2Tþ s2pm T pT þ c 2 s ; (3) with n¼ 5:09, s ¼ 0:512, m ¼ 0:325, c ¼ 0:033, and compared directly with the observed spectrum using a likelihood function. Equation (3) is the standard form for the calorimeter resolution function, modified to account for
a weak pT dependence of the coefficient of the (p1T ) stochastic term and to model better the resolution of low pTjets by using a negative coefficient for the (p2T ) noise term. For brevity, we shall refer to the smeared spectrum as the NLO QCD jet pTspectrum.
The signal term CIðÞ is modeled by subtracting the leading-order (LO) QCD jet cross sectionðQCDLOÞ from the LO jet cross section computed with a contact term. The leading-order jet pT spectra are computed by generating events with and without a CI term using the program PYTHIA 6.422, the Z2 underlying event tune [17,20], and the same CTEQ PDFs used to calculate QCDNLO. The generated events are processed with the full CMS detector
(GeV) T Jet p 1000 1500 2000 NLO )]/QCDΛ +CI( NLO [QCD 0 5 10 15 20 = 3 TeV Λ = 5 TeV Λ = 8 TeV Λ = 12 TeV Λ = 7 TeV s -1 CMS Simulation L = 5 fb | < 0.5 η |
FIG. 1 (color online). The cross section ratios, f¼½QCDNLOþ CIðÞ=QCDNLO, with ¼ 3, 5, 8, and 12 TeV. The points with
error bars are the theoretical values of the cross section ratios. The curves are the results of a fit of Eq. (4) simultaneously to the four cross section ratios. The NLO QCD jet pT spectrum is calculated using the nominal values of the JES, JER, PDF, renormalization and factorization scales for models with destruc-tive interference. The values of the parameters of the fit are given in TableI.
TABLE I. The fit parameters associated with Fig.1. The first row lists the values of the parameters p1, p2, p3, and p4, while the remaining rows list the elements of the associated covariance matrix. p1 p2 p3 p4 1:5 103 3.6 1:9 103 5.2 p1 1:4 106 3:6 104 3:4 107 6:8 105 p2 3:6 104 9:2 102 8:4 105 1:7 102 p3 3:4 107 8:4 105 1:0 107 2:0 105 p4 6:8 105 1:7 102 2:0 105 4:1 103 (GeV) T Jet p 500 1000 1500 2000 NLO )] / QCDΛ + CI( NLO [QCD 0.9 1 1.1 Λ = 8 TeV = 10 TeV Λ = 12 TeV Λ = 14 TeV Λ = 7 TeV s -1 CMS Simulation L = 5 fb | < 0.5 η | destructive interference (GeV) T Jet p 500 1000 1500 2000 NLO )] / QCDΛ + CI( NLO [QCD 0.9 1 1.1 Λ = 8 TeV = 10 TeV Λ = 12 TeV Λ = 14 TeV Λ = 7 TeV s -1 CMS Simulation L = 5 fb | < 0.5 η | constructive interference
FIG. 2 (color online). The cross section ratios, f¼½QCDNLOþ CIðÞ=QCDNLO, with ¼ 8, 10, 12, and 14 TeV, for models
with destructive (top) and constructive (bottom) interference.
simulation program, based on GEANT4 [21]. Interactions between all quarks are included (Appendix A) and we consider models both with destructive and constructive interference between the QCD and CI amplitudes. We note that NLO corrections to the contact interaction model have recently become available [22], and we plan to use these results in future studies. These corrections are expected to change the results by less than 5%.
The jet pTdependence ofCIðÞ is modeled by fitting the ratio f¼ ½QCDNLOþ CIðÞ=QCDNLOsimultaneously to fourPYTHIACI models with ¼ 3, 5, 8, and 12 TeV. The fit is performed in this manner in order to construct a smooth interpolation over the four cross section ratios.
Several functional forms were investigated that gave sat-isfactory fits, including the ansatz [23]
f¼ 1 þ p1 pT 100 GeV p 2 1 TeV2 þ p3 pT 100 GeV p 4 1 TeV2 2 : (4)
In a generator-level study, we verified the adequacy of the extrapolation of Eq. (4) up to 25 TeV. The results of fitting Eq. (4) to models with destructive interference are shown in Fig.1. The fit shown in Fig.1uses the central values of the JES, JER, and PDF parameters and the renormalization (r) and factorization (f) scales set to r¼ f ¼ jetpT. Models with constructive interference are obtained by reversing the sign of the parameter p1. The fit parameters are given in TableI. Figures2and3show model spectra in the jet pT range 500 pT 2000 GeV for values of that are close to the limits reported in this paper. Figure2
shows that the jet production cross section is enhanced at sufficiently high jet pT. However, for interactions that interfere destructively, the cross section can decrease relative to the NLO QCD prediction. For example, for ¼ 10 TeV, the QCDNLOþ CI cross section is lower than the QCDNLO cross section for jet pT<1:3 TeV. Figure3shows the contact interaction signal,CIðÞ, as a function of jet pT.
III. EXPERIMENTAL SETUP
The CMS coordinate system is right-handed with the origin at the center of the detector, the x axis directed toward the center of the LHC ring, the y axis directed upward, and the z axis directed along the counterclockwise proton beam. We define to be the azimuthal angle, to be the polar angle, and the pseudorapidity to be ln ½tan ð=2Þ. The central feature of the CMS apparatus is a supercon-ducting solenoid of 6 m internal diameter, operating with a magnetic field strength of 3.8 T. Within the field volume are the silicon pixel and strip trackers and the barrel and endcap calorimeters with j j < 3. Outside the field vol-ume, in the forward region, there is an iron/quartz-fiber hadron calorimeter (3 < j j < 5). Further details about the CMS detector may be found elsewhere [24].
Jets are built from the five types of reconstructed parti-cles: photons, neutral hadrons, charged hadrons, muons, and electrons, using the CMS particle-flow reconstruction method [25] and the anti-kT algorithm with a distance parameter of 0.7 [26–28]. The jet energy scale correction is derived as a function of the jet pT and , using a pT-balancing technique [9], and applied to all components of the jet four momentum.
The results reported are based on data collected using unprescaled single-jet triggers with pT thresholds that were changed in steps from 240 to 300 GeV during the data-taking period. The trigger thresholds were changed in response to the increase in instantaneous luminosity. (GeV) T Jet p 500 1000 1500 2000 (pb/GeV) T /dp QCD σ - d T /dp QCD+CI σ d -0.006 -0.004 -0.002 0 = 8 TeV Λ = 10 TeV Λ = 12 TeV Λ = 14 TeV Λ = 7 TeV s -1 CMS Simulation L = 5 fb | < 0.5 η | destructive interference (GeV) T Jet p 500 1000 1500 2000 (pb/GeV) T /dp QCD σ - d T /dp QCD+CI σ d 0 0.002 0.004 0.006 = 8 TeV Λ = 10 TeV Λ = 12 TeV Λ = 14 TeV Λ = 7 TeV s -1 CMS Simulation L = 5 fb | < 0.5 η | constructive interference
FIG. 3 (color online). The CI signal spectra, defined as dQCDþCI=dpT dQCD=dpT ðpb=GeVÞ with ¼ 8, 10, 12, and 14 TeV, for models with destructive (top) and constructive (bottom) interference.
The jet trigger efficiency is constant, 98:8%, above 400 GeV, well below the search region. Events with hadron calorimeter noise are removed [29] and each se-lected event must have a primary vertex within 24 cm of the geometric center of the detector along the z axis and within 0.2 cm in the transverse x-y plane, defined by criteria described in [30]. The search is restricted to j j < 0:5 where the effects of contact interactions are predicted to be the largest [1–4]. The jet pT spectrum is
divided into 20 pT bins in the search region507 pT 2116 GeV, where the bin width is approximately equal to the jet resolution pTgiven in Eq. (3). No jets are observed above 2000 GeV transverse energy.
IV. RESULTS
In Fig. 4 we compare the observed inclusive jet pT spectrum with the NLO QCD jet pT spectrum, which is normalized to the total observed jet count in the search region using the normalization factor 4:007 0:009ðstatÞ fb1 (Sec. V). The normalization is the ratio of the observed jet count to the predicted cross section in the search region. The data and the prediction are in good agreement as indicated by two standard criteria, the Kolmogorov-Smirnov probability Pr(KS) of 0.66, and the 2per number of degrees of freedom of23:5=19. TableII
lists the observed jet counts. Figure 5 compares the ob-served jet pT spectrum in the search region with model spectra for different values of, for models with destruc-tive interference. Figure6compares the data with models with constructive interference.
V. STATISTICAL ANALYSIS
Since there are no significant deviations between the observed and predicted spectra, the results are interpreted in terms of lower limits on the CI scale using the models described in Sec. II. The dominant sources of systematic uncertainties are associated with the JES, the PDFs, the JER, the renormalization (r) and factorization (f) scales, and the modeling parameters of Eq. (4). Nonperturbative corrections are less than 1% for transverse momenta above 400 GeV [30], negligible compared with other uncertain-ties, and are therefore not applied to our analysis.
In the search region, the inclusive jet spectrum has a range of 5 orders of magnitude, which causes the limits on to be sensitive to the choice of the normalization factor and the size of the data sets. We have found that a few percent change in the normalization factor can cause limits to change by as much as 50%. Therefore, for the purpose of (GeV) T Jet p 1000 1500 2000 ) -1 (GeV T dN/dp -3 10 -1 10 10 3 10 Data QCD σ 2 ± σ 1 ± = 7 TeV s -1 CMS L = 5 fb | < 0.5 η | Pr(KS) = 0.6617 /NDF = 23.5/19 2 χ (GeV) T Jet p 1000 1500 2000 NLO Data / QCD 0 1 2 3 Data QCD σ 2 ± σ 1 ± = 7 TeV s -1 CMS L = 5 fb | < 0.5 η | Pr(KS) = 0.6617 /NDF = 23.5/19 2 χ
FIG. 4 (color online). The observed jet pTspectrum compared with the NLO QCD jet pT spectrum (top). The bands represent the total uncertainty in the prediction and incorporate the uncer-tainties in the PDFs, jet energy scale, jet energy resolution, the renormalization and factorization scales, and the modeling of the jet pTdependence of the parameters in Eq. (4). The ratio of the observed to the predicted spectrum (bottom). The error bars represent the statistical uncertainties in the expected bin count.
TABLE II. The observed jet count for each jet pT bin in the range 507–2116 GeV.
Bin pT(GeV) Jets Bin pT(GeV) Jets
1 507–548 73792 11 1032–1101 576 2 548–592 47416 12 1101–1172 384 3 592–638 29185 13 1172–1248 243 4 638–686 18187 14 1248–1327 100 5 686–737 11565 15 1327–1410 66 6 737–790 7095 16 1410–1497 34 7 790–846 4413 17 1497–1588 15 8 846–905 2862 18 1588–1684 9 9 905–967 1699 19 1684–1784 1 10 967–1032 1023 20 1784–2116 3
computing limits, we have chosen to sidestep the issue of normalization by considering only the shape of the jet pT spectrum. This we achieve by using a multinomial distri-bution, which is the probability to observe K counts, Nj, j¼ 1; . . . ; K, given the observation of a total count N¼PKj¼1Nj. The likelihood is then defined by
pðDj; !Þ ¼ N! N1! . . . NK! YK j¼1 j N j ; (5)
where K¼ 20 is the number of bins in the search region, Nj is the jet count in the jth jet pTbin, D N1;. . . ; NK, ¼ PK
j¼1jand N are the total cross section and total observed
count, respectively, in the search region, and the symbol ! denotes the nuisance parameters p1;. . . ; p4 in Eq. (4).
We account for systematic uncertainties by integrating the likelihood with respect to a nuisance prior ð!Þ. In practice, the likelihood is averaged over the nuisance parameters, !, using a discrete representation of the prior ð!Þ constructed as described in Sec. VA. This calculation yields the marginal likelihood pðDjÞ
1 M
PM
m¼1pðDj; !mÞ, where M is the number of points sampled from the nuisance prior ð!Þ described in AppendixB 1, which is the basis of the limit calculations. The likelihood functions for models with destructive and constructive interference are shown in Fig.7.
(GeV) T Jet p 1000 1500 2000 ) -1 (GeV T dN/dp -2 10 -1 10 1 10 2 10 3 10 Data = 8 TeV Λ = 10 TeV Λ = 12 TeV Λ = 14 TeV Λ QCD = 7 TeV s -1 CMS L = 5 fb | < 0.5 η | constructive interference (GeV) T Jet p 1000 1500 2000 NLO Data / QCD 0 1 2 3 Data = 8 TeV Λ = 10 TeV Λ = 12 TeV Λ = 14 TeV Λ = 7 TeV s -1 CMS L = 5 fb | < 0.5 η | constructive interference
FIG. 6 (color online). The data compared with model spectra for different values of for models with constructive interfer-ence (top). The ratio of these spectra to the NLO QCD jet pT spectrum (bottom). (GeV) T Jet p 1000 1500 2000 ) -1 (GeV T dN/dp -2 10 -1 10 1 10 2 10 3 10 Data = 8 TeV Λ = 10 TeV Λ = 12 TeV Λ = 14 TeV Λ QCD = 7 TeV s -1 CMS L = 5 fb | < 0.5 η | destructive interference (GeV) T Jet p 1000 1500 2000 NLO Data / QCD 0 1 2 3 Data = 8 TeV Λ = 10 TeV Λ = 12 TeV Λ = 14 TeV Λ = 7 TeV s -1 CMS L = 5 fb | < 0.5 η | destructive interference
FIG. 5 (color online). The data compared with model spectra for different values of for models with destructive interference (top). The ratio of these spectra to the NLO QCD jet pTspectrum (bottom).
A. Uncertainties
In principle, a discrete representation of the nuisance prior ð!Þ can be constructed by sampling simultaneously the JES, JER, PDFs, and the three values of f and r: pT=2, pT, and2pT. However, the CTEQ collaboration [19] does not provide a sampling of PDFs. Instead, CTEQ6.6 contains 44 PDF sets in which the 22 PDF parameters are shifted by approximately1:64 standard deviations. If we assume the Gaussian approximation to be valid, we can construct ap-proximate 20 20 covariance matrices for the jet spectra from the 44 PDF sets. Using these matrices, we generate ensembles of six correlated spectra:QCDNLO,QCDLO, and
ðQCD þ CIðÞÞLO with ¼ 3, 5, 8, and 12 TeV. The generation is performed for models both with destructive and constructive interference. The details of our procedure, which also includes simultaneous sampling of the JES and JER parameters, are given in AppendixB 1.
For a given set of values for the JES, JER, PDF, r, and fparameters, Eq. (4) is fitted to the ratioðQCDNLOþCIÞ= QCDNLO simultaneously to the four models with ¼ 3, 5, 8, and 12 TeV. We then sample a single set of the four nuisance parameters !¼ p1, p2, p3, p4 from a multivariate Gaussian using the fitted values and the asso-ciated 4 4 covariance matrix. The sampling and fitting procedure is repeated 500 times, thereby generating a discrete representation of the nuisance prior ð!Þ that incorporates all uncertainties. We have verified that our conclusions are robust with respect to variations in the size of the sample that represents ð!Þ.
B. Lower limits on
We use the CLs criterion [31,32] to compute upper limits on . For completeness, we give the details of these calculations in Appendix B 2. Using the procedure described in the Appendix, we obtain 95% lower limits on of 9.9 TeVand 14.3 TeV for models with destructive and constructive interference, respectively. These more strin-gent limits supersede those published by CMS based on a measurement of the dijet angular distribution [8]. The current search is more sensitive than the earlier dijet search as evidenced by the expected limits, which for this analysis are 9:5 0:6 TeV and 13:6 1:6 TeV, respectively, obtained using5 fb1of data.
Limits are also computed with a Bayesian method (Appendix B 3) using the marginal likelihood pðDjÞ and two different priors for : a prior flat in and a reference prior [33–35]. Using a flat prior, we find lower limits on of 10.6 TeV and 14.6 TeV at 95% C.L. for models with destructive and constructive interference, respectively. The corresponding limits using the reference prior are 10.1 TeV and 14.1 TeV at 95% C.L., respectively.
VI. SUMMARY
The inclusive jet pT spectrum of 7 TeV proton-proton collision events in the ranges507 pT 2116 GeV and j j < 0:5 has been studied using a data set corresponding to an integrated luminosity of 5:0 fb1. The observed jet pT spectrum is found to be in agreement with the jet pT spectrum predicted using perturbative QCD at NLO when the predicted spectrum is convolved with the CMS jet response function and normalized to the observed spec-trum in the search region. Should additional interactions exist that can be modeled as contact interactions with either destructive or constructive interference, their scale is above 9.9 TeVand 14.3 TeV, respectively, at 95% C.L. We plan to extend this study to the full 8 TeV CMS data set, making use of a recently released program [36] to calculate ) -2 (TeV -2 Λ = λ 0 0.005 0.01 0.015 )λ p(D| 0 0.05 0.1 stats. only all uncert. = 7 TeV s -1 CMS L = 5 fb destructive interference ) -2 (TeV -2 Λ = λ 0 0.005 0.01 0.015 )λ p(D| 0 0.05 0.1 stats. only all uncert. = 7 TeV s -1 CMS L = 5 fb constructive interference
FIG. 7 (color online). The likelihood functions assuming a model with either destructive (top) or constructive (bottom) interference. The dashed curve is the likelihood function includ-ing statistical uncertainties only and the central values of all nuisance parameters. The solid curve is the likelihood margi-nalized over all systematic uncertainties.
at next-to-leading order the inclusive jet pTspectrum with contact interactions.
It is noteworthy that the limits reported in this paper, which are the most sensitive limits published to date, have been obtained reprising the classic method to search for contact interactions, namely, searching for deviations from QCD at high jet transverse momentum.
ACKNOWLEDGMENTS
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MEYS (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES (Croatia); RPF (Cyprus); MoER, SF0690030s09 and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/ IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NKTH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); MSI (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan); MON, RosAtom, RAS and RFBR (Russia); MSTD (Serbia); SEIDI and CPAN (Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei); ThEP, IPST, and NECTEC (Thailand); TUBITAK and TAEK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).
APPENDIX A: PYTHIA 6.422 CONTACT INTERACTION CONFIGURATION
The scale is defined by the CI model in PYTHIA. In order to facilitate the reinterpretation of the results using a different model, we provide the details of the PYTHIA configuration in Table III for ¼ 8 TeV and final state parton transverse momenta, ^pT, in the range 170 ^pT 230 GeV.
APPENDIX B: STATISTICAL DETAILS 1. Nuisance prior
We approximate the nuisance prior ð!Þ starting with two sets of ensembles. In the first, the six 20-bin model spectra QCDNLO, QCDLO, and ½QCD þ CIðÞLO with ¼ 3, 5, 8, and 12 TeV are varied, reflecting random variations in the PDF parameters as well as random choices of the three r and f scales, while keeping the JES and JER parameters fixed at their central values; we call these the PDF ensembles. In the second set of ensembles, the JES and JER parameters are varied simultaneously, while keep-ing the PDF parameters fixed to their central values and the renormalization and factorization scales at their nominal values; we call these the JES/JER ensembles.
A. Generating the PDF ensembles
In the PDF ensembles, each of the six model spectra is sampled from a multivariate Gaussian distribution using the associated20 20 covariance matrix. For each model spectrum, the covariance matrix is approximated by
Cnm¼ X22 i¼1 X22 j¼1 XniXmj; (B1)
whereXni¼ ðXniþ XniÞ=2 and Xniare the cross section values for the nth jet bin associated with the þ and variations of the ith pair of CTEQ6.6 PDF sets. CTEQ [19] publishes approximate 90% intervals. We therefore ap-proximate 68% intervals by dividing each X by 1.64. The correlation induced by the PDF uncertainties across all six model spectra is maintained by using the same set of underlying Gaussian variates during the sampling of the spectra.
B. Generating the JES/JER ensembles
In the JES/JER ensembles, the JES and JER parameters are sampled simultaneously for the five model spectra QCDLO, andðQCD þ CIÞLOwith ¼ 3, 5, 8, and 12 TeV, yielding ensembles of correlated shifts from the central JES, JER, and PDF values of the QCDLO and ðQCD þ CIÞLO spectra. For example, we compute the spectral residuals ¼ QCD0 QCDcentral, where QCD0 is the shifted jet pTspectrum andQCDcentralis the jet pTspectrum computed using the central values of the JES, JER, and PDF parameters. Coherent shifts of the jet energy scale are calculated for every TABLE III. PYTHIA6.422 configuration for ¼ 8 TeV
con-tact interactions.
PYTHIA6.422 settings specific to contact interactions
Settings Description
ITCMð5Þ ¼ 2 switch on contact int. for all quarks RTCMð41Þ ¼ 8000 set contact scale to 8 TeV
RTCMð42Þ ¼ 1 sign of contact int. isþ
MSUBð381Þ ¼ 1 qiqj! qiqj via QCD plus a contact int.
MSUBð382Þ ¼ 1 qiqi! qkqk via QCD plus a contact int.
MSUBð13Þ ¼ 1 qiqi! gg via normal QCD
MSUBð28Þ ¼ 1 qig! qig via normal QCD
MSUBð53Þ ¼ 1 gg! qkqkvia normal QCD
MSUBð68Þ ¼ 1 gg! gg via normal QCD
CKINð3Þ ¼ 170 minimum ^pT for hard int.
jet in every simulated event. The jet pTis shifted by x for each component of the jet energy scale uncertainty, of which there are 16, where x is a Gaussian variate of zero mean and unit variance, and is a jet-dependent uncertainty for a given component. The contributions from all uncertainty compo-nents are summed to obtain an overall shift in the jet pT. From studies of dijet asymmetry and photonþ jet pT bal-ancing, the uncertainty in the jet energy resolution is esti-mated to be 10% in the pseudorapidity rangej j < 0:5 [30]. We sample the jet energy resolution using a procedure iden-tical to that used to sample the jet energy scale but using a single Gaussian variate.
C. Generating the JES/JER/PDF ensemble Another ensemble is created, from the PDF ensembles and the JES/JER ensembles, that approximates simulta-neous sampling from the JES, JER, PDF, renormalization, and factorization parameters. We pick at random a corre-lated set of six spectra from the PDF ensembles and a correlated set of five spectral residuals from the JES/JER ensembles. The JES/JER spectral residuals are added to the corresponding shifted spectrum from the PDF en-sembles, thereby creating a spectrum in which the JES, JER, PDF, r, and f parameters have been randomly shifted. The NLO QCD spectrum (from the PDF ensem-bles) is shifted using the LO QCD JES/JER spectral resid-uals in order to approximate the effect of the JES and JER uncertainties in this spectrum.
The result of the above procedure is an ensemble of sets of properly correlated spectraQCDNLOþ CIðÞ with ¼ 3, 5, 8, and 12 TeV, in which the JES, JER, PDF, r, and f parameters vary randomly. The ansatz in Eq. (4) is then fitted to the quartet of ratios ½QCDNLO þ CIðÞ=QCDNLO as described in Sec. VA to obtain pa-rameter values for p1, p2, p3, and p4. Five hundred sets of these parameters are generated, constituting a discrete approximation to the prior ð!Þ ðp1; p2; p3; p4Þ.
2. CLs calculation
Since CLs is a criterion rather than a method, it is necessary to document exactly how aCLs limit is calcu-lated. Such a calculation requires two elements: a test statistic Q that depends on the quantity of interest and its sampling distribution for two different hypotheses, here >0, which we denote by H, and ¼ 0, which we denote by H0. His the signal plus background hypothesis while H0is the background-only hypothesis. For this study, we use the statistic
QðÞ ¼ tðD; Þ 2 ln ½pðDjÞ=pðDj0Þ; (B2) where pðDjÞ is the marginal likelihood
pðDjÞ ¼Z pðDj; !Þð!Þ d! 1 M XM m¼1 pðDj; !mÞ; (B3)
where M¼ 500 is the number of points ! ¼ p1, p2, p3, p4 sampled from the nuisance prior ð!Þ described in AppendixB 1. We compute the sampling distributions
pðQjHÞ ¼ Z
½Q tðD; ÞpðDjÞdD; (B4) and
pðQjH0Þ ¼Z ½Q tðD; ÞpðDj0ÞdD; (B5) pertaining to the hypotheses H and H0, respectively, and solve
CLs pðÞ=pð0Þ ¼ 0:05; (B6) to obtain a 95% confidence level (CLs) upper limit on , where the p-value pðÞ is defined by
pðÞ ¼ Pr ½QðÞ > Q0ðÞ ; (B7) and Q0 is the observed value of Q.
In practice, theCLs limits are approximated as follows: (1) Choose a value of , say , and compute the
observed value of Q, Q0ð Þ.
(2) Choose at random one of the M¼ 500 sets of nuisance parameters p1, p2, p3, and p4.
(3) Generate a spectrum of K¼ 20 counts, D, accord-ing to the multinomial distribution, Eq. (5), with ¼ , which corresponds to the hypothesis H. Compute Q¼ tðD; Þ and keep track of how often Qð Þ > Q0ð Þ. Call this count n.
(4) Generate another set of 20 counts, D, but with ¼ 0, corresponding to the hypothesis H0. Compute Q¼ tðD; Þ and keep track of how often Qð Þ > Q0ð Þ. Call this count n0.
(5) Repeat 25 000 times steps 2 to 4, compute CLs n=n0, and report ¼ as the upper limit on at 95% C.L. ifCLsis sufficiently close to 0.05; other-wise, keep repeating steps 1 to 4 with different values of . The algorithm starts with two values of that are likely to bracket the solution and the solution is found using a binary search, which typi-cally requires about 10–15 iterations.
3. Bayesian calculation
The Bayesian limit calculations use the marginal like-lihood, Eq. (B3), and two different (formal) priors ðÞ: a prior flat in and a reference prior [33–35], which we calculate numerically [35]. An upper limit on , is computed by solving
Z
0 pðDjÞðÞd=pðDÞ ¼ 0:95; (B8) where pðDÞ is a normalization constant. The integrals are performed using numerical quadrature.
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G. Mantovani,63a,63bM. Menichelli,63aA. Nappi,63a,63b,aF. Romeo,63a,63bA. Saha,63aA. Santocchia,63a,63b A. Spiezia,63a,63bS. Taroni,63a,63bP. Azzurri,64a,64cG. Bagliesi,64aJ. Bernardini,64aT. Boccali,64aG. Broccolo,64a,64c
R. Castaldi,64aR. T. D’Agnolo,64a,64c,cR. Dell’Orso,64aF. Fiori,64a,64b,cL. Foa`,64a,64cA. Giassi,64aA. Kraan,64a F. Ligabue,64a,64cT. Lomtadze,64aL. Martini,64a,eeA. Messineo,64a,64bF. Palla,64aA. Rizzi,64a,64bA. T. Serban,64a,ff P. Spagnolo,64aP. Squillacioti,64a,cR. Tenchini,64aG. Tonelli,64a,64bA. Venturi,64aP. G. Verdini,64aL. Barone,65a,65b F. Cavallari,65aD. Del Re,65a,65bM. Diemoz,65aC. Fanelli,65a,65bM. Grassi,65a,65b,cE. Longo,65a,65bP. Meridiani,65a,c F. Micheli,65a,65bS. Nourbakhsh,65a,65bG. Organtini,65a,65bR. Paramatti,65aS. Rahatlou,65a,65bM. Sigamani,65a
L. Soffi,65a,65bN. Amapane,66a,66bR. Arcidiacono,66a,66cS. Argiro,66a,66bM. Arneodo,66a,66cC. Biino,66a N. Cartiglia,66aS. Casasso,66a,66bM. Costa,66a,66bN. Demaria,66aC. Mariotti,66a,cS. Maselli,66aE. Migliore,66a,66b
V. Monaco,66a,66bM. Musich,66a,cM. M. Obertino,66a,66cN. Pastrone,66aM. Pelliccioni,66aA. Potenza,66a,66b A. Romero,66a,66bM. Ruspa,66a,66cR. Sacchi,66a,66bA. Solano,66a,66bA. Staiano,66aS. Belforte,67a V. Candelise,67a,67bM. Casarsa,67aF. Cossutti,67aG. Della Ricca,67a,67bB. Gobbo,67aM. Marone,67a,67b,c D. Montanino,67a,67b,cA. Penzo,67aA. Schizzi,67a,67bT. Y. Kim,68S. K. Nam,68S. Chang,69D. H. Kim,69 G. N. Kim,69D. J. Kong,69H. Park,69D. C. Son,69T. Son,69J. Y. Kim,70Zero J. Kim,70S. Song,70S. Choi,71 D. Gyun,71B. Hong,71M. Jo,71H. Kim,71T. J. Kim,71K. S. Lee,71D. H. Moon,71S. K. Park,71Y. Roh,71M. Choi,72 J. H. Kim,72C. Park,72I. C. Park,72S. Park,72G. Ryu,72Y. Choi,73Y. K. Choi,73J. Goh,73M. S. Kim,73E. Kwon,73 B. Lee,73J. Lee,73S. Lee,73H. Seo,73I. Yu,73M. J. Bilinskas,74I. Grigelionis,74M. Janulis,74A. Juodagalvis,74
H. Castilla-Valdez,75E. De La Cruz-Burelo,75I. Heredia-de La Cruz,75R. Lopez-Fernandez,75J. Martı´nez-Ortega,75 A. Sanchez-Hernandez,75L. M. Villasenor-Cendejas,75S. Carrillo Moreno,76F. Vazquez Valencia,76 H. A. Salazar Ibarguen,77E. Casimiro Linares,78A. Morelos Pineda,78M. A. Reyes-Santos,78D. Krofcheck,79 A. J. Bell,80P. H. Butler,80R. Doesburg,80S. Reucroft,80H. Silverwood,80M. Ahmad,81M. I. Asghar,81J. Butt,81 H. R. Hoorani,81S. Khalid,81W. A. Khan,81T. Khurshid,81S. Qazi,81M. A. Shah,81M. Shoaib,81H. Bialkowska,82 B. Boimska,82T. Frueboes,82M. Go´rski,82M. Kazana,82K. Nawrocki,82K. Romanowska-Rybinska,82M. Szleper,82
G. Wrochna,82P. Zalewski,82G. Brona,83K. Bunkowski,83M. Cwiok,83W. Dominik,83K. Doroba,83 A. Kalinowski,83M. Konecki,83J. Krolikowski,83M. Misiura,83N. Almeida,84P. Bargassa,84A. David,84 P. Faccioli,84P. G. Ferreira Parracho,84M. Gallinaro,84J. Seixas,84J. Varela,84P. Vischia,84P. Bunin,85I. Golutvin,85
A. Kamenev,85V. Karjavin,85V. Konoplyanikov,85G. Kozlov,85A. Lanev,85A. Malakhov,85P. Moisenz,85 V. Palichik,85V. Perelygin,85M. Savina,85S. Shmatov,85S. Shulha,85V. Smirnov,85A. Volodko,85A. Zarubin,85 S. Evstyukhin,86V. Golovtsov,86Y. Ivanov,86V. Kim,86P. Levchenko,86V. Murzin,86V. Oreshkin,86I. Smirnov,86
V. Sulimov,86L. Uvarov,86S. Vavilov,86A. Vorobyev,86An. Vorobyev,86Yu. Andreev,87A. Dermenev,87 S. Gninenko,87N. Golubev,87M. Kirsanov,87N. Krasnikov,87V. Matveev,87A. Pashenkov,87D. Tlisov,87 A. Toropin,87V. Epshteyn,88M. Erofeeva,88V. Gavrilov,88M. Kossov,88N. Lychkovskaya,88V. Popov,88 G. Safronov,88S. Semenov,88I. Shreyber,88V. Stolin,88E. Vlasov,88A. Zhokin,88V. Andreev,89M. Azarkin,89
I. Dremin,89M. Kirakosyan,89A. Leonidov,89G. Mesyats,89S. V. Rusakov,89A. Vinogradov,89A. Belyaev,90 E. Boos,90V. Bunichev,90M. Dubinin,90,eL. Dudko,90A. Ershov,90A. Gribushin,90V. Klyukhin,90O. Kodolova,90 I. Lokhtin,90A. Markina,90S. Obraztsov,90M. Perfilov,90S. Petrushanko,90A. Popov,90L. Sarycheva,90,aV. Savrin,90
I. Azhgirey,91I. Bayshev,91S. Bitioukov,91V. Grishin,91,cV. Kachanov,91D. Konstantinov,91V. Krychkine,91 V. Petrov,91R. Ryutin,91A. Sobol,91L. Tourtchanovitch,91S. Troshin,91N. Tyurin,91A. Uzunian,91A. Volkov,91
P. Adzic,92,ggM. Djordjevic,92M. Ekmedzic,92D. Krpic,92,ggJ. Milosevic,92M. Aguilar-Benitez,93 J. Alcaraz Maestre,93P. Arce,93C. Battilana,93E. Calvo,93M. Cerrada,93M. Chamizo Llatas,93N. Colino,93 B. De La Cruz,93A. Delgado Peris,93D. Domı´nguez Va´zquez,93C. Fernandez Bedoya,93J. P. Ferna´ndez Ramos,93 A. Ferrando,93J. Flix,93M. C. Fouz,93P. Garcia-Abia,93O. Gonzalez Lopez,93S. Goy Lopez,93J. M. Hernandez,93 M. I. Josa,93G. Merino,93J. Puerta Pelayo,93A. Quintario Olmeda,93I. Redondo,93L. Romero,93J. Santaolalla,93
M. S. Soares,93C. Willmott,93C. Albajar,94G. Codispoti,94J. F. de Troco´niz,94H. Brun,95J. Cuevas,95 J. Fernandez Menendez,95S. Folgueras,95I. Gonzalez Caballero,95L. Lloret Iglesias,95J. Piedra Gomez,95 J. A. Brochero Cifuentes,96I. J. Cabrillo,96A. Calderon,96S. H. Chuang,96J. Duarte Campderros,96M. Felcini,96,hh
M. Fernandez,96G. Gomez,96J. Gonzalez Sanchez,96A. Graziano,96C. Jorda,96A. Lopez Virto,96J. Marco,96 R. Marco,96C. Martinez Rivero,96F. Matorras,96F. J. Munoz Sanchez,96T. Rodrigo,96A. Y. Rodrı´guez-Marrero,96
A. Ruiz-Jimeno,96L. Scodellaro,96I. Vila,96R. Vilar Cortabitarte,96D. Abbaneo,97E. Auffray,97G. Auzinger,97 M. Bachtis,97P. Baillon,97A. H. Ball,97D. Barney,97J. F. Benitez,97C. Bernet,97,fG. Bianchi,97P. Bloch,97
A. Bocci,97A. Bonato,97C. Botta,97H. Breuker,97T. Camporesi,97G. Cerminara,97T. Christiansen,97 J. A. Coarasa Perez,97D. D’Enterria,97A. Dabrowski,97A. De Roeck,97S. Di Guida,97M. Dobson,97 N. Dupont-Sagorin,97A. Elliott-Peisert,97B. Frisch,97W. Funk,97G. Georgiou,97M. Giffels,97D. Gigi,97K. Gill,97
D. Giordano,97M. Girone,97M. Giunta,97F. Glege,97R. Gomez-Reino Garrido,97P. Govoni,97S. Gowdy,97 R. Guida,97S. Gundacker,97J. Hammer,97M. Hansen,97P. Harris,97C. Hartl,97J. Harvey,97B. Hegner,97 A. Hinzmann,97V. Innocente,97P. Janot,97K. Kaadze,97E. Karavakis,97K. Kousouris,97P. Lecoq,97Y.-J. Lee,97
P. Lenzi,97C. Lourenc¸o,97N. Magini,97T. Ma¨ki,97M. Malberti,97L. Malgeri,97M. Mannelli,97L. Masetti,97 F. Meijers,97S. Mersi,97E. Meschi,97R. Moser,97M. U. Mozer,97M. Mulders,97P. Musella,97E. Nesvold,97 L. Orsini,97E. Palencia Cortezon,97E. Perez,97L. Perrozzi,97A. Petrilli,97A. Pfeiffer,97M. Pierini,97M. Pimia¨,97
D. Piparo,97G. Polese,97L. Quertenmont,97A. Racz,97W. Reece,97J. Rodrigues Antunes,97G. Rolandi,97,ii C. Rovelli,97,jjM. Rovere,97H. Sakulin,97F. Santanastasio,97C. Scha¨fer,97C. Schwick,97I. Segoni,97S. Sekmen,97
A. Sharma,97P. Siegrist,97P. Silva,97M. Simon,97P. Sphicas,97,kkD. Spiga,97A. Tsirou,97G. I. Veres,97,u J. R. Vlimant,97H. K. Wo¨hri,97S. D. Worm,97,llW. D. Zeuner,97W. Bertl,98K. Deiters,98W. Erdmann,98 K. Gabathuler,98R. Horisberger,98Q. Ingram,98H. C. Kaestli,98S. Ko¨nig,98D. Kotlinski,98U. Langenegger,98
F. Meier,98D. Renker,98T. Rohe,98L. Ba¨ni,99P. Bortignon,99M. A. Buchmann,99B. Casal,99N. Chanon,99 A. Deisher,99G. Dissertori,99M. Dittmar,99M. Donega`,99M. Du¨nser,99P. Eller,99J. Eugster,99K. Freudenreich,99
C. Grab,99D. Hits,99P. Lecomte,99W. Lustermann,99A. C. Marini,99P. Martinez Ruiz del Arbol,99N. Mohr,99 F. Moortgat,99C. Na¨geli,99,mmP. Nef,99F. Nessi-Tedaldi,99F. Pandolfi,99L. Pape,99F. Pauss,99M. Peruzzi,99
F. J. Ronga,99M. Rossini,99L. Sala,99A. K. Sanchez,99A. Starodumov,99,nnB. Stieger,99M. Takahashi,99 L. Tauscher,99,aA. Thea,99K. Theofilatos,99D. Treille,99C. Urscheler,99R. Wallny,99H. A. Weber,99L. Wehrli,99
C. Amsler,100,ooV. Chiochia,100S. De Visscher,100C. Favaro,100M. Ivova Rikova,100B. Kilminster,100 B. Millan Mejias,100P. Otiougova,100P. Robmann,100H. Snoek,100S. Tupputi,100M. Verzetti,100Y. H. Chang,101 K. H. Chen,101C. Ferro,101C. M. Kuo,101S. W. Li,101W. Lin,101Y. J. Lu,101A. P. Singh,101R. Volpe,101S. S. Yu,101 P. Bartalini,102P. Chang,102Y. H. Chang,102Y. W. Chang,102Y. Chao,102K. F. Chen,102C. Dietz,102U. Grundler,102 W.-S. Hou,102Y. Hsiung,102K. Y. Kao,102Y. J. Lei,102R.-S. Lu,102D. Majumder,102E. Petrakou,102X. Shi,102 J. G. Shiu,102Y. M. Tzeng,102X. Wan,102M. Wang,102B. Asavapibhop,103N. Srimanobhas,103A. Adiguzel,104 M. N. Bakirci,104,ppS. Cerci,104,qqC. Dozen,104I. Dumanoglu,104E. Eskut,104S. Girgis,104G. Gokbulut,104 E. Gurpinar,104I. Hos,104E. E. Kangal,104T. Karaman,104G. Karapinar,104,rrA. Kayis Topaksu,104G. Onengut,104
K. Ozdemir,104S. Ozturk,104,ssA. Polatoz,104K. Sogut,104,ttD. Sunar Cerci,104,qqB. Tali,104,qqH. Topakli,104,pp L. N. Vergili,104M. Vergili,104I. V. Akin,105T. Aliev,105B. Bilin,105S. Bilmis,105M. Deniz,105H. Gamsizkan,105 A. M. Guler,105K. Ocalan,105A. Ozpineci,105M. Serin,105R. Sever,105U. E. Surat,105M. Yalvac,105E. Yildirim,105 M. Zeyrek,105E. Gu¨lmez,106B. Isildak,106,uuM. Kaya,106,vvO. Kaya,106,vvS. Ozkorucuklu,106,wwN. Sonmez,106,xx
K. Cankocak,107L. Levchuk,108J. J. Brooke,109E. Clement,109D. Cussans,109H. Flacher,109R. Frazier,109 J. Goldstein,109M. Grimes,109G. P. Heath,109H. F. Heath,109L. Kreczko,109S. Metson,109D. M. Newbold,109,ll
K. Nirunpong,109A. Poll,109S. Senkin,109V. J. Smith,109T. Williams,109L. Basso,110,yyK. W. Bell,110 A. Belyaev,110,yyC. Brew,110R. M. Brown,110D. J. A. Cockerill,110J. A. Coughlan,110K. Harder,110S. Harper,110
J. Jackson,110B. W. Kennedy,110E. Olaiya,110D. Petyt,110B. C. Radburn-Smith,110
C. H. Shepherd-Themistocleous,110I. R. Tomalin,110W. J. Womersley,110R. Bainbridge,111G. Ball,111 R. Beuselinck,111O. Buchmuller,111D. Colling,111N. Cripps,111M. Cutajar,111P. Dauncey,111G. Davies,111 M. Della Negra,111W. Ferguson,111J. Fulcher,111D. Futyan,111A. Gilbert,111A. Guneratne Bryer,111G. Hall,111
Z. Hatherell,111J. Hays,111G. Iles,111M. Jarvis,111G. Karapostoli,111L. Lyons,111A.-M. Magnan,111 J. Marrouche,111B. Mathias,111R. Nandi,111J. Nash,111A. Nikitenko,111,nnJ. Pela,111M. Pesaresi,111K. Petridis,111
M. Pioppi,111,zzD. M. Raymond,111S. Rogerson,111A. Rose,111M. J. Ryan,111C. Seez,111P. Sharp,111,a A. Sparrow,111M. Stoye,111A. Tapper,111M. Vazquez Acosta,111T. Virdee,111S. Wakefield,111N. Wardle,111 T. Whyntie,111M. Chadwick,112J. E. Cole,112P. R. Hobson,112A. Khan,112P. Kyberd,112D. Leggat,112D. Leslie,112
W. Martin,112I. D. Reid,112P. Symonds,112L. Teodorescu,112M. Turner,112K. Hatakeyama,113H. Liu,113 T. Scarborough,113O. Charaf,114C. Henderson,114P. Rumerio,114A. Avetisyan,115T. Bose,115C. Fantasia,115
A. Heister,115P. Lawson,115D. Lazic,115J. Rohlf,115D. Sperka,115J. St. John,115L. Sulak,115J. Alimena,116 S. Bhattacharya,116G. Christopher,116D. Cutts,116Z. Demiragli,116A. Ferapontov,116A. Garabedian,116 U. Heintz,116S. Jabeen,116G. Kukartsev,116E. Laird,116G. Landsberg,116M. Luk,116M. Narain,116D. Nguyen,116
M. Segala,116T. Sinthuprasith,116T. Speer,116R. Breedon,117G. Breto,117M. Calderon De La Barca Sanchez,117 S. Chauhan,117M. Chertok,117J. Conway,117R. Conway,117P. T. Cox,117J. Dolen,117R. Erbacher,117M. Gardner,117
R. Houtz,117W. Ko,117A. Kopecky,117R. Lander,117O. Mall,117T. Miceli,117D. Pellett,117F. Ricci-Tam,117 B. Rutherford,117M. Searle,117J. Smith,117M. Squires,117M. Tripathi,117R. Vasquez Sierra,117R. Yohay,117 V. Andreev,118D. Cline,118R. Cousins,118J. Duris,118S. Erhan,118P. Everaerts,118C. Farrell,118J. Hauser,118 M. Ignatenko,118C. Jarvis,118G. Rakness,118P. Schlein,118,aP. Traczyk,118V. Valuev,118M. Weber,118J. Babb,119 R. Clare,119M. E. Dinardo,119J. Ellison,119J. W. Gary,119F. Giordano,119G. Hanson,119H. Liu,119O. R. Long,119 A. Luthra,119H. Nguyen,119S. Paramesvaran,119J. Sturdy,119S. Sumowidagdo,119R. Wilken,119S. Wimpenny,119
W. Andrews,120J. G. Branson,120G. B. Cerati,120S. Cittolin,120D. Evans,120A. Holzner,120R. Kelley,120 M. Lebourgeois,120J. Letts,120I. Macneill,120B. Mangano,120S. Padhi,120C. Palmer,120G. Petrucciani,120
M. Pieri,120M. Sani,120V. Sharma,120S. Simon,120E. Sudano,120M. Tadel,120Y. Tu,120A. Vartak,120 S. Wasserbaech,120,aaaF. Wu¨rthwein,120A. Yagil,120J. Yoo,120D. Barge,121R. Bellan,121C. Campagnari,121
M. D’Alfonso,121T. Danielson,121K. Flowers,121P. Geffert,121F. Golf,121J. Incandela,121C. Justus,121 P. Kalavase,121D. Kovalskyi,121V. Krutelyov,121S. Lowette,121R. Magan˜a Villalba,121N. Mccoll,121V. Pavlunin,121
J. Ribnik,121J. Richman,121R. Rossin,121D. Stuart,121W. To,121C. West,121A. Apresyan,122A. Bornheim,122 Y. Chen,122E. Di Marco,122J. Duarte,122M. Gataullin,122Y. Ma,122A. Mott,122H. B. Newman,122C. Rogan,122 M. Spiropulu,122V. Timciuc,122J. Veverka,122R. Wilkinson,122S. Xie,122Y. Yang,122R. Y. Zhu,122V. Azzolini,123 A. Calamba,123R. Carroll,123T. Ferguson,123Y. Iiyama,123D. W. Jang,123Y. F. Liu,123M. Paulini,123H. Vogel,123
K. Stenson,124K. A. Ulmer,124S. R. Wagner,124J. Alexander,125A. Chatterjee,125N. Eggert,125L. K. Gibbons,125 B. Heltsley,125W. Hopkins,125A. Khukhunaishvili,125B. Kreis,125N. Mirman,125G. Nicolas Kaufman,125 J. R. Patterson,125A. Ryd,125E. Salvati,125W. Sun,125W. D. Teo,125J. Thom,125J. Thompson,125J. Tucker,125 J. Vaughan,125Y. Weng,125L. Winstrom,125P. Wittich,125D. Winn,126S. Abdullin,127M. Albrow,127J. Anderson,127
L. A. T. Bauerdick,127A. Beretvas,127J. Berryhill,127P. C. Bhat,127K. Burkett,127J. N. Butler,127V. Chetluru,127 H. W. K. Cheung,127F. Chlebana,127V. D. Elvira,127I. Fisk,127J. Freeman,127Y. Gao,127D. Green,127O. Gutsche,127
J. Hanlon,127R. M. Harris,127J. Hirschauer,127B. Hooberman,127S. Jindariani,127M. Johnson,127U. Joshi,127 B. Klima,127S. Kunori,127S. Kwan,127C. Leonidopoulos,127,bbbJ. Linacre,127D. Lincoln,127R. Lipton,127 J. Lykken,127K. Maeshima,127J. M. Marraffino,127S. Maruyama,127D. Mason,127P. McBride,127K. Mishra,127 S. Mrenna,127Y. Musienko,127,cccC. Newman-Holmes,127V. O’Dell,127O. Prokofyev,127E. Sexton-Kennedy,127
S. Sharma,127W. J. Spalding,127L. Spiegel,127L. Taylor,127S. Tkaczyk,127N. V. Tran,127L. Uplegger,127 E. W. Vaandering,127R. Vidal,127J. Whitmore,127W. Wu,127F. Yang,127J. C. Yun,127D. Acosta,128P. Avery,128
D. Bourilkov,128M. Chen,128T. Cheng,128S. Das,128M. De Gruttola,128G. P. Di Giovanni,128D. Dobur,128 A. Drozdetskiy,128R. D. Field,128M. Fisher,128Y. Fu,128I. K. Furic,128J. Gartner,128J. Hugon,128B. Kim,128
J. Konigsberg,128A. Korytov,128A. Kropivnitskaya,128T. Kypreos,128J. F. Low,128K. Matchev,128 P. Milenovic,128,dddG. Mitselmakher,128L. Muniz,128M. Park,128R. Remington,128A. Rinkevicius,128P. Sellers,128 N. Skhirtladze,128M. Snowball,128J. Yelton,128M. Zakaria,128V. Gaultney,129S. Hewamanage,129L. M. Lebolo,129
S. Linn,129P. Markowitz,129G. Martinez,129J. L. Rodriguez,129T. Adams,130A. Askew,130J. Bochenek,130 J. Chen,130B. Diamond,130S. V. Gleyzer,130J. Haas,130S. Hagopian,130V. Hagopian,130M. Jenkins,130 K. F. Johnson,130H. Prosper,130V. Veeraraghavan,130M. Weinberg,130M. M. Baarmand,131B. Dorney,131
M. Hohlmann,131H. Kalakhety,131I. Vodopiyanov,131F. Yumiceva,131M. R. Adams,132I. M. Anghel,132 L. Apanasevich,132Y. Bai,132V. E. Bazterra,132R. R. Betts,132I. Bucinskaite,132J. Callner,132R. Cavanaugh,132 O. Evdokimov,132L. Gauthier,132C. E. Gerber,132D. J. Hofman,132S. Khalatyan,132F. Lacroix,132C. O’Brien,132
C. Silkworth,132D. Strom,132P. Turner,132N. Varelas,132U. Akgun,133E. A. Albayrak,133B. Bilki,133,eee W. Clarida,133F. Duru,133S. Griffiths,133J.-P. Merlo,133H. Mermerkaya,133,fffA. Mestvirishvili,133A. Moeller,133
J. Nachtman,133C. R. Newsom,133E. Norbeck,133Y. Onel,133F. Ozok,133,gggS. Sen,133P. Tan,133E. Tiras,133 J. Wetzel,133T. Yetkin,133K. Yi,133B. A. Barnett,134B. Blumenfeld,134S. Bolognesi,134D. Fehling,134G. Giurgiu,134 A. V. Gritsan,134Z. J. Guo,134G. Hu,134P. Maksimovic,134M. Swartz,134A. Whitbeck,134P. Baringer,135A. Bean,135
G. Benelli,135R. P. Kenny Iii,135M. Murray,135D. Noonan,135S. Sanders,135R. Stringer,135G. Tinti,135 J. S. Wood,135A. F. Barfuss,136T. Bolton,136I. Chakaberia,136A. Ivanov,136S. Khalil,136M. Makouski,136 Y. Maravin,136S. Shrestha,136I. Svintradze,136J. Gronberg,137D. Lange,137F. Rebassoo,137D. Wright,137 A. Baden,138B. Calvert,138S. C. Eno,138J. A. Gomez,138N. J. Hadley,138R. G. Kellogg,138M. Kirn,138
T. Kolberg,138Y. Lu,138M. Marionneau,138A. C. Mignerey,138K. Pedro,138A. Skuja,138J. Temple,138 M. B. Tonjes,138S. C. Tonwar,138A. Apyan,139G. Bauer,139J. Bendavid,139W. Busza,139E. Butz,139I. A. Cali,139
M. Chan,139V. Dutta,139G. Gomez Ceballos,139M. Goncharov,139Y. Kim,139M. Klute,139K. Krajczar,139,hhh A. Levin,139P. D. Luckey,139T. Ma,139S. Nahn,139C. Paus,139D. Ralph,139C. Roland,139G. Roland,139 M. Rudolph,139G. S. F. Stephans,139F. Sto¨ckli,139K. Sumorok,139K. Sung,139D. Velicanu,139E. A. Wenger,139 R. Wolf,139B. Wyslouch,139M. Yang,139Y. Yilmaz,139A. S. Yoon,139M. Zanetti,139V. Zhukova,139S. I. Cooper,140
B. Dahmes,140A. De Benedetti,140G. Franzoni,140A. Gude,140S. C. Kao,140K. Klapoetke,140Y. Kubota,140 J. Mans,140N. Pastika,140R. Rusack,140M. Sasseville,140A. Singovsky,140N. Tambe,140J. Turkewitz,140 L. M. Cremaldi,141R. Kroeger,141L. Perera,141R. Rahmat,141D. A. Sanders,141E. Avdeeva,142K. Bloom,142
S. Bose,142D. R. Claes,142A. Dominguez,142M. Eads,142J. Keller,142I. Kravchenko,142J. Lazo-Flores,142 S. Malik,142G. R. Snow,142A. Godshalk,143I. Iashvili,143S. Jain,143A. Kharchilava,143A. Kumar,143 S. Rappoccio,143G. Alverson,144E. Barberis,144D. Baumgartel,144M. Chasco,144J. Haley,144D. Nash,144 T. Orimoto,144D. Trocino,144D. Wood,144J. Zhang,144A. Anastassov,145K. A. Hahn,145A. Kubik,145L. Lusito,145
N. Mucia,145N. Odell,145R. A. Ofierzynski,145B. Pollack,145A. Pozdnyakov,145M. Schmitt,145S. Stoynev,145 M. Velasco,145S. Won,145L. Antonelli,146D. Berry,146A. Brinkerhoff,146K. M. Chan,146M. Hildreth,146 C. Jessop,146D. J. Karmgard,146J. Kolb,146K. Lannon,146W. Luo,146S. Lynch,146N. Marinelli,146D. M. Morse,146
T. Pearson,146M. Planer,146R. Ruchti,146J. Slaunwhite,146N. Valls,146M. Wayne,146M. Wolf,146B. Bylsma,147 L. S. Durkin,147C. Hill,147R. Hughes,147K. Kotov,147T. Y. Ling,147D. Puigh,147M. Rodenburg,147C. Vuosalo,147
G. Williams,147B. L. Winer,147E. Berry,148P. Elmer,148V. Halyo,148P. Hebda,148J. Hegeman,148A. Hunt,148
P. Jindal,148S. A. Koay,148D. Lopes Pegna,148P. Lujan,148D. Marlow,148T. Medvedeva,148M. Mooney,148 J. Olsen,148P. Piroue´,148X. Quan,148A. Raval,148H. Saka,148D. Stickland,148C. Tully,148J. S. Werner,148 A. Zuranski,148E. Brownson,149A. Lopez,149H. Mendez,149J. E. Ramirez Vargas,149E. Alagoz,150V. E. Barnes,150 D. Benedetti,150G. Bolla,150D. Bortoletto,150M. De Mattia,150A. Everett,150Z. Hu,150M. Jones,150O. Koybasi,150 M. Kress,150A. T. Laasanen,150N. Leonardo,150V. Maroussov,150P. Merkel,150D. H. Miller,150N. Neumeister,150 I. Shipsey,150D. Silvers,150A. Svyatkovskiy,150M. Vidal Marono,150H. D. Yoo,150J. Zablocki,150Y. Zheng,150 S. Guragain,151N. Parashar,151A. Adair,152B. Akgun,152C. Boulahouache,152K. M. Ecklund,152F. J. M. Geurts,152
W. Li,152B. P. Padley,152R. Redjimi,152J. Roberts,152J. Zabel,152B. Betchart,153A. Bodek,153Y. S. Chung,153 R. Covarelli,153P. de Barbaro,153R. Demina,153Y. Eshaq,153T. Ferbel,153A. Garcia-Bellido,153P. Goldenzweig,153
J. Han,153A. Harel,153D. C. Miner,153D. Vishnevskiy,153M. Zielinski,153A. Bhatti,154R. Ciesielski,154 L. Demortier,154K. Goulianos,154G. Lungu,154S. Malik,154C. Mesropian,154S. Arora,155A. Barker,155 J. P. Chou,155C. Contreras-Campana,155E. Contreras-Campana,155D. Duggan,155D. Ferencek,155Y. Gershtein,155
R. Gray,155E. Halkiadakis,155D. Hidas,155A. Lath,155S. Panwalkar,155M. Park,155R. Patel,155V. Rekovic,155 J. Robles,155K. Rose,155S. Salur,155S. Schnetzer,155C. Seitz,155S. Somalwar,155R. Stone,155S. Thomas,155
M. Walker,155G. Cerizza,156M. Hollingsworth,156S. Spanier,156Z. C. Yang,156A. York,156R. Eusebi,157 W. Flanagan,157J. Gilmore,157T. Kamon,157,iiiV. Khotilovich,157R. Montalvo,157I. Osipenkov,157Y. Pakhotin,157
A. Perloff,157J. Roe,157A. Safonov,157T. Sakuma,157S. Sengupta,157I. Suarez,157A. Tatarinov,157D. Toback,157 N. Akchurin,158J. Damgov,158C. Dragoiu,158P. R. Dudero,158C. Jeong,158K. Kovitanggoon,158S. W. Lee,158
T. Libeiro,158I. Volobouev,158E. Appelt,159A. G. Delannoy,159C. Florez,159S. Greene,159A. Gurrola,159 W. Johns,159P. Kurt,159C. Maguire,159A. Melo,159M. Sharma,159P. Sheldon,159B. Snook,159S. Tuo,159 J. Velkovska,159M. W. Arenton,160M. Balazs,160S. Boutle,160B. Cox,160B. Francis,160J. Goodell,160R. Hirosky,160
A. Ledovskoy,160C. Lin,160C. Neu,160J. Wood,160S. Gollapinni,161R. Harr,161P. E. Karchin,161 C. Kottachchi Kankanamge Don,161P. Lamichhane,161A. Sakharov,161M. Anderson,162D. A. Belknap,162 L. Borrello,162D. Carlsmith,162M. Cepeda,162S. Dasu,162E. Friis,162L. Gray,162K. S. Grogg,162M. Grothe,162
R. Hall-Wilton,162M. Herndon,162A. Herve´,162P. Klabbers,162J. Klukas,162A. Lanaro,162C. Lazaridis,162 R. Loveless,162A. Mohapatra,162I. Ojalvo,162F. Palmonari,162G. A. Pierro,162I. Ross,162A. Savin,162
W. H. Smith,162and J. Swanson162 (CMS Collaboration)
1
Yerevan Physics Institute, Yerevan, Armenia
2Institut fu¨r Hochenergiephysik der OeAW, Wien, Austria 3National Centre for Particle and High Energy Physics, Minsk, Belarus
4Universiteit Antwerpen, Antwerpen, Belgium 5Vrije Universiteit Brussel, Brussel, Belgium 6Universite´ Libre de Bruxelles, Bruxelles, Belgium
7Ghent University, Ghent, Belgium
8Universite´ Catholique de Louvain, Louvain-la-Neuve, Belgium 9Universite´ de Mons, Mons, Belgium
10Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil 11Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
12aUniversidade Estadual Paulista, Sa˜o Paulo, Brazil 12bUniversidade Federal do ABC, Sa˜o Paulo, Brazil 13Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria
14University of Sofia, Sofia, Bulgaria 15Institute of High Energy Physics, Beijing, China 16
State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
17Universidad de Los Andes, Bogota, Colombia 18Technical University of Split, Split, Croatia
19University of Split, Split, Croatia 20Institute Rudjer Boskovic, Zagreb, Croatia
21University of Cyprus, Nicosia, Cyprus 22Charles University, Prague, Czech Republic
23Academy of Scientific Research and Technology of the Arab Republic of Egypt,
24National Institute of Chemical Physics and Biophysics, Tallinn, Estonia 25Department of Physics, University of Helsinki, Helsinki, Finland
26Helsinki Institute of Physics, Helsinki, Finland 27Lappeenranta University of Technology, Lappeenranta, Finland
28DSM/IRFU, CEA/Saclay, Gif-sur-Yvette, France
29Laboratoire Leprince-Ringuet, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France 30Institut Pluridisciplinaire Hubert Curien, Universite´ de Strasbourg,
Universite´ de Haute Alsace Mulhouse, CNRS/IN2P3, Strasbourg, France
31
Centre de Calcul de l’Institut National de Physique Nucleaire et de Physique des Particules, CNRS/IN2P3, Villeurbanne, France
32Universite´ de Lyon, Universite´ Claude Bernard Lyon 1, CNRS-IN2P3, Institut de Physique Nucle´aire de Lyon, Villeurbanne, France 33Institute of High Energy Physics and Informatization, Tbilisi State University, Tbilisi, Georgia
34RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany 35RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany 36RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany
37Deutsches Elektronen-Synchrotron, Hamburg, Germany 38University of Hamburg, Hamburg, Germany 39Institut fu¨r Experimentelle Kernphysik, Karlsruhe, Germany 40Institute of Nuclear Physics ‘‘Demokritos,’’ Aghia Paraskevi, Greece
41University of Athens, Athens, Greece 42University of Ioa´nnina, Ioa´nnina, Greece
43KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary 44Institute of Nuclear Research ATOMKI, Debrecen, Hungary
45University of Debrecen, Debrecen, Hungary 46Panjab University, Chandigarh, India
47
University of Delhi, Delhi, India
48Saha Institute of Nuclear Physics, Kolkata, India 49Bhabha Atomic Research Centre, Mumbai, India 50Tata Institute of Fundamental Research-EHEP, Mumbai, India 51Tata Institute of Fundamental Research-HECR, Mumbai, India 52Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
53aINFN Sezione di Bari, Bari, Italy 53bUniversita` di Bari, Bari, Italy 53cPolitecnico di Bari, Bari, Italy 54aINFN Sezione di Bologna, Bologna, Italy
54bUniversita` di Bologna, Bologna, Italy 55aINFN Sezione di Catania, Catania, Italy
55bUniversita` di Catania, Catania, Italy 56aINFN Sezione di Firenze, Firenze, Italy
56bUniversita` di Firenze, Firenze, Italy
57INFN Laboratori Nazionali di Frascati, Frascati, Italy 58aINFN Sezione di Genova, Genova, Italy
58bUniversita` di Genova, Genova, Italy 59aINFN Sezione di Milano-Bicocca, Milano, Italy
59bUniversita` di Milano-Bicocca, Milano, Italy 60aINFN Sezione di Napoli, Napoli, Italy 60bUniversita` di Napoli ‘‘Federico II,’’ Napoli, Italy 60cUniversita` della Basilicata (Potenza), Napoli, Italy
60d
Universita` G. Marconi (Roma), Napoli, Italy
61aINFN Sezione di Padova, Padova, Italy 61bUniversita` di Padova, Padova, Italy 61cUniversita` di Trento (Trento), Padova, Italy
62aINFN Sezione di Pavia, Pavia, Italy 62bUniversita` di Pavia, Pavia, Italy 63aINFN Sezione di Perugia, Perugia, Italy
63bUniversita` di Perugia, Perugia, Italy 64aINFN Sezione di Pisa, Pisa, Italy
64b
Universita` di Pisa, Pisa, Italy
64cScuola Normale Superiore di Pisa, Pisa, Italy 65aINFN Sezione di Roma, Roma, Italy
65bUniversita` di Roma, Roma, Italy 66aINFN Sezione di Torino, Torino, Italy