Measurement of the weak mixing angle with the Drell-Yan process
in proton-proton collisions at the LHC
S. Chatrchyan et al.* (CMS Collaboration)
(Received 14 October 2011; published 8 December 2011)
A multivariate likelihood method to measure electroweak couplings with the Drell–Yan process at the LHC is presented. The process is described by the dilepton rapidity, invariant mass, and decay angle distributions. The decay angle ambiguity due to the unknown assignment of the scattered constituent quark and antiquark to the two protons in a collision is resolved statistically using correlations between the observables. The method is applied to a sample of dimuon events from proton-proton collisions atffiffiffi
s p
¼ 7 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 1:1 fb1. From the dominant u u, d d ! =Z ! þ process, the effective weak mixing angle parameter is measured to be sin2eff¼ 0:2287 0:0020 ðstat:Þ 0:0025 ðsyst:Þ. This result is consistent
with measurements from other processes, as expected within the standard model.
DOI:10.1103/PhysRevD.84.112002 PACS numbers: 12.15.y, 13.88.+e, 14.70.-e
I. INTRODUCTION
The main goal of the Large Hadron Collider (LHC) [1] is to explore physics at the TeV energy scale via proton-proton collisions. The Drell–Yan process [2] occurs through the annihilation of a quark from one proton with an antiquark from the other proton, creating a virtual neutral gauge boson ( or Z) that subsequently decays to a pair of oppositely charged leptons, as shown in Fig.1. This annihilation process could reveal the existence of a new neutral gauge boson [3,4] or uncover deviations from the standard model of particle physics (SM) in elementary fermion couplings to the known neutral electroweak bosons. Besides quark-antiquark annihilation, new reso-nances decaying into lepton pairs may also be produced at the LHC via the gluon-fusion mechanism.
Analysis of electron-positron annihilations into dilepton or b b pairs at LEP and SLC [5] led to high-precision measurements of the electroweak Z-boson couplings to fermions. The measurement of the weak mixing angle parameter sin2W was performed to a precision of 0:1%. In the SM, the weak mixing angle W describes the rotation of the original W0 and B0 vector boson states into the observed or Z bosons as a result of spontaneous symmetry breaking [6]. Within the SM, sin2
W is the only free parameter that fixes the relative couplings of all fer-mions to the or Z.
Measurements of the weak mixing angle with differ-ent initial and final fermion-antifermion states f1f1 ! =Z ! f2f2 tests the universality of the fermion/
gauge-boson interactions and predictions of the SM. For example, LEP measurements [5] of the inclusive hadronic charge asymmetry provided a measurement of the couplings of light quarks compared to leptons and b quarks. The NuTeV collaboration measured sin2
W to precision of about 1% from neutrino and antineutrino deep inelastic scattering on nucleons [7]. The CDF and D0 experiments [8–10] at the Tevatron reached a simi-lar precision with the Drell–Yan process in proton-antiproton collisions, as did the H1 experiment [11] with electron-proton scattering at HERA. In this paper, we measure the sin2
W parameter to a precision 1% in the proton-proton Drell–Yan process at the LHC with the CMS experiment.
FIG. 1. Top: diagram describing the SM process q q ! =Z ! ‘‘þ. Bottom: definition of the angle in the pro-duction and decay of an intermediate state X, such as gg or qq ! X ! ‘ ‘þ.
*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.
The proton-proton collisions at the LHC pose new chal-lenges compared to previous collider experiments. The interference of the axial-vector and vector couplings leads to an asymmetry in the distribution of the polar angle of the lepton with respect to the direction of the constituent quark from the incoming proton in the quark-antiquark annihila-tion. This type of ‘‘forward-backward’’ asymmetry has been the primary measurement used to extract the cou-plings and sin2
W at the LEP, SLC, and Tevatron experi-ments. However, because of the symmetric proton-proton collision at the LHC, the direction of the quark is not known and can be deduced only on a statistical basis [4,12–14] using the boost direction of the dilepton final state, because of the higher probability for a valence quark from one of the incoming protons to provide the boost. We have developed methods that allow a per-event analytical likelihood description to extract the maximal information about the process at the LHC. This technique exploits more information than the conventional forward-backward asymmetry approach, and the distribution of the polar angle as a function of both dilepton rapidity and mass is an essential component of this method. The technique has applications both for high-precision electroweak measure-ments and for rare-process searches at the LHC.
In this paper, we present a multivariate analysis that uses the full information about the Drell–Yan process q q ! =Z ! ‘‘þ, parameterized as a function of the dilepton rapidity Y, invariant mass squared ^s, and decay angle . This process offers a relatively simple environment for the development of the matrix-element analysis techniques for resonance polarization studies at the LHC. Encouraged by feasibility studies of an analytical matrix-element ap-proach in Ref. [15], we use a formalism based on an analytical description of the elementary interaction (Sec. II). The method is applied to a sample of proton-proton collisions at a center-of-mass energypffiffiffis¼ 7 TeV, corresponding to an integrated luminosity of 1:1 fb1 re-corded by the CMS experiment (Sec. III). We include a description of detector effects in the analytical likelihood model (Sec.IV) and pay particular attention to systematic effects (Sec. V). The result is consistent with measure-ments in other processes, as expected within the SM (Sec.VI).
II. PHENOMENOLOGY OF THE DRELL–YAN PROCESS AT THE LHC
The philosophy of the multivariate likelihood analysis is to first produce a phenomenological model of the process and then introduce detector effects into the model. The parameters of the model may either be fixed to the best known values or left free in the fit, to be determined from data. These parameters may include the physical quantities of interest, such as sin2
W, or a description of detector effects, such as a correction for the momentum scale in the track reconstruction. Therefore, we start with a discussion
of a phenomenological model, and then proceed to detector-specific effects in the application of the analysis to CMS data.
The tree-level coupling of a spin-one gauge-boson to fermions is described by
u
feðV A5Þvf; (1) where vf and uf are the Dirac spinors of the fermion (f) and antifermion ( f), is the polarization vector of the spin-one boson, and V and A are the vector and axial-vector couplings. The couplings of the SM gauge bosons and Z are given in TableI. In the limit of negligible fermion masses, which is a good approximation for both quarks and leptons in the Drell–Yan process near the Z-boson mass, only two helicity states of the fermions are possible. They correspond to amplitudes A"#/ ðV AÞ and A#" / ðVþ AÞ.
The parton-level cross section for the Drell–Yan process can be expressed with the help of the Wigner dJm;m0 matrix, assuming the spin J ¼ 1 intermediate states , Z, and possible new unknown contributions (indicated by an el-lipsis below), as ^ qqð^s; cos; WÞ /1 ^s X 1;2;1;2¼";# ð2J þ 1ÞdJ¼1 12;12ð Þ2 Aqq!1;2A !‘‘ 1;2 þ A qq!Z 1;2ðWÞA Z!‘‘ 1;2ðWÞ ^s ð^s m2Þ þ im ZZ þ . . . 2 ; (2)
where 1, 2, 1, and 2 are the helicity states of the quark, antiquark, lepton, and antilepton, and the dilepton decay angle is defined in the center-of-mass frame of the dilepton system as shown in Fig. 1. The effects of transverse motion of the incoming constituent quark and antiquark in their annihilation are minimized by using the Collins–Soper frame [17]. In this frame, the angle is defined as the angle between the lepton momentum and a z0-axis that bisects the angle between the direction
TABLE I. Vector and axial-vector couplings of the SM gauge bosons to the charged fermion fields [16].
V A ! eeþ, þ, þ 1 0 ! uu, c c, tt þ2=3 0 ! d d, s s, b b 1=3 0 Z ! eeþ, þ, þ 3þ12sin2W 6 sinð2WÞ 1 2 sinð2WÞ Z ! uu, c c, tt þ38sin2W 6 sinð2WÞ þ1 2 sinð2WÞ Z ! d d, s s, b b 3þ4sin2W 6 sinð2WÞ 1 2 sinð2WÞ
of one proton and the direction opposite that of the other proton in the dilepton rest frame. Should there be new states contributing to the cross section with the same or different spin, they will either contribute with inter-ference if produced in q q annihilation, or without
interference if produced in gluon fusion (gg), for example.
The parton-level cross section in Eq. (2) can be further simplified for the SM intermediate states and Z with spin J ¼ 1 as ^ qqð^s; cos; WÞ / 3ðqVq! Þ2ð!‘‘ V Þ2 2 ^s ð1 þ cos 2Þ þ3 2 ^s ð^s m2 ZÞ2þ m2Z2Z ½ððqq!Z V Þ2þ ð qq!Z A Þ2ÞððZ!‘‘V Þ2þ ðZ!‘‘A Þ2Þð1 þ cos2 Þ þ 8qq!Z V qq!Z A Z!‘‘V Z!‘‘A cos þ3ð ^s m2ZÞ qq! V !‘‘ V ð^s m2 ZÞ2þ m2Z2Z ½qq!Z V Z!‘‘V ð1 þ cos2 Þ þ 2qq!Z A Z!‘‘A cos : (3)
Equation (3) implies that the asymmetry in the polar angle arises from terms linear in cos. The value of the asymmetry depends on the dilepton invariant mass m ¼ffiffiffi
^s p
, quark flavor q, and weak mixing angle W. It could also be affected by deviations of couplings from SM ex-pectations or by the presence of new contributions.
The differential cross section of the proton-proton Drell–Yan process can be expressed as a product of the parton-level cross section in Eqs. (2) or (3) and the parton distribution functions (PDFs) faðxi;^sÞ [18] describing the probability for partons of type a to have a fraction xiof the proton momentum p ¼pffiffiffis=2: dppðpx1;px2;cos;WÞ dx1dx2dcos / X q¼u;d;s;c;b ð ^qqð^s;sgnðx1x2Þcos;WÞfqðx1;^sÞfqðx2;^sÞ þ ^qqð^s;sgnðx2x1Þcos;WÞfqðx2;^sÞfqðx1;^sÞÞ: (4) The expression sgnðx1 x2Þ refers to the sign of the dif-ference (x1 x2), reflecting the fact that the quark direc-tion is assumed to coincide with the boost of the q q system. This assumption introduces a dilution in the odd-power terms in cos.
It is convenient to convert from the two variables ðx1; x2Þ to ðY; ^sÞ, the dilepton rapidity and the square of the dilepton mass, as Y ¼1 2ln ^E þp^ z ^ E p^z ¼1 2ln x 1 x2 ; (5) ^s ¼ ^E2 ^p2¼ x 1x2s; (6) where ^E is the dilepton system energy, ^p and ^pz are its momentum and longitudinal momentum in the laboratory frame, and ^p ¼ jp^zj at leading order in QCD.
After transformation of the variables, the Drell–Yan process in proton-proton interactions can be expressed as follows: dppðY; ^s; cos; WÞ dYd^sd cos / X q¼u;d;s;c;b ½ ^even qq ð^s; cos2; WÞ þ Dqqð^s; YÞ ^odd qqð^s; cos; WÞ Fqqð^s; YÞ: (7) The parton factor is defined as
Fqqð^s; YÞ ¼ fqðeþYpffiffiffiffiffiffiffi^s=s;^sÞfqðeYpffiffiffiffiffiffiffi^s=s;^sÞ þ fqðeY ffiffiffiffiffiffiffi ^s=s p ;^sÞfqðeþY ffiffiffiffiffiffiffi ^s=s p ;^sÞ; (8) and the dilution factor is defined as
Dqqð^s; YÞ ¼
fqðeþjYjpffiffiffiffiffiffiffi^s=s;^sÞfqðejYjpffiffiffiffiffiffiffi^s=s;^sÞ fqðejYjpffiffiffiffiffiffiffi^s=s;^sÞfqðeþjYjpffiffiffiffiffiffiffi^s=s;^sÞ fqðeþY ffiffiffiffiffiffiffi ^s=s p ;^sÞfqðeY ffiffiffiffiffiffiffi ^s=s p ;^sÞ þ fqðeY ffiffiffiffiffiffiffi ^s=s p ;^sÞfqðeþY ffiffiffiffiffiffiffi ^s=s p ;^sÞ : (9)
The two components of the parton cross section contain either an even or odd power of cos
^ even q q ð^s; cos2; WÞ ¼ 1 2ð ^qqð^s; þ cos ; WÞ þ ^qqð^s; cos; WÞÞ; (10) ^ odd q qð^s; cos; WÞ ¼ 1 2ð ^qqð^s; þ cos ; WÞ ^q qð^s; cos; WÞÞ: (11) The factors Fqqð^s; YÞ and Dqqð^s; YÞ both arise from the PDFs and can be extracted from parameterizations such as in Refs. [19–22]. We choose to extract PDFs numerically from the leading-order (LO) parameterization CTEQ6[19]
to match the LO model of the process. We parameterize the PDFs analytically using polynomial and exponential func-tions in the relevant range of x and with coefficients that are also functions of ^s. The relevant range of x for this analysis is 1:1 103< x < 1:4 101, motivated by the detector acceptance and the dilepton mass selection criteria pre-sented in Sec.IV. This analytical parameterization is illus-trated in Fig.2. We choose an analytical parameterization because of the computational speed and ease of implemen-tation. Its performance has been cross-checked with nu-merical computations. For systematic uncertainty studies, we check the performance against simulations with other PDF models [18,23], such as next-to-leading-order (NLO)
CTEQ[20],MSTW[21], andNNPDF[22].
The function Fqqð^s; YÞ is the effective cross section factor that scales the elementary parton-level cross section. This factor quickly decreases as the energy scale ap-proaches values comparable to the full proton energies, as illustrated in Fig. 3 for Y ¼ 0 production. The factor Dqqð^s; YÞ reflects the fact that the quark direction is gen-erally unknown and is taken as the boost direction of the dilepton system, because of the higher probability for valence quarks to provide the boost. For q ¼ u or d this factor ranges between 0 and 1 as jYj changes from 0 to 4, as illustrated in Fig.4for ^s around the Z pole. From Eq. (9) it follows that Dqq ¼ 0 for q ¼ s, c, b under the assumption fqðx; Q2Þ ¼ fqðx; Q2Þ, which is a good approximation in the current PDF model. A challenge at the LHC is that the dilution factor Dqqis small for the typical range of Y values in the detector acceptance region, as discussed below.
Information about sin2W or individual fermion couplings is contained in the shape of the three-dimensional distri-butions in Eq. (7) and enters through the elementary cou-plings of the electroweak bosons and fermions in the process q q ! =Z ! ‘‘þ.
Figure 5 illustrates the projections of the differential cross section from Eq. (7) in Y, m ¼pffiffiffi^s, and cos for the five different quark flavors and combined. The relative fractions of the different quark flavors are 0.450, 0.375, 0.103, 0.048, and 0.025 for u u, d d, s s, c c, and b b, respec-tively. The results of the analytical model leading to Eq. (7) show good agreement with the predictions from conven-tional LO numerical Monte Carlo (MC) simulation using
x -4 10 10-3 10-2 10-1 1 ) 2 xf(x,Q 0 0.5 1 1.5 2 u d d u s c b g(x0.1)
FIG. 2 (color online). Analytical parameterization of the par-ton distribution functions xfaðx; Q2Þ at Q ¼ 100 GeV using the
CTEQ6[19] numerical computation for the various quarks,
anti-quarks, and the gluon. The gluon distribution is scaled by a factor of 0.1. m (GeV) 2 10 103 , 0) 2 (mq q F× 2m 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 u u d d s s c c b b gg(x0.1)
FIG. 3 (color online). Distribution of the effective cross sec-tion factor 2mFqqðm2; Y ¼ 0Þ defined in Eq. (8) for five quark
flavors (from top to bottom q ¼ u, d, s, c, b) for proton-proton collision energies of 7 TeV as a function of the dilepton mass m. An equivalent factor for gluon-fusion production is shown for comparison and is scaled by a factor of 0.1.
Y -4 -3 -2 -1 0 1 2 3 4 , Y) Z 2 (mq q D 0 0.2 0.4 0.6 0.8 1 u u d d
FIG. 4 (color online). The dilution factor Dqqð^s ¼ m2Z; YÞ for
uu (top, red boxes) and d d (bottom, blue crosses) production as a function of the dilepton rapidity Y. The prediction from the
PYTHIA simulation (boxes and crosses) of the q q ! =Z !
þ process and the analytical distributions (solid curves) from Eq. (9) are shown.
thePYTHIAgenerator [24] with LOCTEQ6[19] PDFs. The above cross section is parameterized at leading order in both strong (QCD) and electroweak (EWK) interactions. Effects from NLO QCD contributions are studied with a detailed NLOPOWHEG[25–27] simulation, which includes
contributions from both initial-state gluon radiation and quark-gluon scattering. Effects from NLO EWK contribu-tions are expected to be small compared to the precision of this analysis. EWK corrections are absorbed in a definition of the effective weak mixing parameter, sin2
eff [16]. We use sin2
eff in place of sin2W for the rest of this paper. We apply the above technique to the measurement of the weak mixing angle. We take the SM description of elec-troweak interactions and PDFs in the proton as given, and allow only the effective weak mixing angle eff to be unconstrained. More generally, the above formalism with the multivariate analysis of the Drell–Yan process allows us to study the elementary couplings of fermions to elec-troweak neutral fields, such as =Z in the SM, as well as the structure functions of the proton.
III. DETECTION OF THE DRELL–YAN EVENTS WITH CMS
We apply the above method in an analysis of the q q ! =Z ! þprocess and measure sin2
eff. The choice of þ, as opposed to eeþ, is motivated by the more reliable description of the detector and background effects, as well as the fact that this final state has not yet been studied for sin2
eff measurements in q q interactions. However, we do not expect any limitations in the method for future application to other final states. The expected multivariate distributions in Eq. (7) are modified by smear-ing due to detector resolution and photon final-state radia-tion (FSR), and by acceptance effects and nonuniform reconstruction as a function of the observables. All these effects are taken into account in the analytical parameteri-zation, as shown below.
A detailed description of the CMS detector can be found in Ref. [28]. The central feature of CMS is a 3.8 T super-conducting solenoid of 6 m internal diameter. Within the field volume are the silicon pixel and strip tracker, the crystal electromagnetic calorimeter (ECAL), and the brass/scintillator hadron calorimeter (HCAL). This analy-sis of the dimuon final state does not rely strongly on ECAL or HCAL measurements. Muons are measured in the window jj < 2:5 with the tracker and muon system. The pseudorapidity is defined as ln cotð=2Þ with the polar angle measured in the laboratory frame.
The silicon tracking detector (tracker) [29] consists of 1440 silicon pixel and 15 148 silicon strip detector mod-ules. The pixel modules provide two-dimensional mea-surements of the hit position in the module planes, which translate into three-dimensional measurements in space, and are arranged in three layers in the barrel and two layers in the forward regions. The silicon strip detector is com-posed of 10 layers in the barrel region, four of which are double-sided, and 12 layers in the endcap, where three out of six rings are with double-sided modules. Precise deter-mination of the position of all silicon modules (alignment) is one of the critical aspects for achieving the designed
Y -4 -3 -2 -1 0 1 2 3 4 Fraction / 0.2 0 0.005 0.01 0.015 0.02 0.025 0.03 m (GeV) 60 70 80 90 100 110 120 Fraction / 2 GeV -5 10 -4 10 -3 10 -2 10 -1 10 1 q q Σ u u d d s s c c b b * θ cos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Fraction / 0.1 0 0.02 0.04 0.06 0.08
FIG. 5 (color online). Distributions of Y (top), m (middle), and cos (bottom), from PYTHIA simulation (points) of the q q ! =Z ! þprocess and analytical distributions from Eq. (7). Distributions for five quark flavors are shown combined q q (black circles) and separately, in order of decreasing contribution: uu (red boxes), d d (blue crosses), s s (green diamonds), c c (magenta triangles), and b b (cyan stars). Distributions are nor-malized to unit area and are shown as fractions of events per bin.
resolutions of muon track parameters and is an important element of this analysis [30]. The muon system has detec-tion planes composed of three distinct detector technolo-gies installed outside the solenoid and embedded in the steel return yoke: drift tubes (in the barrel, jj < 1:2), cathode strip chambers (in the endcaps, 0:9 < jj < 2:5), and resistive plate chambers (in both barrel and endcap regions, jj < 1:6) [29].
This analysis uses data from proton-proton collisions at ffiffiffi
s p
¼ 7 TeV collected during 2010 and 2011, and corre-sponding to ð1:07 0:05Þ fb1 of integrated luminosity. The signal and background processes q q ! =Z ! þ and þ have been simulated with the NLO QCD generator POWHEG. Parton showering is simulated using PYTHIA. The NLO PDFs used are CT10 [20]. Background samples of W þ jets and tt are generated using MADGRAPH [31], PYTHIA, and TAUOLA [32]. Backgrounds from WW, WZ, ZZ, and QCD are generated usingPYTHIA. Generated events are processed through the CMS detector simulation and reconstruction. The detector simulation is based onGEANT4[33,34].
Muon candidates are selected from a sample triggered online by events with at least two muons within the volume defined by jj < 2:4 and with transverse momentum (pT) requirements. These requirements depend on the period of data-taking; however, they always accept two muons with pT of at least 8 and 13 GeV, respectively. Offline, muon tracks are first reconstructed independently in the tracker and the muon system. Muon candidates are then recon-structed by two different algorithms [35]. The global muon algorithm matches tracks in the tracker to tracks in the muon system, and then refits the individual hits in the tracker and muon system to one overall track. The tracker muon algorithm extrapolates tracks in the tracker with pT> 0:5 GeV and p > 2:5 GeV to the muon system, and a track is taken to be a muon candidate if it matches at least one track segment in the muon system. Both algorithms take into account energy loss and multiple scattering in the steel yoke of the CMS magnet. Selection criteria demand at least 10 hits in the tracker, including one in the pixel detector, at least one hit in the muon system, and a normalized 2< 10 for the global fit.
Muons are required to have a small impact parameter, less than 2 mm measured with respect to the beam spot in the plane perpendicular to the beam direction. This re-quirement removes cosmic-ray muons and background events with displaced vertices. We further require the angle between the two muon tracks to be larger than 2.5 mrad in the laboratory frame when the direction of one of the tracks is reversed. This removes any remaining cosmic-ray back-ground and has negligible effect on the signal. To isolate single muons from muons overlapping with jets, the sum of the transverse momentum of tracks in the tracker (exclud-ing the muon in question) within a surround(exclud-ing cone of R pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðÞ2þ ð Þ2< 0:3 is required to be less than
15% of the measured transverse momentum of the muon, where and are the differences in pseudorapidity and in azimuthal angle in radians between the muon and the track. The ECAL and HCAL are not used for muon isolation, to reduce the effect from FSR and to maximize the amount of signal events.
The kinematic requirements in the laboratory frame are jj < 2:4 and pT > 18 and 8 GeV for the two muons. We introduce additional requirements in the Collins–Soper frame in order to simplify the acceptance parameterization: jj < 2:3 and p
T> 18 GeV, where and pTare defined with respect to the z0-axis, described previously. We also require the dimuon transverse momentum in the laboratory frame to be less than 25 GeV in order to suppress the contribution of events with hard jet radiation. Dilepton events are selected from events containing two oppositely charged, isolated, high-pTmuons with a dilepton invariant mass m in the range 80–100 GeV. The dimuon rapidity Y is calculated from the lepton four-momenta as shown in Eq. (5). Restrictions on and Y are motivated by detector acceptance effects, as discussed in Sec.IV. The number of selected events in the data is N ¼ 297 364.
IV. ANALYSIS METHOD
We use an unbinned extended maximum-likelihood fit that simultaneously describes the signal and background yields and the parameters of the ðY; ^s; cosÞ distributions. The likelihood function is written as
L ¼ expðnsig nbkgÞ YN
i
ðnsig Psigð ~xi; eff; ~ Þ
þ nbkg Pbkgð ~xi; ~ ÞÞ; (12) where each event candidate i is characterized by a set of three observables ~xi¼ fY; ^s; cosgi, nsigis the number of signal events, which includes all intermediate states (, Z, and their interference), nbkg is the small number of back-ground events,Psigð ~xi; ~ Þ andPbkgð ~xi; ~ Þ are the probabil-ity densprobabil-ity functions for signal and background processes, and ~ represent the parameters of these functions. The signal probability density function is defined as
PsigðY; ^s; cos; effÞ ¼ GðY; ^s; cosÞ Zþ1
1 dxRðxÞPidealðY; ^s x; cos ;
effÞ: (13) The ideal distributionPidealðY; ^s; cos; effÞ in Eq. (13) is the Drell–Yan cross section defined in Eq. (7). We correct Pideal for detector effects, such as acceptance, parameter-ized with GðY; ^s; cosÞ, and resolution and photon emis-sion (FSR), parameterized withRðxÞ where x is the change in the dilepton center-of-mass energy squared.
The acceptance function GðY; ^s; cosÞ describes the nonuniform reconstruction efficiency as a function of the
three observables, which includes effects from online trigger requirements, detector acceptance, reconstruction algorithms, and selection requirements. The most impor-tant effect is the loss of particles near the beam directions and the second-most-important effect is the minimum transverse momentum requirement on the leptons. Otherwise, the efficiency across the acceptance range, defined by the selection requirements jj < Ymax ¼ 2:3 and pT> pmin¼ 18 GeV, is close to uniform. The above selection requirements define a sharp boundary in ðY; ^s; cosÞ space, which can be expressed as limits on cos for given Y and ^s values as follows:
j cosj < tanhðY max jYjÞ; (14) j cosj < ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 4p2 min=^s q : (15)
This boundary is illustrated in Fig.6in the ðY; cosÞ plane for a fixed value ^s ¼ m2
Z.
The effect of smearing the muon track parameters, such as the muon momentum and direction, due to detector resolution and FSR, is most evident in the invariant mass distribution. This effect is parameterized with the function RðxÞ in Eq. (13). Both acceptance and resolution effects are illustrated in Fig. 7, where the analytical parameteri-zation of Y, m ¼pffiffiffi^s, and cosis in good agreement with LO simulation in both QCD and EWK, as generated by
PYTHIA. Although a wider m range is investigated, the analysis is performed in the range 80 < m < 100 GeV to reduce uncertainties from FSR. In this illustration, FSR is included and the major detector effects are introduced in the following way: for the three track parameters (pT, , ), we apply Gaussian random smearing with standard deviation of pT ¼ 0:025pTþ 0:0001p2T (with pT in
GeV), ¼ ¼ 0:001 rad, and neglect resolution ef-fects on the track origin. This simplified simulation of detector effects is found useful to isolate production model uncertainties from the detector effect parameterization.
Y -2 -1 0 1 2 * limitsθ cos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
FIG. 6 (color online). Accepted cosrange as a function of Y for ^s ¼ m2
Zand for the kinematic selection used in this analysis.
The outer boundary corresponds to Eq. (14) and the horizontal lines near cos¼ 0:92 correspond to Eq. (15).
Y -4 -3 -2 -1 0 1 2 3 4 Fraction / 0.2 0 0.005 0.01 0.015 0.02 0.025 0.03 m (GeV) 60 70 80 90 100 110 120 Fraction / 0.5 GeV 0.02 0.04 0.06 0.08 0.1 0.12 ideal detector * θ cos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Fraction / 0.04 0 0.005 0.01 0.015 0.02 0.025 0.03
FIG. 7 (color online). Distributions of Y (top), m (middle), and cos (bottom), fromPYTHIAsimulation (points) of the q q ! =Z ! þ process and its analytical parameterization (smooth curve). Combined distributions from Fig. 5appear in red at the top of each plot (red circles for an ‘‘ideal’’ simulation), while distributions after acceptance and resolution effects, in-cluding photon FSR, appear in blue below (blue squares for a simplified ‘‘detector’’ simulation). Distributions are normalized to unit area and are shown as fractions of events per bin.
Further studies are performed with full GEANT4-based
modeling of the CMS detector using thePOWHEG simula-tion of the dimuon events and withPYTHIAsimulation of the parton showering and FSR. In the parameterization of the acceptance functionGðY; ^s; cosÞ, we model the small deviations from a uniform efficiency with empirical poly-nomial functions that include correlations of the two ob-servables within the boundaries of the ðY; cosÞ plane defined above. This efficiency parameterization is derived from the simulation with a fit where the parameters of the polynomial functions are left unconstrained. The main effect is a loss of efficiency in the vicinity of the acceptance boundaries. A similar approach is later employed as part of the systematic uncertainty studies where the parameters of the efficiency model are left free in the fit to data.
In the parameterization of the resolution functionRðxÞ, FSR is modeled with PYTHIA and resolution effects are taken from the full CMS detector simulation, including the effects of tracker alignment on the tracking resolution. The function RðxÞ is approximated with a sum of four Gaussian functions, to allow for the analytical convolution in Eq. (13) and be flexible enough to describe both detector resolution and FSR effects. Parameters of theRðxÞ func-tion are left free in the fit to the simulated MC sample. The overall shift of the Z mass in the resolution functionRðxÞ is left free in the fit to data, effectively allowing the energy scale to be determined from the data.
The background contribution is estimated by MC simu-lation; the QCD component has been cross-checked with data. The total expected background is about 0.05% of the signal yield. The background consists of the crossfeed from the q q ! Z= ! þ process, QCD, tt, and di-boson production in nearly equal contributions. The proba-bility density function for the background Pbkgð ~xi; ~ Þ is parameterized in a similar manner to that shown in Eq. (13) with an acceptance range defined by Eqs. (14) and (15) and the distributions within the acceptance boundaries parame-terized with an empirical polynomial function. The number of background events nbkgis fixed to the expected value of 157 events.
In Fig. 8 we show the cos distributions in the data separately for the jYj < 1 and jYj > 1 regions, and compare them to the POWHEG-based simulation of the qq ! =Z ! þ process in the CMS detector. Together with Fig.4, these distributions illustrate the chal-lenge of analyzing Drell–Yan events at the LHC. While the acceptance effects on the cos distribution are moderate for smaller values of jYj, the dilution is strong, as shown in Fig.4. In contrast, the larger values of jYj have a smaller dilution effect, but the cos range is strongly truncated because of the limited acceptance, as shown in Fig. 6. Therefore, the optimal analysis of the angular distributions requires proper accounting for such correlations among the three observables. At the same time, Fig. 8 shows good agreement between the data and MC simulation. Residual
differences in the distributions can be explained by the somewhat different value of sin2
eff ¼ 0:2311 used in the simulation compared to the best value describing the data, and by several systematic effects accounted for below, such as the tracker misalignment, the momentum scale in the track reconstruction, and FSR modeling.
A ‘‘blind’’ analysis of the data is performed, in which the fit result is not examined until a review of the entire analysis is complete, including the evaluation of all asso-ciated systematic uncertainties. However, while the analy-sis is performed ‘‘blind,’’ the quality of the fits to the MC simulation and data is examined. We test the performance of the fitting procedure using samples generated using Monte Carlo simulations, with each separate sample con-taining the same number of events observed in the data. Signal events are generated with thePOWHEG-based CMS detector simulation with an input value of sin2
eff ¼ 0:2311. The number of background events is Poisson
* θ cos -1 -0.5 0 0.5 1 Events / 0.04 0 2 4 6 3 10 ×
POWHEG and CMS simulation CMS data = 7 TeV s at -1 CMS 1.1 fb |Y| < 1
POWHEG and CMS simulation
CMS data * θ cos -1 -0.5 0 0.5 1 Events / 0.04 0 1 2 3 4 3 10 ×
POWHEG and CMS simulation CMS data = 7 TeV s at -1 CMS 1.1 fb |Y| > 1
POWHEG and CMS simulation CMS data
FIG. 8 (color online). Distribution of cos for data (points)
and POWHEG-based detector simulation with sin2
W ¼ 0:2311
(histogram) of the q q ! =Z ! þ process for jYj < 1 (top) and jYj > 1 (bottom).
distributed according to expectation. After the corrections discussed below are applied, the pull distribution is in agreement with a unit-width Gaussian distribution centered at zero. A comparison of the MC sample
projections and the probability density functions are shown in Fig.9.
We examine the quality of the fit to the data by com-paring the data distributions to the likelihood model
Y -2 -1 0 1 2 Events / 0.1 0 50 100 3 10 × Y -2 -1 0 1 2 Events / 0.1 0 50 100 3 10 ×
POWHEG and CMS simulation fit projection = 7 TeV s CMS simulation at m [GeV] 80 85 90 95 100 Events / 0.8 GeV 0 200 400 600 3 10 × m [GeV] 80 85 90 95 100 Events / 0.8 GeV 0 200 400 600 3 10 × datdum fit projection = 7 TeV s CMS simulation at
POWHEG and CMS simulation
* θ cos -1 -0.5 0 0.5 1 Events / 0.04 0 50 100 3 10 × * θ cos -1 -0.5 0 0.5 1 Events / 0.04 0 50 100 3 10 ×
POWHEG and CMS simulation
fit projection
= 7 TeV s CMS simulation at
FIG. 9 (color online). Distributions of Y (top), m (middle), and cos(bottom) from thePOWHEG-based detector simulation with sin2
W ¼ 0:2311 of the q q ! =Z ! þ process (points).
The MC sample corresponds to an integrated luminosity of 16 fb1. The lines show the projections of the probability density functions.
Y -2 -1 0 1 2 Events / 0.1 0 2 4 6 8 3 10 × Y -2 -1 0 1 2 Events / 0.1 0 2 4 6 8 3 10 × CMS data fit projection = 7 TeV s at -1 CMS 1.1 fb m (GeV) 80 85 90 95 100 Events / 0.8 GeV 0 20 40 3 10 × m (GeV) 80 85 90 95 100 Events / 0.8 GeV 0 20 40 3 10 × CMS data fit projection = 7 TeV s at -1 CMS 1.1 fb * θ cos -1 -0.5 0 0.5 1 Events / 0.04 0 2 4 6 3 10 × * θ cos -1 -0.5 0 0.5 1 Events / 0.04 0 2 4 6 3 10 × CMS data fit projection = 7 TeV s at -1 CMS 1.1 fb
FIG. 10 (color online). Distributions of Y (top), m (middle), and cos (bottom) in the analysis of q q ! =Z ! þ events from CMS (points). The lines show the projections of the probability density functions.
expectations, and comparing the fit likelihood valueL and the observed statistical uncertainty to those expected with the generated samples. Projections of the data and the probability density functions are shown in Fig. 10. They exhibit similar agreement as with the simulation shown in Fig.9. Correction for the energy scale is already included in the fit model. The observed statistical error on sin2
effof 0:0020 is in good agreement with what is expected from the MC samples discussed above. We find only small differences when comparing the likelihood value L for generated experiments from the likelihood model, the
POWHEG-based CMS detector simulation, and the data. The level of agreement is consistent with typical differ-ences due to imperfect efficiency function modeling and NLO effects discussed below. The variations do not affect the result of the analysis within the systematic uncertain-ties assigned.
V. SYSTEMATIC UNCERTAINTIES
The list of systematic uncertainties on the measurement of sin2eff and associated corrections to the fit values, as discussed below, is shown in TableII. These uncertainties arise from both theoretical assumptions and detector modeling.
We follow the PDF4LHC working group’s recommen-dation [23] in estimating uncertainties from the PDFs. We reweight a large MC sample generated with CT10 [20]
PDFs to obtain samples equivalent to MSTW 2008 [21] and NNPDF 2.1 [22] PDFs. We vary the internal degrees of freedom of the PDFs for all three sets of models. We also use this technique to vary s, but find its uncertainties to have negligible effects compared to any of the PDF variations. We find a change in the value of sin2
eff of þ4:8 104 and þ3:4 104 in using the PDFs from
MSTW and NNPDF, respectively. The variations in the value of sin2eff within each MC simulation due to the PDF uncertainties are þ13:012:1 104; þ3:94:1 104, and 7:3 104 for CT10, MSTW, and NNPDF, respectively. The envelope of the above variations corresponds to the total systematic uncertainty of 0:0013.
The FSR is modeled with PYTHIAin the
parameteriza-tion of the resoluparameteriza-tion funcparameteriza-tionRðxÞ. As a cross-check, we use four alternative FSR models for generation, with simplified detector simulation discussed above: PYTHIA,
PHOTOS [36], and two different modes in HORACE [37]. All three generator programs perform Oð Þ calculations of FSR and provide similar results, leading to differences in the fitted values of sin2
eff of about 0.001. In addition, the
HORACE generator allows the exact Oð Þ calculation and multiple-photon radiation from all charged states, which is the state-of-the-art EWK calculation. We found that this has a larger effect on the analysis when a wide range of values for the dimuon invariant mass m is used. However, with the mass range 80 < m < 100 GeV, the differences in the relevant part of the radiative tail become small. We perform cross-fits of the four generated samples and the four corresponding resolution functionsRðxÞ, finding dif-ferences in the fitted sin2
effvalues of at most 0.0011. The
PYTHIAsample typically results in larger differences from the other generators, and the assigned systematic uncer-tainty of 0:0011 covers these deviations. The assigned error conservatively covers the FSR uncertainty in the measurement when the fraction of FSR radiation is re-weighted in simulation. This reweighting technique is based on the comparison of the FSR fractions between data and thePYTHIAsimulation.
Effects from NLO EWK contributions are expected to be small compared to the statistical precision of our measurement. Calculations with the ZFITTER [38] pro-gram indicate that the variation of the effective value of sin2
eff for light quarks is within 0.0002 of the lepton values. It is only the heavier b quark that requires corrections of the order 0.001. However, given that only about 2.5% of the dileptons are produced in b b interactions, and no angular asymmetry can be measured because of the dilution factor with this initial state, these corrections have a negligible effect on our measurements.
Parameterization of the likelihood function models both the initial-state interactions and the PDFs at LO. The requirement that the dimuon transverse momentum pT be less than 25 GeV suppresses the contribution of events with hard jet radiation and reduces the effects from NLO pro-cesses. This requirement also ensures that the transforma-tion between the laboratory frame and the Collins–Soper frame is small, and that our analytical description of ac-ceptance effects is correct, without any loss of acac-ceptance coverage. With generated samples, we observe a bias of 0:0012 0:0006 in the fit value of sin2
eff, which is attributed to NLO effects. In this test, perfect CMS detector conditions are simulated, which removes most of the de-tector effects discussed below. To be conservative, we apply a correction of þ0:0012 and assign a systematic uncertainty of 0:0012 to cover all effects associated with the LO model. For example, we have investigated
TABLE II. Corrections to the fit values and systematic uncer-tainties in the measurement of sin2
eff.
source correction uncertainty
PDF - 0:0013
FSR - 0:0011
LO model (EWK) - 0:0002
LO model (QCD) þ0:0012 0:0012
resolution and alignment þ0:0007 0:0013
efficiency and acceptance - 0:0003
background - 0:0001
the dependence of the expected and observed shift in the fit result as a function of the pTrequirement over a wide range of pT. The results are stable within the uncertainty quoted. The distribution of pT exhibits only a small difference between the data and the MC simulation. We reweight the MC simulation to match the pT distribution to the data and observe that the results of the fit to the reweighted MC events are consistent with the case without reweighting to within 0.0004. Treating the correction as an additive or multiplicative factor does not affect the final result, as long as the observed value of sin2
eff is close to what is expected.
The detector resolution in the muon track reconstruction is affected by contributions from the silicon tracker align-ment. We perform a realistic simulation of the alignment procedure to model the statistical precision of the track reconstruction. We observe a bias of 0:0013 in the fit result of sin2
effwhen the realistic simulation of alignment is used in place of perfect conditions. We find that while the statistical precision of the track reconstruction is well modeled by the realistic simulation, the biases from 2-invariant detector deformations [30] may not neces-sarily be well reproduced in the MC simulation. We have investigated nine basic distortions in the tracker recon-struction geometry, which follow from the cylindrical symmetry of the system [30,39]. In each case, the proce-dure of the tracker alignment is repeated after the distortion is introduced. The effects of the remaining distortions on sin2
eff are all smaller than 0.001. The typical initial dis-tortions are taken to be 200 m, which is the approximate value of the constraints from the detector survey, the placement tolerance, and the observed agreement in the alignment procedure.
In the end, constraints on the above distortions in the tracker reconstruction geometry come from the data. We have observed that distortions affecting the sin2
eff fit values also introduce a bias in the mass of the dimuon pair m as a function of cos. We observe a linear trend in the bias of the average value of m as a function of cos, with a slope of 0:072 GeV, in the realistic simulation that is twice as large as that observed in data, 0:039 GeV, when both are compared to simulation with the ideal geometry model. We also observe a bias in the value of sin2effthat is twice as large when an additional systematic distortion is introduced in the realistic simulation, resulting in the slope of the average m value versus cos depen-dence also becoming twice as large. From these studies, we assign a correction of þ0:0007 to the fit value of sin2eff due to alignment effects and a systematic uncertainty of 0:0013 to cover the range of possible deviations ob-served. In order to minimize the uncertainties from the energy scale bias in the track reconstruction, the shift of the Z mass in the resolution functionRðxÞ is left free in the fit, effectively allowing the energy scale to be determined from the fit to the data. Consistency between the fit value
from the data and the expectation from the MC simulation is found to be within 0.1 GeV.
We find very weak sensitivity to the efficiency parame-terization GðY; ^s; cosÞ across the acceptance range because the efficiency is symmetric in cos. This leads to negligible effects on the odd terms in the angular distri-bution that are sensitive to sin2
eff. The sign of Y is defined by the dimuon system direction along the counterclock-wise beam and has no preferred direction. The sign of cos is defined by the charge of the ‘‘forward’’ lepton. The cylindrical symmetry of CMS, combined with the random nature of the forward direction, leads to a symme-try in the efficiency function. This has been verified with a detailed GEANT4–based simulation of the CMS detector, including calibration and alignment effects. Even in the extreme case ofGðY; ^s; cosÞ being flat across the accep-tance range, negligible changes in the fit results are ob-served with simulated samples. We also allow parameters of the model to be free in the fit to data. We assign a systematic uncertainty of 0.0003 due to efficiency and acceptance parameterization, which is the level of consis-tency of results from these studies.
The number of background events nbkg is fixed to the expected value and is varied according to its associated uncertainties. We assign a 50% uncertainty to the QCD rate, based on studies with wrong-sign lepton pairs. The relative size of the sum of the EWK background processes is expected to be reproduced by simulation to a precision of better than 20%. However, in the mass range 80 < m < 100 GeV, the fraction of background is only 0.05%, and the fit results are insensitive to the exact treatment of the background. The measured sin2
eff value remains stable within 0.0001, even when the background is removed from the model.
VI. RESULTS AND DISCUSSION
We have presented a likelihood method to analyze the Drell–Yan process at the LHC. The process is described by the correlated dilepton rapidity, invariant mass, and decay angle distributions. The quark direction in the elementary parton collisions, which is not directly accessible in the proton-proton collisions at the LHC, is modeled statis-tically using correlations between the observables. The result of the analysis, which includes systematic uncertain-ties and corrections from TableII, is
sin2
eff ¼ 0:2287 0:0020 ðstat:Þ 0:0025 ðsyst:Þ: This measurement of the effective weak mixing angle in the predominantly u u, d d ! =Z ! þprocesses in proton-proton collisions is consistent with measurements in other processes [5,7–11], as expected within the stan-dard model.
The dominant systematic uncertainties in the measure-ment include modeling of the PDFs, FSR, effects beyond the leading order in QCD, as well as detector uncertainties
primarily due to tracker alignment. With increased statis-tics of the Drell–Yan process at the LHC, a further reduc-tion of the systematic uncertainties will become critical. Understanding the tracker alignment will certainly improve as the collaboration gains further experience. Therefore, we expect the limiting uncertainties to come from the Drell–Yan process modeling.
Uncertainties from PDFs will decrease as better con-straints on the proton model become available from the LHC and elsewhere. In fact, the Drell–Yan process is itself a useful input to the PDF model constraints, and the methods discussed in this paper can be used to constrain the parameters in the PDF model. However, one must be careful not to mix information used for PDF constraints from the Drell–Yan process with measurements using the same events, unless the correlations are properly taken into account. Uncertainties from the FSR model may be im-proved as higher-order electroweak calculations are inte-grated with the higher-order QCD calculations of the matrix element in the Drell–Yan process, such as the incorporation ofPOWHEGandHORACE.
The LO approximations in the model may be further improved as NLO matrix elements are employed in the likelihood approach and more variables are integrated into the analysis. We view the current LO formalism as a conceptual step in developing multivariate matrix-element approaches to resonance polarization analyses, which can be applied to precision measurements, as well as potential new resonances that may be discovered at the LHC. The evolution of this method may also allow several parameters of the electroweak couplings to be determined simulta-neously, such as a measurement of the vector and axial-vector couplings of the light quarks separately from the lepton couplings.
ACKNOWLEDGMENTS
We would like to thank Kirill Melnikov and Alessandro Vicini for useful discussions of NLO QCD and EWK effects. We wish to congratulate our colleagues in the CERN accelerator departments for the excellent perform-ance of the LHC machine. We thank the technical and administrative staff at CERN and other CMS institutes. This work was supported by the Austrian Federal Ministry of Science and Research; the Belgium Fonds de la Recherche Scientifique, and Fonds voor Wetenschappelijk Onderzoek; the Brazilian Funding Agencies (CNPq, CAPES, FAPERJ, and FAPESP); the Bulgarian Ministry of Education and Science; CERN; the Chinese Academy of Sciences, Ministry of Science and Technology, and National Natural Science
Foundation of China; the Colombian Funding Agency (COLCIENCIAS); the Croatian Ministry of Science, Education and Sport; the Research Promotion Foundation, Cyprus; the Estonian Academy of Sciences and NICPB; the Academy of Finland, Finnish Ministry of Education and Culture, and Helsinki Institute of Physics; the Institut National de Physique Nucle´aire et de Physique des Particules/CNRS, and Commissariat a` l’E´ nergie Atomique et aux E´ nergies Alternatives/CEA, France; the Bundesministerium fu¨r Bildung und Forschung, Deutsche Forschungsgemeinschaft, and Helmholtz-Gemeinschaft Deutscher Forschungszentren, Germany; the General Secretariat for Research and Technology, Greece; the National Scientific Research Foundation, and National Office for Research and Technology, Hungary; the Department of Atomic Energy and the Department of Science and Technology, India; the Institute for Studies in Theoretical Physics and Mathematics, Iran; the Science Foundation, Ireland; the Istituto Nazionale di Fisica Nucleare, Italy; the Korean Ministry of Education, Science and Technology and the World Class University program of NRF, Korea; the Lithuanian Academy of Sciences; the Mexican Funding Agencies (CINVESTAV, CONACYT, SEP, and UASLP-FAI); the Ministry of Science and Innovation, New Zealand; the Pakistan Atomic Energy Commission; the State Commission for Scientific Research, Poland; the Fundac¸a˜o para a Cieˆncia e a Tecnologia, Portugal; JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan); the Ministry of Science and Technologies of the Russian Federation, the Russian Ministry of Atomic Energy and the Russian Foundation for Basic Research; the Ministry of Science and Technological Development of Serbia; the Ministerio de Ciencia e Innovacio´n, and Programa Consolider-Ingenio 2010, Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the National Science Council, Taipei; the Scientific and Technical Research Council of Turkey, and Turkish Atomic Energy Authority; the Science and Technology Facilities Council, UK; the US Department of Energy, and the US National Science Foundation. Individuals have received support from the Marie-Curie programme and the European Research 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 a` la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); and the Council of Science and Industrial Research, India.
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A. Pin,8K. Piotrzkowski,8N. Schul,8N. Beliy,9T. Caebergs,9E. Daubie,9G. A. Alves,10L. Brito,10 D. De Jesus Damiao,10M. E. Pol,10M. H. G. Souza,10W. L. Alda´ Ju´nior,11W. Carvalho,11E. M. Da Costa,11 C. De Oliveira Martins,11S. Fonseca De Souza,11D. Matos Figueiredo,11L. Mundim,11H. Nogima,11V. Oguri,11 W. L. Prado Da Silva,11A. Santoro,11S. M. Silva Do Amaral,11A. Sznajder,11T. S. Anjos,12,cC. A. Bernardes,12,c
F. A. Dias,12,dT. R. Fernandez Perez Tomei,12E. M. Gregores,12,cC. Lagana,12F. Marinho,12P. G. Mercadante,12,c S. F. Novaes,12Sandra S. Padula,12N. Darmenov,13,bV. Genchev,13,bP. Iaydjiev,13,bS. Piperov,13M. Rodozov,13
S. Stoykova,13G. Sultanov,13V. Tcholakov,13R. Trayanov,13M. Vutova,13A. Dimitrov,14R. Hadjiiska,14 A. Karadzhinova,14V. Kozhuharov,14L. Litov,14M. Mateev,14B. Pavlov,14P. Petkov,14J. G. Bian,15G. M. Chen,15 H. S. Chen,15C. H. Jiang,15D. Liang,15S. Liang,15X. Meng,15J. Tao,15J. Wang,15J. Wang,15X. Wang,15Z. Wang,15 H. Xiao,15M. Xu,15J. Zang,15Z. Zhang,15Y. Ban,16S. Guo,16Y. Guo,16W. Li,16Y. Mao,16S. J. Qian,16H. Teng,16
B. Zhu,16W. Zou,16A. Cabrera,17B. Gomez Moreno,17A. A. Ocampo Rios,17A. F. Osorio Oliveros,17 J. C. Sanabria,17N. Godinovic,18D. Lelas,18K. Lelas,18R. Plestina,18,eD. Polic,18I. Puljak,18Z. Antunovic,19
M. Dzelalija,19M. Kovac,19V. Brigljevic,20S. Duric,20K. Kadija,20J. Luetic,20S. Morovic,20A. Attikis,21 M. Galanti,21J. Mousa,21C. Nicolaou,21F. Ptochos,21P. A. Razis,21M. Finger,22M. Finger, Jr.,22Y. Assran,23,f
A. Ellithi Kamel,23,gS. Khalil,23,hM. A. Mahmoud,23,iA. Radi,23,jA. Hektor,24M. Kadastik,24M. Mu¨ntel,24 M. Raidal,24L. Rebane,24A. Tiko,24V. Azzolini,25P. Eerola,25G. Fedi,25M. Voutilainen,25S. Czellar,26 J. Ha¨rko¨nen,26A. Heikkinen,26V. Karima¨ki,26R. Kinnunen,26M. J. Kortelainen,26T. Lampe´n,26K. Lassila-Perini,26 S. Lehti,26T. Linde´n,26P. Luukka,26T. Ma¨enpa¨a¨,26E. Tuominen,26J. Tuominiemi,26E. Tuovinen,26D. Ungaro,26
L. Wendland,26K. Banzuzi,27A. Karjalainen,27A. Korpela,27T. Tuuva,27D. Sillou,28M. Besancon,29 S. Choudhury,29M. Dejardin,29D. Denegri,29B. Fabbro,29J. L. Faure,29F. Ferri,29S. Ganjour,29A. Givernaud,29
P. Gras,29G. Hamel de Monchenault,29P. Jarry,29E. Locci,29J. Malcles,29M. Marionneau,29L. Millischer,29 J. Rander,29A. Rosowsky,29I. Shreyber,29M. Titov,29S. Baffioni,30F. Beaudette,30L. Benhabib,30L. Bianchini,30
M. Bluj,30,kC. Broutin,30P. Busson,30C. Charlot,30T. Dahms,30L. Dobrzynski,30S. Elgammal,30 R. Granier de Cassagnac,30M. Haguenauer,30P. Mine´,30C. Mironov,30C. Ochando,30P. Paganini,30D. Sabes,30
R. Salerno,30Y. Sirois,30C. Thiebaux,30C. Veelken,30A. Zabi,30J.-L. Agram,31,lJ. Andrea,31D. Bloch,31 D. Bodin,31J.-M. Brom,31M. Cardaci,31E. C. Chabert,31C. Collard,31E. Conte,31,lF. Drouhin,31,lC. Ferro,31 J.-C. Fontaine,31,lD. Gele´,31U. Goerlach,31S. Greder,31P. Juillot,31M. Karim,31,lA.-C. Le Bihan,31Y. Mikami,31
P. Van Hove,31F. Fassi,32D. Mercier,32C. Baty,33S. Beauceron,33N. Beaupere,33M. Bedjidian,33O. Bondu,33 G. Boudoul,33D. Boumediene,33H. Brun,33J. Chasserat,33R. Chierici,33D. Contardo,33P. Depasse,33 H. El Mamouni,33J. Fay,33S. Gascon,33B. Ille,33T. Kurca,33T. Le Grand,33M. Lethuillier,33L. Mirabito,33
S. Perries,33V. Sordini,33S. Tosi,33Y. Tschudi,33P. Verdier,33S. Viret,33D. Lomidze,34G. Anagnostou,35 S. Beranek,35M. Edelhoff,35L. Feld,35N. Heracleous,35O. Hindrichs,35R. Jussen,35K. Klein,35J. Merz,35 N. Mohr,35A. Ostapchuk,35A. Perieanu,35F. Raupach,35J. Sammet,35S. Schael,35D. Sprenger,35H. Weber,35
M. Weber,35B. Wittmer,35V. Zhukov,35,mM. Ata,36E. Dietz-Laursonn,36M. Erdmann,36T. Hebbeker,36 C. Heidemann,36A. Hinzmann,36K. Hoepfner,36T. Klimkovich,36D. Klingebiel,36P. Kreuzer,36D. Lanske,36,a J. Lingemann,36C. Magass,36M. Merschmeyer,36A. Meyer,36P. Papacz,36H. Pieta,36H. Reithler,36S. A. Schmitz,36 L. Sonnenschein,36J. Steggemann,36D. Teyssier,36M. Bontenackels,37V. Cherepanov,37M. Davids,37G. Flu¨gge,37
H. Geenen,37M. Giffels,37W. Haj Ahmad,37F. Hoehle,37B. Kargoll,37T. Kress,37Y. Kuessel,37A. Linn,37 A. Nowack,37L. Perchalla,37O. Pooth,37J. Rennefeld,37P. Sauerland,37A. Stahl,37D. Tornier,37M. H. Zoeller,37
M. Aldaya Martin,38W. Behrenhoff,38U. Behrens,38M. Bergholz,38,nA. Bethani,38K. Borras,38A. Cakir,38 A. Campbell,38E. Castro,38D. Dammann,38G. Eckerlin,38D. Eckstein,38A. Flossdorf,38G. Flucke,38A. Geiser,38
J. Hauk,38H. Jung,38,bM. Kasemann,38P. Katsas,38C. Kleinwort,38H. Kluge,38A. Knutsson,38M. Kra¨mer,38 D. Kru¨cker,38E. Kuznetsova,38W. Lange,38W. Lohmann,38,nB. Lutz,38R. Mankel,38M. Marienfeld,38 I.-A. Melzer-Pellmann,38A. B. Meyer,38J. Mnich,38A. Mussgiller,38J. Olzem,38A. Petrukhin,38D. Pitzl,38 A. Raspereza,38M. Rosin,38R. Schmidt,38,nT. Schoerner-Sadenius,38N. Sen,38A. Spiridonov,38M. Stein,38 J. Tomaszewska,38R. Walsh,38C. Wissing,38C. Autermann,39V. Blobel,39S. Bobrovskyi,39J. Draeger,39 H. Enderle,39U. Gebbert,39M. Go¨rner,39T. Hermanns,39K. Kaschube,39G. Kaussen,39H. Kirschenmann,39 R. Klanner,39J. Lange,39B. Mura,39S. Naumann-Emme,39F. Nowak,39N. Pietsch,39C. Sander,39H. Schettler,39 P. Schleper,39E. Schlieckau,39M. Schro¨der,39T. Schum,39H. Stadie,39G. Steinbru¨ck,39J. Thomsen,39C. Barth,40
J. Bauer,40J. Berger,40V. Buege,40T. Chwalek,40W. De Boer,40A. Dierlamm,40G. Dirkes,40M. Feindt,40 J. Gruschke,40M. Guthoff,40,bC. Hackstein,40F. Hartmann,40M. Heinrich,40H. Held,40K. H. Hoffmann,40 S. Honc,40I. Katkov,40,mJ. R. Komaragiri,40T. Kuhr,40D. Martschei,40S. Mueller,40Th. Mu¨ller,40M. Niegel,40 O. Oberst,40A. Oehler,40J. Ott,40T. Peiffer,40G. Quast,40K. Rabbertz,40F. Ratnikov,40N. Ratnikova,40M. Renz,40
S. Ro¨cker,40C. Saout,40A. Scheurer,40P. Schieferdecker,40F.-P. Schilling,40M. Schmanau,40G. Schott,40 H. J. Simonis,40F. M. Stober,40D. Troendle,40J. Wagner-Kuhr,40T. Weiler,40M. Zeise,40E. B. Ziebarth,40
G. Daskalakis,41T. Geralis,41S. Kesisoglou,41A. Kyriakis,41D. Loukas,41I. Manolakos,41A. Markou,41 C. Markou,41C. Mavrommatis,41E. Ntomari,41E. Petrakou,41L. Gouskos,42T. J. Mertzimekis,42A. Panagiotou,42
N. Saoulidou,42E. Stiliaris,42I. Evangelou,43C. Foudas,43,bP. Kokkas,43N. Manthos,43I. Papadopoulos,43 V. Patras,43F. A. Triantis,43A. Aranyi,44G. Bencze,44L. Boldizsar,44C. Hajdu,44,bP. Hidas,44D. Horvath,44,o A. Kapusi,44K. Krajczar,44,pF. Sikler,44,bG. I. Veres,44,pG. Vesztergombi,44,pN. Beni,45J. Molnar,45J. Palinkas,45 Z. Szillasi,45V. Veszpremi,45J. Karancsi,46P. Raics,46Z. L. Trocsanyi,46B. Ujvari,46S. B. Beri,47V. Bhatnagar,47
N. Dhingra,47R. Gupta,47M. Jindal,47M. Kaur,47J. M. Kohli,47M. Z. Mehta,47N. Nishu,47L. K. Saini,47 A. Sharma,47A. P. Singh,47J. Singh,47S. P. Singh,47S. Ahuja,48B. C. Choudhary,48P. Gupta,48A. Kumar,48 A. Kumar,48S. Malhotra,48M. Naimuddin,48K. Ranjan,48R. K. Shivpuri,48S. Banerjee,49S. Bhattacharya,49 S. Dutta,49B. Gomber,49S. Jain,49S. Jain,49R. Khurana,49S. Sarkar,49R. K. Choudhury,50D. Dutta,50S. Kailas,50
V. Kumar,50P. Mehta,50A. K. Mohanty,50,bL. M. Pant,50P. Shukla,50T. Aziz,51M. Guchait,51,qA. Gurtu,51 M. Maity,51,rD. Majumder,51G. Majumder,51K. Mazumdar,51G. B. Mohanty,51B. Parida,51A. Saha,51 K. Sudhakar,51N. Wickramage,51S. Banerjee,52S. Dugad,52N. K. Mondal,52H. Arfaei,53H. Bakhshiansohi,53,s
S. M. Etesami,53,tA. Fahim,53,sM. Hashemi,53H. Hesari,53A. Jafari,53,sM. Khakzad,53A. Mohammadi,53,u M. Mohammadi Najafabadi,53S. Paktinat Mehdiabadi,53B. Safarzadeh,53M. Zeinali,53,tM. Abbrescia,54a,54b L. Barbone,54a,54bC. Calabria,54a,54bA. Colaleo,54aD. Creanza,54a,54cN. De Filippis,54a,54c,bM. De Palma,54a,54b L. Fiore,54aG. Iaselli,54a,54cL. Lusito,54a,54bG. Maggi,54a,54cM. Maggi,54aN. Manna,54a,54bB. Marangelli,54a,54b
S. My,54a,54cS. Nuzzo,54a,54bN. Pacifico,54a,54bG. A. Pierro,54aA. Pompili,54a,54bG. Pugliese,54a,54c F. Romano,54a,54cG. Roselli,54a,54bG. Selvaggi,54a,54bL. Silvestris,54aR. Trentadue,54aS. Tupputi,54a,54bG. Zito,54a
G. Abbiendi,55aA. C. Benvenuti,55aD. Bonacorsi,55aS. Braibant-Giacomelli,55a,55bL. Brigliadori,55a P. Capiluppi,55a,55bA. Castro,55a,55bF. R. Cavallo,55aM. Cuffiani,55a,55bG. M. Dallavalle,55aF. Fabbri,55a A. Fanfani,55a,55bD. Fasanella,55a,bP. Giacomelli,55aM. Giunta,55aC. Grandi,55aS. Marcellini,55aG. Masetti,55b
M. Meneghelli,55a,55bA. Montanari,55aF. L. Navarria,55a,55bF. Odorici,55aA. Perrotta,55aF. Primavera,55a A. M. Rossi,55a,55bT. Rovelli,55a,55bG. Siroli,55a,55bR. Travaglini,55a,55bS. Albergo,56a,56bG. Cappello,56a,56b
M. Chiorboli,56a,56bS. Costa,56a,56bR. Potenza,56a,56bA. Tricomi,56a,56bC. Tuve,56a,56bG. Barbagli,57a V. Ciulli,57a,57bC. Civinini,57aR. D’Alessandro,57a,57bE. Focardi,57a,57bS. Frosali,57a,57bE. Gallo,57aS. Gonzi,57a,57b M. Meschini,57aS. Paoletti,57aG. Sguazzoni,57aA. Tropiano,57a,bL. Benussi,58S. Bianco,58S. Colafranceschi,58,v
F. Fabbri,58D. Piccolo,58P. Fabbricatore,59R. Musenich,59A. Benaglia,60a,60b,bF. De Guio,60a,60b L. Di Matteo,60a,60bS. Gennai,60a,bA. Ghezzi,60a,60bS. Malvezzi,60aA. Martelli,60a,60bA. Massironi,60a,60b,b D. Menasce,60aL. Moroni,60aM. Paganoni,60a,60bD. Pedrini,60aS. Ragazzi,60a,60bN. Redaelli,60aS. Sala,60a T. Tabarelli de Fatis,60a,60bS. Buontempo,61aC. A. Carrillo Montoya,61a,bN. Cavallo,61a,wA. De Cosa,61a,61b O. Dogangun,61a,61bF. Fabozzi,61a,wA. O. M. Iorio,61a,bL. Lista,61aM. Merola,61a,61bP. Paolucci,61aP. Azzi,62a N. Bacchetta,62a,bP. Bellan,62a,62bD. Bisello,62a,62bA. Branca,62aR. Carlin,62a,62bP. Checchia,62aT. Dorigo,62a
U. Dosselli,62aF. Fanzago,62aF. Gasparini,62a,62bU. Gasparini,62a,62bA. Gozzelino,62aS. Lacaprara,62a,x I. Lazzizzera,62a,62cM. Margoni,62a,62bM. Mazzucato,62aA. T. Meneguzzo,62a,62bM. Nespolo,62a,bL. Perrozzi,62a
N. Pozzobon,62a,62bP. Ronchese,62a,62bF. Simonetto,62a,62bE. Torassa,62aM. Tosi,62a,62b,bS. Vanini,62a,62b P. Zotto,62a,62bG. Zumerle,62a,62bP. Baesso,63a,63bU. Berzano,63aS. P. Ratti,63a,63bC. Riccardi,63a,63bP. Torre,63a,63b
P. Vitulo,63a,63bC. Viviani,63a,63bM. Biasini,64a,64bG. M. Bilei,64aB. Caponeri,64a,64bL. Fano`,64a,64b P. Lariccia,64a,64bA. Lucaroni,64a,64b,bG. Mantovani,64a,64bM. Menichelli,64aA. Nappi,64a,64bF. Romeo,64a,64b
A. Santocchia,64a,64bS. Taroni,64a,64b,bM. Valdata,64a,64bP. Azzurri,65a,65cG. Bagliesi,65aJ. Bernardini,65a,65b T. Boccali,65aG. Broccolo,65a,65cR. Castaldi,65aR. T. D’Agnolo,65a,65cR. Dell’Orso,65aF. Fiori,65a,65bL. Foa`,65a,65c
A. Giassi,65aA. Kraan,65aF. Ligabue,65a,65cT. Lomtadze,65aL. Martini,65a,yA. Messineo,65a,65bF. Palla,65a F. Palmonari,65aG. Segneri,65aA. T. Serban,65aP. Spagnolo,65aR. Tenchini,65aG. Tonelli,65a,65b,bA. Venturi,65a,b
P. G. Verdini,65aL. Barone,66a,66bF. Cavallari,66aD. Del Re,66a,66b,bE. Di Marco,66a,66bM. Diemoz,66a D. Franci,66a,66bM. Grassi,66a,bE. Longo,66a,66bP. Meridiani,66aS. Nourbakhsh,66aG. Organtini,66a,66b F. Pandolfi,66a,66bR. Paramatti,66aS. Rahatlou,66a,66bM. Sigamani,66aN. Amapane,67a,67bR. Arcidiacono,67a,67c S. Argiro,67a,67bM. Arneodo,67a,67cC. Biino,67aC. Botta,67a,67bN. Cartiglia,67aR. Castello,67a,67bM. Costa,67a,67b N. Demaria,67aA. Graziano,67a,67bC. Mariotti,67aS. Maselli,67aE. Migliore,67a,67bV. Monaco,67a,67bM. Musich,67a M. M. Obertino,67a,67cN. Pastrone,67aM. Pelliccioni,67a,67bA. Potenza,67a,67bA. Romero,67a,67bM. Ruspa,67a,67c R. Sacchi,67a,67bV. Sola,67a,67bA. Solano,67a,67bA. Staiano,67aA. Vilela Pereira,67aS. Belforte,68aF. Cossutti,68a G. Della Ricca,68a,68bB. Gobbo,68aM. Marone,68a,68bD. Montanino,68a,68bA. Penzo,68aS. G. Heo,69S. K. Nam,69
S. Chang,70J. Chung,70D. H. Kim,70G. N. Kim,70J. E. Kim,70D. J. Kong,70H. Park,70S. R. Ro,70D. C. Son,70 T. Son,70J. Y. Kim,71Zero J. Kim,71S. Song,71H. Y. Jo,72S. Choi,73D. Gyun,73B. Hong,73M. Jo,73H. Kim,73 T. J. Kim,73K. S. Lee,73D. H. Moon,73S. K. Park,73E. Seo,73K. S. Sim,73M. Choi,74S. Kang,74H. Kim,74 J. H. Kim,74C. Park,74I. C. Park,74S. Park,74G. Ryu,74Y. Cho,75Y. Choi,75Y. K. Choi,75J. Goh,75M. S. Kim,75
B. Lee,75J. Lee,75S. Lee,75H. Seo,75I. Yu,75M. J. Bilinskas,76I. Grigelionis,76M. Janulis,76D. Martisiute,76 P. Petrov,76M. Polujanskas,76T. Sabonis,76H. Castilla-Valdez,77E. De La Cruz-Burelo,77I. Heredia-de La Cruz,77
R. Lopez-Fernandez,77R. Magan˜a Villalba,77J. Martı´nez-Ortega,77A. Sa´nchez-Herna´ndez,77 L. M. Villasenor-Cendejas,77S. Carrillo Moreno,78F. Vazquez Valencia,78H. A. Salazar Ibarguen,79 E. Casimiro Linares,80A. Morelos Pineda,80M. A. Reyes-Santos,80D. Krofcheck,81J. Tam,81P. H. Butler,82
R. Doesburg,82H. Silverwood,82M. Ahmad,83I. Ahmed,83M. I. Asghar,83H. R. Hoorani,83S. Khalid,83 W. A. Khan,83T. Khurshid,83S. Qazi,83M. A. Shah,83M. Shoaib,83G. Brona,84M. Cwiok,84W. Dominik,84
K. Doroba,84A. Kalinowski,84M. Konecki,84J. Krolikowski,84T. Frueboes,85R. Gokieli,85M. Go´rski,85 M. Kazana,85K. Nawrocki,85K. Romanowska-Rybinska,85M. Szleper,85G. Wrochna,85P. Zalewski,85 N. Almeida,86P. Bargassa,86A. David,86P. Faccioli,86P. G. Ferreira Parracho,86M. Gallinaro,86,bP. Musella,86
A. Nayak,86J. Pela,86,bP. Q. Ribeiro,86J. Seixas,86J. Varela,86S. Afanasiev,87I. Belotelov,87P. Bunin,87 M. Gavrilenko,87I. Golutvin,87A. Kamenev,87V. Karjavin,87G. Kozlov,87A. Lanev,87P. Moisenz,87V. Palichik,87
V. Perelygin,87S. Shmatov,87V. Smirnov,87A. Volodko,87A. Zarubin,87V. Golovtsov,88Y. Ivanov,88V. Kim,88 P. Levchenko,88V. Murzin,88V. Oreshkin,88I. Smirnov,88V. Sulimov,88L. Uvarov,88S. Vavilov,88A. Vorobyev,88
An. Vorobyev,88Yu. Andreev,89A. Dermenev,89S. Gninenko,89N. Golubev,89M. Kirsanov,89N. Krasnikov,89 V. Matveev,89A. Pashenkov,89A. Toropin,89S. Troitsky,89V. Epshteyn,90M. Erofeeva,90V. Gavrilov,90 V. Kaftanov,90,aM. Kossov,90,bA. Krokhotin,90N. Lychkovskaya,90V. Popov,90G. Safronov,90S. Semenov,90
V. Stolin,90E. Vlasov,90A. Zhokin,90A. Belyaev,91E. Boos,91M. Dubinin,91,dL. Dudko,91A. Ershov,91 A. Gribushin,91O. Kodolova,91I. Lokhtin,91A. Markina,91S. Obraztsov,91M. Perfilov,91S. Petrushanko,91
L. Sarycheva,91V. Savrin,91A. Snigirev,91V. Andreev,92M. Azarkin,92I. Dremin,92M. Kirakosyan,92 A. Leonidov,92G. Mesyats,92S. V. Rusakov,92A. Vinogradov,92I. Azhgirey,93I. Bayshev,93S. Bitioukov,93
V. Grishin,93,bV. Kachanov,93D. Konstantinov,93A. Korablev,93V. Krychkine,93V. Petrov,93R. Ryutin,93 A. Sobol,93L. Tourtchanovitch,93S. Troshin,93N. Tyurin,93A. Uzunian,93A. Volkov,93P. Adzic,94,zM. Djordjevic,94 M. Ekmedzic,94D. Krpic,94,zJ. Milosevic,94M. Aguilar-Benitez,95J. Alcaraz Maestre,95P. Arce,95C. Battilana,95 E. Calvo,95M. Cerrada,95M. Chamizo Llatas,95N. Colino,95B. De La Cruz,95A. Delgado Peris,95C. Diez Pardos,95 D. Domı´nguez Va´zquez,95C. Fernandez Bedoya,95J. P. Ferna´ndez Ramos,95A. Ferrando,95J. Flix,95M. C. Fouz,95
P. Garcia-Abia,95O. Gonzalez Lopez,95S. Goy Lopez,95J. M. Hernandez,95M. I. Josa,95G. Merino,95 J. Puerta Pelayo,95I. Redondo,95L. Romero,95J. Santaolalla,95M. S. Soares,95C. Willmott,95C. Albajar,96 G. Codispoti,96J. F. de Troco´niz,96J. Cuevas,97J. Fernandez Menendez,97S. Folgueras,97I. Gonzalez Caballero,97 L. Lloret Iglesias,97J. M. Vizan Garcia,97J. A. Brochero Cifuentes,98I. J. Cabrillo,98A. Calderon,98S. H. Chuang,98
J. Duarte Campderros,98M. Felcini,98,aaM. Fernandez,98G. Gomez,98J. Gonzalez Sanchez,98C. Jorda,98 P. Lobelle Pardo,98A. Lopez Virto,98J. Marco,98R. Marco,98C. Martinez Rivero,98F. Matorras,98 F. J. Munoz Sanchez,98J. Piedra Gomez,98,bbT. Rodrigo,98A. Y. Rodrı´guez-Marrero,98A. Ruiz-Jimeno,98 L. Scodellaro,98M. Sobron Sanudo,98I. Vila,98R. Vilar Cortabitarte,98D. Abbaneo,99E. Auffray,99G. Auzinger,99
P. Baillon,99A. H. Ball,99D. Barney,99A. J. Bell,99,ccD. Benedetti,99C. Bernet,99,eW. Bialas,99P. Bloch,99 A. Bocci,99S. Bolognesi,99M. Bona,99H. Breuker,99K. Bunkowski,99T. Camporesi,99G. Cerminara,99
T. Christiansen,99J. A. Coarasa Perez,99B. Cure´,99D. D’Enterria,99A. De Roeck,99S. Di Guida,99 N. Dupont-Sagorin,99A. Elliott-Peisert,99B. Frisch,99W. Funk,99A. Gaddi,99G. Georgiou,99H. Gerwig,99
D. Gigi,99K. Gill,99D. Giordano,99F. Glege,99R. Gomez-Reino Garrido,99M. Gouzevitch,99P. Govoni,99 S. Gowdy,99R. Guida,99L. Guiducci,99M. Hansen,99C. Hartl,99J. Harvey,99J. Hegeman,99B. Hegner,99 H. F. Hoffmann,99V. Innocente,99P. Janot,99K. Kaadze,99E. Karavakis,99P. Lecoq,99P. Lenzi,99C. Lourenc¸o,99
T. Ma¨ki,99M. Malberti,99L. Malgeri,99M. Mannelli,99L. Masetti,99A. Maurisset,99G. Mavromanolakis,99 F. Meijers,99S. Mersi,99E. Meschi,99R. Moser,99M. U. Mozer,99M. Mulders,99E. Nesvold,99M. Nguyen,99 T. Orimoto,99L. Orsini,99E. Palencia Cortezon,99E. Perez,99A. Petrilli,99A. Pfeiffer,99M. Pierini,99M. Pimia¨,99
D. Piparo,99G. Polese,99L. Quertenmont,99A. Racz,99W. Reece,99J. Rodrigues Antunes,99G. Rolandi,99,dd T. Rommerskirchen,99C. Rovelli,99,eeM. Rovere,99H. Sakulin,99C. Scha¨fer,99C. Schwick,99I. Segoni,99 A. Sharma,99P. Siegrist,99P. Silva,99M. Simon,99P. Sphicas,99,ffD. Spiga,99M. Spiropulu,99,dM. Stoye,99
![TABLE I. Vector and axial-vector couplings of the SM gauge bosons to the charged fermion fields [16].](https://thumb-eu.123doks.com/thumbv2/123dokorg/5561073.66271/2.918.505.839.504.657/table-vector-vector-couplings-bosons-charged-fermion-fields.webp)
