ISSN 1063�7796, Physics of Particles and Nuclei, 2014, Vol. 45, No. 1, pp. 211–213. © Pleiades Publishing, Ltd., 2014.

211

1 In the process q → Z/γ* → l+l– both vector andaxial�vector couplings of electroweak bosons to fermi�ons are present. This gives rise to an asymmetry in theemission direction of leptons. This asymmetrydepends on the di�lepton invariant mass, quark flavor,rapidity and sin2θW. Deviations from the StandardModel prediction for AFB may indicate the existence ofa new neutral gauge boson [1], quark�lepton compos�iteness [2], existence of supersymmetric particles, orextra dimensions [3]. Measurement of forward�back�ward asymmetry can also improve QCD measure�ments with higher order corrections and constrainParton Distribution Functions (PDFs). Moreover, themeasurement of the asymmetry at the Z�pole can pro�vide a precise measurement of sin2θW.

The differential cross�section for the parton levelprocess can be written as:

(1)

where θ is the emission angel of the negative leptonrelativ to the quark momentum in the center�of�massframe, and A and B depend on the weak isospin andcharge of the incoming fermions. The cross secctionfor the forward (σF, cosθ > 0) and backward (σB,cosθ < 0) events are then:

(2)

(3)

1 The article is published in the original.

q

dσd θcos( )���������������� A 1 θ2

cos+( ) B θcos ,+=

σFdσ

θcos( )d���������������� θcos( )d

0

1

∫ A 1 13��+⎝ ⎠

⎛ ⎞ B 12��,×+= =

σBdσ

θcos( )d���������������� θcos( )d

1–

0

∫ A 1 13��+⎝ ⎠

⎛ ⎞ B 12��,×–= =

and the asymmetry parameter AFB is given by:

(4)

The potential of the CMS experiment to measurethe forward�backward asymmetry for dilepton pairs upto the highest masses that will be accessible at the LHCin pp collisions at 14 TeV have been investigated indetails on Monte�Carlo [4, 5]. For correct measure�ments and final data analysis it is necessary to keep allpossible sources of the systemtic uncertainties undercontrol. These systematic uncertainties can be relatedto the accuracy of theoretical calculations, accuracy ofphenomenological determination of PDFs and theexperimental uncertainties—detector resolutionquality of fits etc.

The measurement of AFB by CMS in pp collisionshave been performed using 2011 data corresponding to5 fb–1 integrated luminosity [6]. A detailed descriptionof the CMS detector can be found in [7].

The signal (Z/γ* → μ+μ–, e+e–) and the Z → ττprocess, which is considered as a background in thisanalysis, are simulated using POWHEG at next�to�leading order (NLO). Parton showering is simulatedusing PYTHIA v6.4.24 [8] with tune Z2, while theNLO parton distribution function (PDF) is CT10 [9].The W + jets and tt background events are generatedusing MADGRAPH [10] and PYTHIA; the TAUOLApackage is used to describe τ decays [11]. Event sam�ples of WW, WZ, ZZ, and QCD multijet backgroundsare generated using PYTHIA. The generated eventsare processed with the GEANT4�based [12] CMSdetector simulation and reconstructed with the samesoftware as the collision data. The signal MC samplesinclude pileup conditions (multiple pp interactionsoccurring in the same bunch crossing) matching thoseobserved in the 2011 data sample.

For both lepton channels, the main sources ofbackground are Z → ττ and QCD dijets for the low

AFBσF σB–σF σB+��������������� 3B

8A����� .= =

Measurement of the Forward�Backward Asymmetry of µ+µ– Pairs in CMS1

I. N. Gorbunov and S. V. Shmatov on behalf of the CMS CollaborationJoint Institute for Nuclear Research, Dubna, 141980 Russia

Abstract—The measurement of the forward�backward asymmetry AFB and the effective weak mixing anglewith the Drell–Yan process at the LHC is presented. The samples of 2011 collected by the CMS experimentat the LHC, corresponding to an integrated luminosity of 5 fb–1 and 1.1 fb–1, were used. The results are con�sistent with the standard model expectations.

DOI: 10.1134/S1063779614010389

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PHYSICS OF PARTICLES AND NUCLEI Vol. 45 No. 1 2014

GORBUNOV, SHMATOV

mass region and tt for the high mass region. Diboson(WW, WZ, and ZZ) and inclusive W production pro�cesses are less important sources of background. Thetotal background contribution to the data ranges from0.17% to 0.21% in the dimuon channel and from0.68% to 0.80% in the dielectron channel.

The AFB measurement consists of determining theangular distributions of leptons for each dileptoninvariant mass bin. Lepton candidates are selectedfrom an online�trigger�selected sample.

Collins–Soper frame [13] have been used to reducethe uncertainties due to the transverse momentum ofthe incoming quarks. In this frame, θ is defined to bethe angle between the negative muon momentum anda z' axis that bisects the angle between q and q.

The forward�backward asymmetry is diluted by theevents in which the assumed quark and antiquarkdirections are incorrect. The asymmetry is furtherreduced by the acceptance requirements. No correc�tions are applied for either of these effects. To correctfor FSR, mass resolution, efficiencies, and otherdetector effects, we unfold the forward and backwardmass spectra in each |y| bin.

Systematic uncertainties are estimated in each M�|y| bin using MC events for both the raw and the Bornlevel analyses. All systematic uncertainties areassumed to be independent and are combined inquadrature. The resulting total experimental system�atic uncertainty is at most 0.09 in AFB; however, formost of the bins the total experimental uncertainty is

20

–2

40030020060 10050 70M(I+I–), GeV

(data – MC)/σdata

0.1

0

–0.1

0.2

0.3

0.4

0.5AFB

CMS5 fb

1– at s 7 TeV=

|y| < 1.00

Bom LevelPOWHEG (CT10) + PYTHIA(Z2)with PDF uncertainties

Data with statistical ⊕ systematic error bars

Data with statistical error bars

20

–2

40030020060 10050 70M(I+I–), GeV

(data – MC)/σdata

0.1

0

–0.1

0.2

0.3

0.4

0.5AFB

CMS5 fb

1– at s 7 TeV=

1.00 < |y| < 1.25

20

–2

40030020060 10050 70M(I+I–), GeV

(data – MC)/σdata

0.1

0

–0.1

0.2

0.3

0.4

0.5AFB

CMS5 fb

1– at s 7 TeV=

1.25 < |y| < 1.50

20

–2

40030020060 10050 70M(I+I–), GeV

(data – MC)/σdata

0.1

0

–0.1

0.2

0.3

0.4

0.5AFB

CMS5 fb

1– at s 7 TeV=

1.50 < |y| < 2.40

The unfolded and combined (μ+μ

– and e+e–) measurement of AFB at the Born level in four |y| bins for pT(l) > 20 GeV and|h(l)| < 2.4. The data points are shown with both statistical error bars and combined statistical and systematic error bars. The errorbars on the MC points are the PDF uncertainties. Beneath each plot is shown the difference between data and MC, normalizedby the combined statistical and systamatic uncertaity. The green and yellow bands indicate the 1σ and 2σ differences of data fromtheory predictions.

PHYSICS OF PARTICLES AND NUCLEI Vol. 45 No. 1 2014

MEASUREMENT OF THE FORWARD�BACKWARD ASYMMETRY 213

less than 0.02. The largest uncertainty coming fromPDF is found to be 0.012.

Figure shows the measured and simulated AFB as afunction of mass and rapidity in the 40 < Mll < 400 GeVmass range and in 4 rapidity bins. Here simulatedrefers to Monte�Carlo generated events passedthrough full CMS simulation and reconstruction, withthe same selection cuts applied as in data. The mea�sured values are consistent with Monte�Carlo simula�tion predictions.

A multivariate likelihood method to measure theeffective weak mixing angle in the predominantly u

d → Z/γ* → μ+μ– processes was used with a data

from proton�proton collisions at = 7 TeV corre�sponding to an integrated luminosity of 1.1 fb–1 [14].The measured value is to be sin2θeff = 0.2287 ±0.0020 (stat.) ± 0.0025 (syst.), as expected within thestandard model.

New methods to extract AFB from data are underdevelopment now. There is also an ongoing work toimprove result of AFB measurement using 2012 datawith integarted luminosity more than 20 fb–1 includingnew systematic study and new implementation of cor�rection factors. New results of AFB measurements for

= 8 TeV data will be presented in the upcominganalysis.

ACKNOWLEDGMENTS

We thank our colleagues from the CMS Collabora�tions for their advice and fruitful discussions, in par�ticular Jeffrey Berryhill, Efe Yazgan and AlexanderLanyov.

REFERENCES1. D. London and J. L. Rosner, Phys. Rev. D 34, 1530

(1986); J. L. Rosner, Phys. Rev. D 35, 2244 (1987);

M. Cvetic and S. Godfrey, World Scientific 383 (1987);J. Rosner, Phys. Rev. D 54, 1078 (1996); A. Bodek andU. Baur, arXiv:hep�ph/0102160; F. Abe et al., Phys.Rev. Lett. 79, 2192 (1997).

2. F. Abe et al., Phys. Rev. Lett. 79, 2198 (1997).

3. H. Davoudiasl, J. L. Hewett, and T. G. Rizzo, Phys.Rev. Lett. 84, 2080 (2000).

4. CMS Collaboration, “CMS physics technical designreport, volume II: physics performance,” J. Phys. G:Nucl. Part. Phys. 34, 995 (2007).

5. A. Lanyov and S. Shmatov, “Studies of Drell–Yandimuon events in the CMS experiment,” Nucl. Phys. B177–178, 304 (2008); arXiv:0707.4151.

6. CMS Collaboration, “Measurement of the Forward�

Backward asymmetry of l+l– pairs in CMS at = 7TeV,” CMS�PAS�EWK�11�004; arXiv:1207.3973;Accepted to Phys. Lett. B.

7. CMS Collaboration, “The CMS experiment at theCERN LHC JIN�STl,” 3, S08004 (2008).

8. T. Sjostrand, S. Mrenna, and P. Z. Skands, “PYTHIA6.4 physics and manual,” JHEP 05, 026 (2006).

9. H.�L. Lai, M. Guzzi, J. Huston et al., “New parton dis�tributions for collider physics,” Phys. Rev. D 82,074024 (2010).

10. J. Alwall, P. Demin, S. de Visscher et al., “Mad�Graph/MadEvent v4: the new web generation,” JHEP09, 028 (2007).

11. N. Davidson, G. Nanava, T. Przedzinski et al., Univer�sal Interface of TAUOLA Technical and Physics Docu�mentation, arXiv:1002.0543.

12. S. Agostinelli et al., “Geant4 simulation toolkit,” Nucl.Instrum. Meth. A 505, 250 (2003); arXiv:1002.0543.

13. J. C. Collins and D. E. Soper, Phys. Rev. D 16 (7), 2219(1977).

14. CMS Collaboration, “Measurement of the weak mix�ing angle with the Drell–Yan process in Proton–Pro�ton collisions at the LHC,” Phys. Rev. D 84, 112002(2011); arXiv:1110.2682.

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