Published for SISSA by Springer Received: June 3, 2016 Revised: July 29, 2016 Accepted: August 20, 2016 Published: August 29, 2016 Measurement of the angular coe(cid:14)cients in Z-boson J events using electron and muon pairs from data taken p H at s = 8 TeV with the ATLAS detector E P 0 8 ( 2 0 1 The ATLAS collaboration 6 E-mail: atlas.publications@cern.ch ) 1 Abstract: The angular distributions of Drell-Yan charged lepton pairs in the vicinity 5 of the Z-boson mass peak probe the underlying QCD dynamics of Z-boson production. 9 This paper presents a measurement of the complete set of angular coe(cid:14)cients A de- 0(cid:0)7 scribing these distributions in the Z-boson Collins-Soper frame. The data analysed cor- p respond to 20.3fb(cid:0)1 of pp collisions at s = 8TeV, collected by the ATLAS detector at the CERN LHC. The measurements are compared to the most precise (cid:12)xed-order calculations currently available (O((cid:11)2)) and with theoretical predictions embedded in Monte s Carlo generators. The measurements are precise enough to probe QCD corrections beyond the formal accuracy of these calculations and to provide discrimination between di(cid:11)erent parton-shower models. A signi(cid:12)cant deviation from the O((cid:11)2) predictions is observed for s A (cid:0)A . Evidence is found for non-zero A , consistent with expectations. 0 2 5;6;7 Keywords: Hadron-Hadron scattering (experiments) ArXiv ePrint: 1606.00689 Open Access, Copyright CERN, doi:10.1007/JHEP08(2016)159 for the bene(cid:12)t of the ATLAS Collaboration. Article funded by SCOAP3. Contents 1 Introduction 1 2 Theoretical predictions 4 3 The ATLAS experiment and its data and Monte Carlo samples 8 3.1 ATLAS detector 8 3.2 Data and Monte Carlo samples 8 J H 4 Data analysis 9 4.1 Event selection 9 E 4.2 Backgrounds 10 P 4.3 Angular distributions 15 0 8 5 Coe(cid:14)cient measurement methodology 15 5.1 Templates 15 ( 5.2 Likelihood 17 2 5.3 Combinations and alternative parameterisations 20 0 6 Measurement uncertainties 21 1 6.1 Uncertainties from data sample size 21 6 6.2 Uncertainties from Monte Carlo sample size 22 ) 6.3 Experimental systematic uncertainties 22 1 6.4 Theoretical systematic uncertainties 23 5 6.5 Systematic uncertainties related to the methodology 24 6.6 Summary of uncertainties 25 9 7 Results 31 7.1 Compatibility between channels 31 7.2 Results in the individual and combined channels 31 7.3 Cross-checks 34 8 Comparisons with theory 37 9 Summary 48 A Theoretical formalism 49 B Additional templates 51 C Regularisation 52 D Categorisation of statistical uncertainties 57 { 1 { E Quantifying A 58 5;6;7 F Additional results 61 The ATLAS collaboration 83 1 Introduction J The angular distributions of charged lepton pairs produced in hadron-hadron collisions via the Drell-Yan neutral current process provide a portal to precise measurements of the H production dynamics through spin correlation e(cid:11)ects between the initial-state partons and E the(cid:12)nal-stateleptonsmediatedbyaspin-1intermediatestate,predominantlythe Z boson. P In the Z-boson rest frame, a plane spanned by the directions of the incoming protons can 0 be de(cid:12)ned, e.g. using the Collins-Soper (CS) reference frame [1]. The lepton polar and azimuthal angular variables, denoted by cos(cid:18) and (cid:30) in the following formalism, are de(cid:12)ned 8 in this reference frame. The spin correlations are described by a set of nine helicity density ( matrix elements, which can be calculated within the context of the parton model using 2 perturbative quantum chromodynamics (QCD). The theoretical formalism is elaborated 0 in refs. [2{5]. 1 The full (cid:12)ve-dimensional di(cid:11)erential cross-section describing the kinematics of the two Born-level leptons from the Z-boson decay can be decomposed as a sum of nine har- 6 monic polynomials, which depend on cos(cid:18) and (cid:30), multiplied by corresponding helicity ) cross-sections that depend on the Z-boson transverse momentum (pZ), rapidity (yZ), and T 1 invariant mass (mZ). It is a standard convention to factorise out the unpolarised cross- 5 section, denoted in the literature by (cid:27)U+L, and to present the (cid:12)ve-dimensional di(cid:11)erential 9 cross-section as an expansion into nine harmonic polynomials P (cos(cid:18);(cid:30)) and dimension- i less angular coe(cid:14)cients A (pZ;yZ;mZ), which represent ratios of helicity cross-sections 0(cid:0)7 T with respect to the unpolarised one, (cid:27)U+L, as explained in detail in appendix A: d(cid:27) 3 d(cid:27)U+L = (1.1) dpZ dyZ dmZ dcos(cid:18) d(cid:30) 16(cid:25)dpZ dyZ dmZ T T (cid:26) 1 (cid:2) (1+cos2(cid:18))+ A (1(cid:0)3cos2(cid:18))+A sin2(cid:18) cos(cid:30) 0 1 2 1 + A sin2(cid:18) cos2(cid:30)+A sin(cid:18) cos(cid:30)+A cos(cid:18) 2 3 4 2 (cid:27) +A sin2(cid:18) sin2(cid:30)+A sin2(cid:18) sin(cid:30)+A sin(cid:18) sin(cid:30) : 5 6 7 The dependence of the di(cid:11)erential cross-section on cos(cid:18) and (cid:30) is thus completely man- ifest analytically. In contrast, the dependence on pZ, yZ, and mZ is entirely contained T in the A coe(cid:14)cients and (cid:27)U+L. Therefore, all hadronic dynamics from the production i mechanism are described implicitly within the structure of the A coe(cid:14)cients, and are fac- i torised from the decay kinematics in the Z-boson rest frame. This allows the measurement { 1 { precision to be essentially insensitive to all uncertainties in QCD, quantum electrodynam- ics (QED), and electroweak (EW) e(cid:11)ects related to Z-boson production and decay. In particular, EW corrections that couple the initial-state quarks to the (cid:12)nal-state leptons have a negligible impact (below 0.05%) at the Z-boson pole. This has been shown for the LEP precision measurements [6, 7], when calculating the interference between initial-state and (cid:12)nal-state QED radiation. When integrating over cos(cid:18) or (cid:30), the information about the A and A coe(cid:14)cients 1 6 is lost, so both angles must be explicitly used to extract the full set of eight coe(cid:14)cients. Integrating eq. (1.1) over cos(cid:18) yields: J d(cid:27) 1 d(cid:27)U+L = (1.2) H dpZ dyZ dmZ d(cid:30) 2(cid:25)dpZ dyZ dmZ T T (cid:26) (cid:27) E 1 3(cid:25) 1 3(cid:25) (cid:2) 1+ A cos2(cid:30)+ A cos(cid:30)+ A sin2(cid:30)+ A sin(cid:30) ; 4 2 16 3 2 5 16 7 P 0 while integrating over (cid:30) yields: 8 d(cid:27) 3 d(cid:27)U+L (cid:26) 1 (cid:27) = (1+cos2(cid:18))+ A (1(cid:0)3cos2(cid:18))+A cos(cid:18) : ( dpZ dyZ dmZ dcos(cid:18) 8dpZ dyZ dmZ 2 0 4 T T 2 (1.3) At leading order (LO) in QCD, only the annihilation diagram qq(cid:22)! Z is present and 0 only A is non-zero. At next-to-leading order (NLO) in QCD (O((cid:11) )), A also become 1 4 s 0(cid:0)3 non-zero. TheLam-Tungrelation[8{10], whichpredictsthat A (cid:0)A = 0duetothespin-1 0 2 6 of the gluon in the qg ! Zq and qq(cid:22)! Zg diagrams, is expected to hold up to O((cid:11) ), but s ) can be violated at higher orders. The coe(cid:14)cients A are expected to become non-zero, 5;6;7 1 while remaining small, only at next-to-next-to-leading order (NNLO) in QCD (O((cid:11)2)), s because they arise from gluon loops that are included in the calculations [11, 12]. The 5 coe(cid:14)cients A and A depend on the product of vector and axial couplings to quarks and 9 3 4 leptons, and are sensitive to the Weinberg angle sin2(cid:18) . The explicit formulae for these W dependences can be found in appendix A. The full set of coe(cid:14)cients has been calculated for the (cid:12)rst time at O((cid:11)2) in refs. [2{5]. s More recent discussions of these angular coe(cid:14)cients may be found in ref. [13], where the predictions in the NNLOPS scheme of the Powheg [14{17] event generator are shown for Z-boson production, and in ref. [18], where the coe(cid:14)cients are explored in the context of W-boson production, for which the same formalism holds. The CDF Collaboration at the Tevatron published [19] a measurement of some of the angular coe(cid:14)cients of lepton pairs produced near the Z-boson mass pole, using 2.1 fb(cid:0)1 p of proton-anti-proton collision data at a centre-of-mass energy s = 1:96TeV. Since the measurement was performed only in projections of cos(cid:18) and (cid:30), the coe(cid:14)cients A and 1 A were inaccessible. They further assumed A and A to be zero since the sensitivity to 6 5 7 these coe(cid:14)cients was beyond the precision of the measurements; the coe(cid:14)cients A 0;2;3;4 were measured as a function of pZ. These measurements were later used by CDF [20] to T infer an indirect measurement of sin2(cid:18) , or equivalently, the W-boson mass in the on- W shell scheme, from the average A coe(cid:14)cient. These (cid:12)rst measurements of the angular 4 { 2 { coe(cid:14)cients demonstrated the potential of this not-yet-fully explored experimental avenue for investigating hard QCD and EW physics. Measurements of the W-boson angular coe(cid:14)cients at the LHC were published by both ATLAS [21] and CMS [22]. More recently, a measurement of the Z-boson angular coe(cid:14)cientswith Z ! (cid:22)(cid:22)decayswaspublishedbyCMS[23], wherethe(cid:12)rst(cid:12)vecoe(cid:14)cients p were measured with 19.7 fb(cid:0)1of proton-proton (pp) collision data at s = 8TeV. The measurement was performed in two yZ bins, 0 < jyZj < 1 and 1 < jyZj < 2:1, each with eight bins in pZ up to 300GeV. The violation of the Lam-Tung relation was observed, as T predicted by QCD calculations beyond NLO. J H This paper presents an inclusive measurement of the full set of eight A coe(cid:14)cients i E using charged lepton pairs (electrons or muons), denoted hereafter by ‘. The measurement is performed in the Z-boson invariant mass window of 80{100GeV, as a function of pZ, P T and also in three bins of yZ. These results are based on 20.3 fb(cid:0)1 of pp collision data 0 p collectedat s = 8TeVbytheATLASexperiment[24]attheLHC.Withthemeasurement 8 techniques developed for this analysis, the complete set of coe(cid:14)cients is extracted with ( (cid:12)ne granularity over 23 bins of pZ up to 600GeV. The measurements, performed in the CS T 2 reference frame [1], are (cid:12)rst presented as a function of pZ, integrating over yZ. Further T measurements divided into three bins of yZ are also presented: 0 < jyZj < 1, 1 < jyZj < 2, 0 and 2 < jyZj < 3:5. The Z=(cid:13)(cid:3) ! e+e(cid:0) and Z=(cid:13)(cid:3) ! (cid:22)+(cid:22)(cid:0) channels where both leptons 1 fall within the pseudorapidity range j(cid:17)j < 2:4 (hereafter referred to as the central-central 6 or ee and (cid:22)(cid:22) channels) are used for the yZ-integrated measurement and the (cid:12)rst two CC CC ) yZ bins. The Z=(cid:13)(cid:3) ! e+e(cid:0) channel where one of the electrons instead falls in the region 1 j(cid:17)j > 2:5 (referred to hereafter as the central-forward or ee channel) is used to extend CF the measurement to the high-yZ region encompassed by the third yZ bin. In this case, 5 however, because of the fewer events available for the measurement itself and to evaluate 9 the backgrounds (see section 4), the measurement is only performed for pZ up to 100GeV T using projections of cos(cid:18) and (cid:30), making A and A inaccessible in the 2 < jyZj < 3:5 bin. 1 6 The high granularity and precision of the speci(cid:12)c measurements presented in this paper provide a stringent test of the most precise perturbative QCD predictions for Z-boson production in pp collisions and of Monte Carlo (MC) event generators used to simulate Z-boson production. This paper is organised as follows. Section 2 summarises the theoretical formalism used to extract the angular coe(cid:14)cients and presents the (cid:12)xed-order QCD predictions for their variations as a function of pZ. Section 3 describes brie(cid:13)y the ATLAS T detector and the data and MC samples used in the analysis, while section 4 presents the dataanalysisandbackgroundestimatesforeachofthethreechannelsconsidered. Section 5 describesthe(cid:12)tmethodologyusedtoextracttheangularcoe(cid:14)cientsinthefullphasespace as a function of pZ and section 6 gives an overview of the statistical and systematic uncer- T tainties of the measurements. Sections 7 and 8 present the results and compare them to various predictions from theoretical calculations and MC event generators, and section 9 summarises and concludes the paper. { 3 { ^ y l ^ x φ CS θ CS ^ z p p J Figure1. SketchoftheCollins-Soperreferenceframe,inwhichtheangles (cid:18) and(cid:30) arede(cid:12)ned CS CS H withrespecttothenegativelychargedlepton ‘(seetext). Thenotations x^;y^andz^denotetheunit vectors along the corresponding axes in this reference frame. E P 2 Theoretical predictions 0 8 Thedi(cid:11)erentialcross-sectionineq.(1.1)iswrittenforpureZ bosons,althoughitalsoholds ( for the contribution from (cid:13)(cid:3) and its interference with the Z boson. The tight invariant mass window of 80{100GeV is chosen to minimise the (cid:13)(cid:3) contribution, although the pre- 2 dicted A coe(cid:14)cients presented in this paper are e(cid:11)ective coe(cid:14)cients, containing this small 0 i contribution from (cid:13)(cid:3). This contribution is not accounted for explicitly in the detailed 1 formalism described in appendix A, which is presented for simplicity for pure Z-boson 6 production. Throughout this paper, the leptons from Z-boson decays are de(cid:12)ned at the ) Born level, i.e. before (cid:12)nal-state QED radiation, when discussing theoretical calculations 1 or predictions at the event-generator level. The pZ and yZ dependence of the coe(cid:14)cients varies strongly with the choice of spin 5 T quantisation axis in the Z-boson rest frame (z-axis). In the CS reference frame adopted for 9 this paper, the z-axis is de(cid:12)ned in the Z-boson rest frame as the external bisector of the angle between the momenta of the two protons, as depicted in (cid:12)gure 1. The positive direction of the z-axis is de(cid:12)ned by the direction of positive longitudinal Z-boson momentum in the laboratory frame. To complete the coordinate system, the y-axis is de(cid:12)ned as the normal vector to the plane spanned by the two incoming proton momenta and the x-axis is chosen to de(cid:12)ne a right-handed Cartesian coordinate system with the other two axes. Polar and azimuthal angles are calculated with respect to the negatively charged lepton and are labelled (cid:18) and (cid:30) , respectively. In the case where pZ = 0, the direction of the CS CS T y-axis and the de(cid:12)nition of (cid:30) are arbitrary. Historically, there has been an ambiguity in CS the de(cid:12)nition of the sign of the (cid:30) angle in the CS frame: this paper adopts the recent CS convention followed by refs. [13, 23], whereby the coe(cid:14)cients A and A are positive. 1 3 The coe(cid:14)cients are not explicitly used as input to the theoretical calculations nor in the MC event generators. They can, however, be extracted from the shapes of the angular distributions with the method proposed in ref. [3], owing to the orthogonality of the P polynomials. The weighted average of the angular distributions with respect to i any speci(cid:12)c polynomial isolates an average reference value or moment of its corresponding { 4 { coe(cid:14)cient. ThemomentofapolynomialP(cos(cid:18);(cid:30))overaspeci(cid:12)crangeofpZ, yZ, andmZ T is de(cid:12)ned to be: R P(cos(cid:18);(cid:30))d(cid:27)(cos(cid:18);(cid:30))dcos(cid:18)d(cid:30) hP(cos(cid:18);(cid:30))i = : (2.1) R d(cid:27)(cos(cid:18);(cid:30))dcos(cid:18)d(cid:30) The moment of each harmonic polynomial can thus be expressed as (see eq. (1.1)): (cid:18) (cid:19) 1 3 2 1 1 h (1(cid:0)3cos2(cid:18))i = A (cid:0) ; hsin2(cid:18)cos(cid:30)i = A ; hsin2(cid:18)cos2(cid:30)i = A ; 0 1 2 2 20 3 5 10 J 1 1 1 hsin(cid:18)cos(cid:30)i = A ; hcos(cid:18)i = A ; hsin2(cid:18)sin2(cid:30)i = A ; (2.2) H 3 4 5 4 4 5 1 1 E hsin2(cid:18)sin(cid:30)i = A ; hsin(cid:18)sin(cid:30)i = A : 6 7 5 4 P 0 One thus obtains a representation of the e(cid:11)ective angular coe(cid:14)cients for Z=(cid:13)(cid:3) pro- 8 duction. These e(cid:11)ective angular coe(cid:14)cients display in certain cases a dependence on yZ, ( which arises mostly from the fact that the interacting quark direction is unknown on an event-by-event basis. As the method of ref. [3] relies on integration over the full phase 2 space of the angular distributions, it cannot be applied directly to data, but is used to 0 compute all the theoretical predictions shown in this paper. 1 The inclusive (cid:12)xed-order perturbative QCD predictions for Z-boson production at 6 NLO and NNLO were obtained with DYNNLO v1.3 [25]. These inclusive calculations ) are formally accurate to O((cid:11)2). The Z-boson is produced, however, at non-zero transverse s momentum only at O((cid:11) ), and therefore the calculation of the coe(cid:14)cients as a function 1 s of pZ is only NLO. Even though the (cid:12)xed-order calculations do not provide reliable abso- 5 T lute predictions for the pZ spectrum at low values, they can be used for pZ > 2.5GeV T T 9 for the angular coe(cid:14)cients. The results were cross-checked with NNLO predictions from FEWZ v3.1.b2 [26{28] and agreement between the two programs was found within uncertainties. The renormalisation and factorisation scales in the calculations were set to q EZ = (mZ)2+(pZ)2 [29] on an event-by-event basis. The calculations were done using T T the CT10 NLO or NNLO parton distribution functions (PDFs) [30], depending on the order of the prediction. The NLO EW corrections a(cid:11)ect mostly the leading-order QCD cross-section normali- sation in the Z-pole region and have some impact on the pZ distribution, but they do not T a(cid:11)ect the angular correlations at the Z-boson vertex. The DYNNLO calculation was done at leading order in EW, using the G scheme [31]. This choice determines the value of A (cid:22) 4 at low pZ, and for the purpose of the comparisons presented in this paper, both A and T 3 A obtained from DYNNLO are rescaled to the values predicted when using the measured 4 value of sin2(cid:18)e(cid:11) = 0:23113 [32]. W The theoretical predictions are shown in (cid:12)gure 2 and tabulated in table 1 for three illustrative pZ bins. The binning in pZ is chosen based on the experimental resolution at T T low pZ and on the number of events at high pZ and has the following boundaries (in GeV) T T { 5 { pZ =5(cid:0)8GeV pZ =22(cid:0)25:5GeV pZ =132(cid:0)173GeV T T T NLO NNLO NLO NNLO NLO NNLO A 0:0115+0:0006 0:0150+0:0006 0:1583+0:0008 0:1577+0:0041 0:8655+0:0008 0:8697+0:0017 0 (cid:0)0:0003 (cid:0)0:0008 (cid:0)0:0009 (cid:0)0:0018 (cid:0)0:0006 (cid:0)0:0023 A 0:0113+0:0004 0:0060+0:0010 0:1588+0:0014 0:1161+0:0092 0:8632+0:0013 0:8012+0:0073 2 (cid:0)0:0004 (cid:0)0:0017 (cid:0)0:0009 (cid:0)0:0028 (cid:0)0:0009 (cid:0)0:0215 A (cid:0)A 0:0002+0:0007 0:0090+0:0014 (cid:0)0:0005+0:0016 0:0416+0:0036 0:0023+0:0015 0:0685+0:0200 0 2 (cid:0)0:0005 (cid:0)0:0013 (cid:0)0:0012 (cid:0)0:0067 (cid:0)0:0011 (cid:0)0:0082 A 0:0052+0:0004 0:0074+0:0020 0:0301+0:0013 0:0405+0:0014 0:0600+0:0013 0:0611+0:0018 1 (cid:0)0:0003 (cid:0)0:0008 (cid:0)0:0013 (cid:0)0:0038 (cid:0)0:0015 (cid:0)0:0023 A 0:0004+0:0002 0:0012+0:0003 0:0066+0:0003 0:0070+0:0017 0:0545+0:0003 0:0584+0:0018 3 (cid:0)0:0001 (cid:0)0:0006 (cid:0)0:0005 (cid:0)0:0020 (cid:0)0:0016 (cid:0)0:0047 A 0:0729+0:0023 0:0757+0:0021 0:0659+0:0019 0:0672+0:0018 0:0253+0:0007 0:0247+0:0024 4 (cid:0)0:0006 (cid:0)0:0025 (cid:0)0:0003 (cid:0)0:0050 (cid:0)0:0002 (cid:0)0:0018 A 0:0001+0:0002 0:0001+0:0007 <0:0001 0:0011+0:0013 (cid:0)0:0004+0:0005 0:0044+0:0042 5 (cid:0)0:0002 (cid:0)0:0007 (cid:0)0:0030 (cid:0)0:0005 (cid:0)0:0026 A (cid:0)0:0002+0:0002 0:0013+0:0006 0:0004+0:0006 0:0017+0:0043 0:0003+0:0003 0:0028+0:0017 J 6 (cid:0)0:0003 (cid:0)0:0005 (cid:0)0:0004 (cid:0)0:0015 (cid:0)0:0006 (cid:0)0:0018 A7 <0:0001 0:0014+(cid:0)00::00000074 0:0002+(cid:0)00::00000037 0:0024+(cid:0)00::00001133 0:0003+(cid:0)00::00000047 0:0048+(cid:0)00::00002172 H E Table 1. Summary of predictions from DYNNLO at NLO and NNLO for A , A , A (cid:0)A , A , 0 2 0 2 1 A , A , A , A , and A at low (5{8GeV), mid (22{25.5GeV), and high (132{173GeV) pZ for P 3 4 5 6 7 T the yZ-integrated con(cid:12)guration. The uncertainty represents the sum of statistical and systematic 0 uncertainties. 8 ( used consistently throughout the measurement: 2 pZ;boundary[GeV] = f0; 2:5; 5:0; 8:0; 11:4; 14:9; 18:5; 22:0; 0 T 25:5; 29:0; 32:6; 36:4; 40:4; 44:9; 50:2; 56:4; (2.3) 1 63:9; 73:4; 85:4; 105:0; 132:0; 173:0; 253:0; 600:0g: 6 ) The predictions show the following general features. The A and A coe(cid:14)cients in- 0 2 1 creaseasafunctionofpZ andthedeviationsfromlowest-orderexpectationsarequitelarge, T even at modest values of pZ = 20{50GeV. The A and A coe(cid:14)cients are relatively small 5 T 1 3 even at large pZ, with a maximum value of 0:08. In the limit where pZ = 0, all coe(cid:14)cients 9 T T except A are expected to vanish at NLO. The NNLO corrections are typically small for all 4 coe(cid:14)cients except A , for which the largest correction has a value of (cid:0)0:08, in agreement 2 withtheoriginaltheoreticalstudies[2]. Thetheoreticalpredictionsfor A arenotshown 5;6;7 because these coe(cid:14)cients are expected to be very small at all values of pZ: they are zero T at NLO and the NNLO contribution is large enough to be observable, namely of the order of 0:005 for values of pZ in the range 20{200GeV. T The statistical uncertainties of the calculations, as well as the factorisation and renormalisation scale and PDF uncertainties, were all considered as sources of theoretical uncertainties. The statistical uncertainties of the NLO and NNLO predictions in absolute units are typically 0:0003 and 0:003, respectively. The larger statistical uncertainties of the NNLOpredictionsareduetothelongercomputationaltimerequiredthanfortheNLOpre- dictions. Thescaleuncertaintieswereestimatedbyvaryingtherenormalisationandfactori- sation scales simultaneously up and down by a factor of two. As stated in ref. [2], the theoretical uncertainties due to the choice of these scales are very small for the angular coe(cid:14)- cientsbecausetheyareratiosofcross-sections. Theresultingvariationsofthecoe(cid:14)cientsat NNLO were found in most cases to be comparable to the statistical uncertainty. The PDF { 6 { A0 1.2 A10.12 ATLASSimulation ATLASSimulation 1 s = 8 TeV 0.1 s = 8 TeV 0.8 DYNNLO (NNLO) 0.08 DYNNLO (NNLO) DYNNLO (NLO) DYNNLO (NLO) 0.6 0.06 0.4 0.04 0.2 0.02 0 0 −0.2 −0.02 1 10 102 1 10 102 pZ [GeV] pZ [GeV] J T T A2 1.2 A30.12 H 1 AsT =L A8S TeSVimulation 0.1 AsT =L A8S TeSVimulation E 0.8 DYNNLO (NNLO) 0.08 DYNNLO (NNLO) P DYNNLO (NLO) DYNNLO (NLO) 0.6 0.06 0 0.4 0.04 8 0.2 0.02 ( 0 0 2 −0.2 −0.02 0 1 10 102 1 10 102 pZ [GeV] pZ [GeV] T T 1 A2 0.2 A4 0.2 6 -A0 ATLASSimulation ATLASSimulation s = 8 TeV s = 8 TeV ) 0.15 0.15 DYNNLO (NNLO) DYNNLO (NNLO) DYNNLO (NLO) DYNNLO (NLO) 1 0.1 0.1 5 9 0.05 0.05 0 0 1 10 102 1 10 102 pZ [GeV] pZ [GeV] T T Figure 2. The angular coe(cid:14)cients A and the di(cid:11)erence A (cid:0)A , shown as a function of pZ, 0(cid:0)4 0 2 T as predicted from DYNNLO calculations at NLO and NNLO in QCD. The NLO predictions for A (cid:0)A are compatible with zero, as expected from the Lam-Tung relation [8{10]. The error bars 0 2 showthetotaluncertaintyofthepredictions, includingcontributionsfromstatisticaluncertainties, QCDscalevariationsandPDFs. ThestatisticaluncertaintiesoftheNNLOpredictionsaredominant and an order of magnitude larger than those of the NLO predictions. uncertainties were estimated using the CT10 NNLO eigenvector variations, as obtained fromFEWZandnormalisedto68%con(cid:12)dencelevel. Theywerefoundtobesmallcompared totheNNLOstatisticaluncertainty,namelyoftheorderof0:001forA and0:002forA . 0(cid:0)3 4 { 7 { 3 The ATLAS experiment and its data and Monte Carlo samples 3.1 ATLAS detector TheATLASexperiment[24]attheLHCisamulti-purposeparticledetectorwithaforward- backwardsymmetriccylindricalgeometryandanear4(cid:25) coverageinsolidangle.1 Itconsists of an inner tracking detector, electromagnetic (EM) and hadronic calorimeters, and a muon spectrometer. The inner tracker provides precision tracking of charged particles in the pseudorapidity range j(cid:17)j < 2:5. This region is matched to a high-granularity EM sampling calorimeter covering the pseudorapidity range j(cid:17)j < 3:2 and a coarser granularity calorimeteruptoj(cid:17)j = 4:9. Ahadroniccalorimetersystemcoverstheentirepseudorapidity J range up to j(cid:17)j = 4:9. The muon spectrometer provides triggering and tracking capabilities H in the range j(cid:17)j < 2:4 and j(cid:17)j < 2:7, respectively. A (cid:12)rst-level trigger is implemented in E hardware, followed by two software-based trigger levels that together reduce the accepted P event rate to 400Hz on average. For this paper, a central lepton is one found in the 0 region j(cid:17)j < 2:4 (excluding, for electrons, the electromagnetic calorimeter barrel/end-cap transitionregion1:37 < j(cid:17)j < 1:52),whileaforwardelectronisonefoundintheregion2:5 < 8 j(cid:17)j < 4:9 (excluding the transition region 3:16 < j(cid:17)j < 3:35 between the electromagnetic ( end-cap and forward calorimeters). 2 3.2 Data and Monte Carlo samples 0 1 The data were collected by the ATLAS detector in 2012 at a centre-of-mass energy of p s = 8TeV, and correspond to an integrated luminosity of 20.3fb(cid:0)1. The mean num- 6 ber of additional pp interactions per bunch crossing (pile-up events) in the data set is ) approximately 20. 1 The simulation samples used in the analysis are shown in table 2. The four event 5 generators used to produce the Z=(cid:13)(cid:3) ! ‘‘ signal events are listed in table 2. The baseline PowhegBox (v1/r2129) sample [14{17], which uses the CT10 NLO set of PDFs [33], is 9 interfacedtoPythia8(v.8.170)[34]withtheAU2setoftunedparameters[35]tosimulate the parton shower, hadronisation and underlying event, and to Photos (v2.154) [36] to simulate QED (cid:12)nal-state radiation (FSR) in the Z-boson decay. The alternative signal samplesarefromPowhegBoxinterfacedtoHerwig(v.6.520.2)[37]forthepartonshower and hadronisation, Jimmy (v4.31) [38] for the underlying event, and Photos for FSR. The Sherpa (v.1.4.1) [39{42] generator is also used, and has its own implementation of the parton shower, hadronisation, underlying event and FSR, and uses the CT10 NLO PDF set. These alternative samples are used to test the dependence of the analysis on di(cid:11)erent matrix-element calculations and parton-shower models, as discussed in section 6. ThePowheg(v2.1)+MiNLOeventgenerator[43]wasusedfortheZ+jetprocessatNLO to normalise certain reference coe(cid:14)cients for the ee analysis, as described in section 5. CF The number of events available in the baseline PowhegBox + Pythia 8 signal sample corresponds to approximately 4 (25) times that in the data below (above) pZ = 105GeV. T 1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in thecentreofthedetectorandthe z-axisalongthebeampipe. The x-axispointsfromtheIPtothecentre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r;(cid:30)) are used in the transverse plane, (cid:30) being the azimuthal angle around the z-axis. The pseudorapidity is de(cid:12)ned in terms of the polar p angle (cid:18) as (cid:17)=(cid:0)lntan((cid:18)=2). Angular distance is measured in units of (cid:1)R(cid:17) ((cid:1)(cid:17))2+((cid:1)(cid:30))2. { 8 {

Measurement of the angular coefficients in Z-boson events using electron and muon pairs from

Similar Measurement of the angular coefficients in Z-boson events using electron and muon pairs from