Measurement of Inclusive W and Z Production in ATLAS

. A summary of ﬁve ATLAS W and Z inclusive measurements are presented, these are a mixture of analyses using the 2010 and 2011 datasets of p s = 7 TeV proton-proton collisions at the LHC. The 2010 data is used to measure the cross sections of the Z , W + and W (cid:0) bosons which are then used with the HERA deep inelastic scattering data to determine the strange quark density of the proton. Three analyses that use 2011 data are shown; a measurement of the forward-backward asymmetry of the Z =(cid:13) (cid:3) boson, from which the e (cid:11) ective weak mixing angle is extracted; a measurement of the angular correlations of Drell-Yan lepton pairs from resonant Z decays; and a measurement of the high mass Drell-Yan di (cid:11) erential cross section.


Introduction
Measurements of electroweak processes, such as those summarised here from ATLAS [1] are important for probing the standard model in the new energy regime of the LHC and improve the theoretical predictions with additional constraints. Furthermore the proton Parton Distribution Functions (PDFs) which are extrapolated from the phase space of previous experiments can be constrained by measurements such as these, as clearly seen in sections 2 and 3.

Measurements
The Z, W + and W − production cross sections have been measured both inclusively and differentially in the electron and the muon decay channels [2] using about 35 pb −1 of 2010 data. The separate channels are corrected to a common region in phase space and then combined using a χ 2 minimisation method. The common phase space region is defined as p l T > 20 GeV and 66 < m ll < 116 GeV for the Z bosons, where p l T is the transverse momentum of the leptons and m ll is the invariant mass of the lepton pair. The W ± decays are required to have p l T > 20 GeV, p ν T > 25 GeV and m lν T > 40 GeV, where p l T (p ν T ) and m lν T are the transverse momentum of the charged lepton (neutrino) and the transverse mass of the lepton-neutrino pair. Fig. 1 shows the fiducial inclusive cross sections of the Z and (W + + W − ) plotted against each other. The uncertainty is dominated by the ∼ 1% systematic uncertainty (excluding the 3.4% luminosity uncertainty). The measurement is compared to theoretical predictions obtained from nextto-next-to-leading-order (NNLO) FEWZ2.0 [3] with either the MSTW2008 [4], HERAPDF1.5 [5], ABKM09 [6]    measured as a function of the pseudorapidity, η, of the charged lepton for the W ± decays and as a functon of the rapidity, y, of the Z boson for the Z decays. These can be seen for the combined electron and muon channels W ± decays in fig. 2 compared with calculated predictions, which use a combination of NNLO FEWZ and DYNNLO [8,9]. The typical data precision is about 2%. The uncertainties shown for the theoretical predictions are a convolution of the PDF uncertainties, considered by the authors of the various PDF sets to correspond to 68% CL, and a residual numerical uncertainty of below 0.5%. There is broad agreement between the data and the theoretical predictions but again data demonstrate the ability to discriminate between different PDF sets. The importance of measuring the cross sections of the W + and W − bosons separately can be seen, as the level of agreement with the theoretical predictions differs between the two.  Figure 2. Combined electron and muon fiducial differential cross sections of the W + → l + ν l and W − → l −ν l processes [2].

Determination of the Strange Quark Density of the Proton
If one assumes SU(3) flavour symmetry, the light quark sea distributions in the proton should be equal, but due to their higher mass, the strange quarks may be suppressed. Information for this currently comes from neutrino scattering experiments which probe the proton in a higher x region than the analysis described here [10]. The Z, W + and W − cross section measurements described in the previous section are used with the deep inelastic scattering data from the H1 and ZEUS experiments at HERA [5]. Two NNLO PDF fits are performed using the HERAFitter framework [5,11]. The first fit, referred to as the fixeds fit, fully couples the strange quark sea with the down quark sea by settings/d = 0.5, wheres andd are the anti-strange and anti-down sea quark distributions respectively. The second fit, referred to as the frees fit, parameterises xs with two free strangeness parameters. Both fits assume xs = xs by default and both have good χ 2 per degree of freedom giving 546.1/567 with 13 free parameters for the fixeds fit and 538.4/565 with 15 degrees of freedom for the frees fit. However, when considering the partial χ 2 from only the ATLAS data, it is seen that the data prefers the frees fit, giving χ 2 = 44.5 for 30 data points for the fixeds fit which significantly improves to 33.9 for the freē s fit. Fig. 3 shows the Z differential cross section from section 2 compared to predictions from the two fits. It can be seen that the frees fit does a better job in describing the data. The level of suppression of the strange sea can  Figure 3. Combined fiducial differential cross section of Z → l + l − decays compared to predictions from the two NNLO PDF fits [10]. be determined from the frees fit by considering the ratio r s = 0.5(s+s)/d, which is found to be r s = 1.00 +0.25 −0.28 , when evaluated at the intial scale of 1.9 GeV and x = 0.023. The uncertainty on r s is dominated by an experimental uncertainty of ±0.20. This is consistent with no suppression of the strange quark sea at very low x. This value of r s is compared to those obtained from other PDF sets in fig. 4, where it can be seen that only CT10 [12] is in agreement, while ABKM09, NNPDF2.1 [13,14] and MSTW2008 all have much smaller values of r s . These differences arise from the variation in the treatment of the strange quark sea suppression in the different fits.

Decays
Due to the V-A nature of the weak interaction, the Z couples differently to left and right handed fermions, resulting in a forward backward asymmetry of the qq → Z/γ * → l + l − process with respect to the direction of the incoming quark. The asymmetry, A FB , is expressed as  The analysis measures the forward-backward asymmetry in three different channels. The CC Electron Channel considers two electrons in the centre of the detector, requiring kinematic cuts on both electrons of E T > 25 GeV and |η| < 2.47 excluding 1.37 < |η| < 1.52, where E T is the transverse energy. The CF Electron Channel requires one electron to be in the centre of the detector (passing the CC requirements) and one in the forward region, requiring E T > 25 GeV and 2.5 < |η| < 4.9 excluding 3.16 < |η| < 3.35. Finally, the Muon Channel requires both muons to be in the centre of the detector, giving a kinematic region of p T > 20 GeV and |η| < 2.4. The forward-backward asymmetry is calculated for each channel, this is then unfolded to the Born level, as shown in fig. 5. The data is compared to Pythia6.4 [16] MC with NNLO k-factors applied which are calculated with PHOZPR [17] using MSTW2008 PDFs. It is clear from the ratio ∆/σ in the lower section of the plots in fig. 5 that there is good data and MC agreement, where ∆ is the difference between data and MC and σ is the quadratic sum of the data and MC uncertainties. The measurement of the forward-backward asymmetry allows the effective electroweak mixing angle to be extracted. This is the electroweak mixing angle, commonly defined as , with higher order loop corrections included. To extract the electroweak mixing angle the A FB dependence on m ll is used before the unfolding to the Born level. It is compared to a number of MC templates using a χ 2 test in an invariant mass range of 70 < m ll < 250 GeV, with each template produced with a different value of sin 2 θ e f f W . Each of the three channels are fitted and then combined to give a single value of sin 2 θ e f f W , these are compared to previous results in fig. 6. The three channels show good agreement and the combined result has a value of sin 2 θ e f f W = 0.2297 ± 0.0010 which has a 0.17% statistical uncertainty and a 0.39% systematic uncertainty, dominated by the PDF uncertainty. The combined measurement is in good agreement with the CMS and DØ results and only 1.8σ from the PDG global fit value [18]. This is currently the most precise measurement of sin 2 θ e f f W from a LHC experiment and the first hadron collider measure-

Angular Correlation of Drell-Yan Lepton Pairs
Previous measurements of the p T of the W and Z vector bosons [19,20] have demonstrated the difficulty theoretical predictions have in describing those distributions; understanding of which is important for W mass measurements. In the analysis presented here [21] the φ * η variable, previously used at the DØ experiment is examined. The variable is defined as φ * η ≡ tan(φ acop /2) · sin(θ * η ), where φ acop ≡ π − ∆φ and cos(θ * η ) ≡ tanh[(η − − η + )/2], with ∆φ being the difference in the azimuthal angle between the leptons, and η ± being the pseudorapidity of each lepton. As such, φ * η is dependant only on the angles of the two leptons which can be measured with much better resolution than the momentum, particularly at low p T . The φ * η variable is correlated with p Z T /m ll , allowing the same physics to be probed. The differential cross section is measured as a function of φ * η in the electron and muon channels. A kinematic region of p l T > 20 GeV and |η l | < 2.4 is used at the Z resonance in the invariant mass range 66 < m ll < 116 GeV using 4.6 fb −1 of 2011 data. The normalised differential cross section, 1/σ f id · dσ f id /dφ * η , was determined from data and from an analytical QCD prediction [22], these are compared to the prediction from RESBOS [23], as shown by the ratio in fig. 7. RESBOS resums the next-tonext-to-leading-logarithms (NNLL) and matches to a leading order QCD result, with k-factors correcting to next-toleading order (NLO), while the analytical prediction contains NNLL matched to an NLO QCD result from MCFM [24]. The experimental uncertainty is statistically dominated, with a statistical uncertainty between 0.30% and 1.61%; the systematic uncertainty varies between 0.13% and 0.58%. The difference between the RESBOS prediction and the data is smaller than the RESBOS PDF uncertainty, which varies from 4% to 6% for φ * η < 0.1 and φ * η > 0.1 respectively. The analytical calculation describes the data less well, but is still largely in agreement within the relatively large theoretical uncertainty. Neither prediction demonstrates the ability to describe the detailed shape of the distribution.

High Mass Drell-Yan Cross Section
The Drell-Yan differential mass cross section has been measured in the electron channel [25] in an invariant mass range of 116 < m ee < 1500 GeV with 4.9 fb −1 of 2011 data. A kinematic region of |η e | < 2.5 and p e T > 25 GeV is used. This extends the standard model measurement of the Z resonance and is complementary to Z searches. The measurement is sensitive to the behaviour of PDFs for x 10 −3 and higher order electroweak corrections. Fig. 8 shows the invariant mass distribution of the electron pair, where good agreement between data and MC can be cross section unfolded to the Born level. Comparisons to theoretical predictions are made using FEWZ3.1 [26] at NNLO using the G µ electroweak scheme with a number of different PDF sets. The theoretical predictions have NLO electroweak corrections applied which take into consideration initial and final state QED radiation and interference between the two. Leading order photon induced corrections have also been applied using the MSTW2005qed PDF set [27]. The upper ratio plot shows the ratio of the theoretical predictions to the data, with predictions produced using either the MSTW2008, HERAPDF1.5, CT10, ABM11 [28] or NNPDF2.3 [29] PDF sets. It can be seen that the data is consistent with all of the PDF sets considered. The lower ratio plot demonstrates the importance of the photon induced corrections, with the dashed line showing the MSTW2008 prediction without the photon induced corrections. The corrections are of the order of the 68% CL uncertainty from the MSTW2008 error sets. ATLAS is the first LHC experiment to include these photon induced corrections to the theoretical predictions which this measurement demonstrates can be sizable.

Conclusions
The analyses presented here cover a range of measurements of inclusive W and Z production at ATLAS. The inclusive cross section measurements show the potential to constrain the PDFs, this is then used to determine the strange quark density of the proton at small x which is found to be consistent with no suppression of thes PDF relative tod. Measurement of the forward-backward asymmetry shows good consistency with the standard model predictions. A value of sin 2 θ e f f W is extracted which is in agreement with other experiments and is currently the most precise measurement of sin 2 θ e f f W from the LHC. The relative differential cross section, 1/σ f id · dσ f id /dφ * η , is measured with small experimental uncertainties and while largely showing agreement with predictions demonstrates the current inability of theory to recreate the detailed shape of the φ * η differential cross section. Finally, the measurement of the high mass Drell-Yan differential cross section shows consistency with theoretical predictions using a number of PDF sets and demonstrates the importance of including photon induced corrections in theoretical predictions.