Inclusive and differential W and Z at CMS and ATLAS

TL;DR

This paper reviews electroweak precision measurements of W and Z bosons at the LHC by ATLAS and CMS, highlighting improved accuracy in key parameters and differential cross sections compared to previous experiments.

Contribution

It summarizes recent measurements of W and Z boson production, mass, and electroweak parameters, emphasizing advancements in measurement precision at the LHC.

Findings

Improved measurement accuracy of $ ext{sin}^2 heta_W$ at the LHC.

Precise determination of W and Z production cross sections.

Enhanced understanding of Drell-Yan differential cross sections.

Abstract

Several electroweak precision measurements are performed by the ATLAS and CMS collaborations at the LHC. The main ones are carried out using Drell-Yan production of single W and Z boson. They regard the measurement of the production cross sections of W and Z bosons, the mass of the W boson, and $\sin^2\theta_W$. The results of the $\sin^2\theta_W$ measurements have an accuracy of approximately twice that reached at LEP and SLD. Other measurements reported are about the Drell-Yan differential production cross section.

Equations

$${\sin }^2{\theta }_W=1-\frac{m_W^2}{m_Z^2}$$

$$\frac{d\sigma }{d(\cos {\theta }^{\ast })}\propto 1+{\cos }^2{\theta }^{\ast }+A_4\cos {\theta }^{\ast }$$

$$A_{FB}=\frac{3}{8}{A}_4=\frac{{\sigma }_F-{\sigma }_B}{{\sigma }_F+{\sigma }_B}$$

$${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }=0.23101\pm 0.00053=0.23101\pm 0.00036(stat)\pm 0.00018(syst)\pm 0.00016(theory)\pm 0.00031(PDF).$$

$${\sin }^2{\theta }_{\mathrm{eff}}^{\ell }=0.23140\pm 0.00036=0.23140\pm 0.00021(stat)\pm 0.00016(syst)\pm 0.00024(PDF).$$

$$R_{W/Z}(p_T)=\left(\frac{1}{{\sigma }_W}\frac{d{\sigma }_W(p_T)}{d{p}_T}\right){\left(\frac{1}{{\sigma }_Z}\frac{d{\sigma }_Z(p_T)}{d{p}_T}\right)}^{-1}$$

Full text

1 Introduction

The LHC and other hadron colliders measure many parameters of the Standard Model (SM) and they give very important inputs to the global SM fits [1]. One relevant SM parameter is the W boson mass $m_{W}$, measured at the Tevatron and at the LHC. This can be compared to the SM prediction obtained using the measurement of the top quark mass $m_{t}$, which is precisely measured at the LHC and Tevatron, and the Higgs boson mass $m_{H}$, which is precisely measured at the LHC. In this respect, a global electroweak fit to SM parameters yields an indirect estimate of $m_{W}=80358\pm 8$ MeV [1], thus with a precision of $10^{-4}$.

Other SM parameters which are discussed in this presentation are the measurements of the weak mixing angle ($\sin^{2}\theta_{W}$) and the measurement of differential cross sections of the Z boson. These studies are based on large samples of $\gamma^{*}/$Z decays to electrons and muons, collected during the Run 1 or Run 2 of the LHC. The measurement of $\sin^{2}\theta_{W}$ provides an indirect measurement of $m_{W}$, through the relation:

[TABLE]

Different experiments use Z boson decays into muon pairs and, whenever possible, also into electron pairs. The standard selection of Z decays requires both leptons to have a pseudo-rapidity $|\eta|<2.4$ (or 2.5), but ATLAS also uses electron pairs with a forward electron which does not traverse the tracker and is identified and measured in the calorimeters.

2 Measurement of $\sin^{2}\theta_{W}$

The most precise measurement of $\sin^{2}\theta_{W}$ at hadron colliders is based on the forward-backward asymmetry $A_{FB}$ in Drell–Yan $qq\to\ell^{+}\ell^{-}$ events, where $\ell$ stands for muon ($\mu$) or electron (e). The forward-backward asymmetry is defined using the angle $\theta^{*}$ between the outcoming lepton and the incoming quark in the Collins–Soper reference frame. A needed ingredient to define $\theta^{*}$ is the direction of the incoming quark. At the LHC, which is a pp collider, the direction of the quark is not know event-by-event, but can be approximated to be the same as the longitudinal component of the Z boson momentum because antiquarks originate from the sea and tend to have lower momentum than quarks which are predominantly valence quarks. Given the uncertainties in the quark assignment at the LHC, which are largest for central events, the observed asymmetry is reduced, compared to the true one and this effect is referred as dilution. When the Z boson has no longitudinal momentum, the observed asymmetry becomes 0 as it becomes impossible to identify the quark direction. The differential cross section at leading order is:

[TABLE]

where $\theta^{*}$ is the polar angle of the negative lepton in the Collins–Soper frame of the dilepton system and $A_{FB}$ is defined as:

[TABLE]

where $\sigma_{F}$ and $\sigma_{B}$ are the cross sections for leptons in the forward and backward hemispheres in terms of $\theta^{*}$. The weak mixing angle, $\sin^{2}\theta_{W}$, is related to the masses of the W and Z bosons through the relation in Eq. 1. In the improved Born approximation the effective mixing angle, $\sin^{2}\theta^{\ell}_{\rm eff}$ , is defined, which absorbs some of the higher-order corrections.

2.1 Measurement of $\sin^{2}\theta^{\ell}_{\rm eff}$ at CMS

CMS measured $\sin^{2}\theta^{\ell}_{\rm eff}$ , using Z decays into electrons and muons collected at 8 TeV during Run 1. The CMS measurement is based on a template fit of the $\cos\theta^{*}$ distributions. An event weighting [2] is used to build $\cos\theta^{*}$ templates, and weights are used for parton distribution function (PDF) replicas to also constrain PDFs with data.

The asymmetry measurement is carried out in 6 bins for the dilepton rapidity $y_{\ell\ell}$ and in 12 bins for the dilepton invariant mass $m_{\ell\ell}$. The measured data and the results of the fit are shown in Fig. 1. The PDF uncertainties mainly affect AFB far from the Z boson peak while $\sin^{2}\theta^{\ell}_{\rm eff}$ has the largest effect on the peak. By eff using weights proportional to $\exp(-\chi^{2}/2)$, which is equivalent to profiling over the PDF replicas, the uncertainty due to PDF decreases from 0.00057 to 0.00030.

The final CMS results [4] is:

[TABLE]

2.2 Measurement of $\sin^{2}\theta^{\ell}_{\rm eff}$ and triple differential distributions at ATLAS

The ATLAS collaboration previously carried out a measurement of $\sin^{2}\theta^{\ell}_{\rm eff}$ using data collected at 7 TeV. The result is:

[TABLE]

The most recent analysis consists in a triple differential cross section measurement, differential in $m_{\ell\ell}$, $\cos\theta^{*}$ and $y_{\ell\ell}$ [3]. The analysis is carried our using 8 TeV data in the Z$/\gamma\to\mu\mu$ and Z$/\gamma\to$ee channels, where both leptons are central, and also in Z$/\gamma\to$ee channel with one central and one forward electron. The analysis is performed in a total of 504+504+104 bins. Figure 2 shows the measurement as function of $y_{\ell\ell}$ in various $\cos\theta^{*}$ bins, positive and negative and for three different $m_{\ell\ell}$ ranges, below, on and above the Z peak. The data show good agreement with the predictions of POWHEG. These measurements can be used to extract the measurement of $\sin^{2}\theta^{\ell}_{\rm eff}$.

3 Measurement of W boson mass at ATLAS

The mass of the W boson is measured by ATLAS collaboration using leptonic decays in 4.6 fb*-1* of data recorded in 2011 at $\sqrt{s}=7$ TeV [5]. Since it is not possible to fully reconstruct the W boson mass, the measurement relies on mass-sensitive final state variables, the transverse momentum of the charged lepton $p_{T}^{\ell}$ and the W boson transverse mass $m_{T}$, defined as $m_{T}=\sqrt{2p_{T}^{\ell}p_{T}^{miss}(1-\cos\phi)}$ where $p_{T}^{miss}$ is the neutrino missing transverse momentum, estimated with the vector sum of the transverse energy of all clusters reconstructed in the calorimeters excluding the lepton deposits. Templates of these distributions, obtained from simulation with different values of $m_{W}$, are compared to the observed distributions and a $\chi^{2}$ minimisation is performed to extract the W boson mass.

Muon momentum scale and resolution corrections are derived using Z$\to\mu\mu$ (ee) decays. The combined uncertainty is dominated by the finite size of the Z boson sample. The total muon calibration and efficiency uncertainty in the W boson mass is 9.8 MeV when estimated using the $p_{T}^{\ell}$ distribution and 9.7 MeV using $m_{T}$. The hadronic recoil calibration enters the definition of $m_{T}$, and it is sensitive to pileup and underlying event description. Resolution mismodelling is estimated with Z boson events in data, and transferred to the W boson sample. The uncertainties from the hadronic recoil calibration affect the W boson mass by 2.6 MeV when fitting the $p_{T}^{\ell}$ distribution and by 13 MeV for $m_{T}$.

The simulated samples of inclusive vector-boson production are based on the Powheg MC generator interfaced to Pythia 8, but provide an imperfect modelling of all the observed distributions. Ancillary measurements of Drell–Yan processes are used to validate (and tune) the model and to assess systematic uncertainties. The W and Z boson samples are reweighted to include the effects of higher-order QCD and EW corrections, as well as the results of fits to measured distributions which improve the agreement of the simulated lepton kinematic distributions with the data.

The QCD parameters of the parton shower model (PYTHIA 8) were determined by fits to the transverse momentum distribution of the Z boson measured at 7 TeV, and it is extrapolated to the W using the ratio:

[TABLE]

the uncertainties propagated in the ratio are the statistical precision of the Z data, c-quark and b-quark variations, factorisation scale variation in the QCD ISR, decorrelating W and Z for the heavy flavour initiated production while correlating for the light quark production, leading order PS PDF variations. The uncertainty from the PDFs on the fixed-order predictions dominate the total uncertainty in the measurement and amounts to 8.0 MeV in the $p_{T}^{\ell}$ fit, and to 8.7 MeV in the $m_{T}$ fit.

The final combination of all categories gives: $m_{W}=80370\pm 7(stat.)\pm 11(exp.syst.)\pm 14(mod.syst.)MeV$, where the first uncertainty is statistical, the second corresponds to the experimental systematic uncertainty, and the third to the physics modelling systematic uncertainty. The final measurement uncertainty is dominated by modelling uncertainties, mainly the strong interaction uncertainties. Lepton calibration uncertainties are the dominant sources of experimental systematic uncertainty for the extraction of $m_{W}$ from the $p_{T}^{\ell}$ distribution.