GoKawiilEvent samples and selection criteria
The dataset used for this analysis, roughly half of the full 2016 sample, ensures an optimal performance of the CMS detector, especially for the reconstruction of charged particle tracks47. The data and simulation were processed with the most recent version of the reconstruction software, including improvements to particle identification and reconstruction developed for this analysis, and with the latest detector calibration and description of the operating conditions.
We simulate W and Z boson production at NNLO in QCD using the MINNLO PS Wj and Zj40,41 (rev. 3900) processes in POWHEG-BOX-V2 (refs. 57,58,59), interfaced with PYTHIA 8.240 (ref. 42) for the parton shower and hadronization, and with PHOTOS++3.61 (refs. 60,61) for final-state photon radiation. The Z boson event samples simulate all contributions to the dilepton final state, including those from virtual photons. We use the CP5 underlying event tune62, with the hard primordial-k T parameter set to 2.225 GeV, obtained from a dedicated optimization using the \({p}_{{\rm{T}}}^{{\rm{\mu \mu }}}\) data in ref. 63. The (G μ , m W , m Z ) and \(({G}_{{\rm{\mu }}},{\sin }^{2}{\theta }_{\mathrm{eff}},{m}_{{\rm{Z}}})\) EW input schemes are used for W and Z boson production, respectively. The CT18Z PDF set44 at NNLO accuracy was chosen for the nominal analysis, before unblinding the result, given its good description of our W and Z data and because the expected shifts in m W from using other modern PDF sets are within its uncertainties. Additional NNLO PDF sets are studied using event-level weights in the POWHEG MINNLO PS sample: NNPDF3.1 (ref. 64), NNPDF4.0 (ref. 65), CT18 (ref. 44), MSHT20 (ref. 66) and PDF4LHC21 (ref. 67). We also consider the MSHT20aN3LO approximate N3LO PDF set68. The POWHEG MINNLO PS generator is also used to simulate events with W or Z bosons decaying to τ leptons, with the same theory corrections on the boson production kinematic distributions as those applied to the samples with muonic decays. To ensure that the MC sample size is not a notable source of uncertainty in the measurement, simulated samples of more than 4 billion W boson production events and 400 million Z boson production events have been produced. The EW production of lepton pairs or of a W boson in association with a quark through photon–photon or photon–quark scattering is simulated at LO using PYTHIA 8.240 (ref. 69). Top quark and diboson production are simulated at NLO QCD accuracy using MADGRAPH 5_aMC@NLO v.2.6.5 (ref. 70) and POWHEG-BOX-V2 (ref. 71), respectively, interfaced with PYTHIA 8.240 for the parton shower and hadronization. Quarkonia production is simulated using PYTHIA 8 interfaced with PHOTOS++ v.3.61 for final-state photon radiation. Single-muon events have been simulated for additional validation of the muon reconstruction and calibration.
Although the muon system is not used for the muon momentum evaluation, it is crucial for triggering and identification. The selected muons must have a reconstructed track in both the silicon tracker and the muon detectors, with a consistent track fit for hits in both detector subsystems, and pass additional quality criteria to ensure a high purity of the selected events. We use the ‘medium’ identification working point25, whose efficiency is better than 98% for signal muons. The muons must have a transverse impact parameter smaller than 500 μm with respect to the beam line and be isolated from hadronic activity in the detector. The muon isolation is defined as the pileup-corrected ratio between \({p}_{{\rm{T}}}^{{\rm{\mu }}}\) and the sum of the p T of all other reconstructed physics objects within a cone centred around the muon26. The isolation of selected muons must be smaller than 15%, using a cone of radius \(\Delta R=\sqrt{{(\Delta \phi )}^{2}+{(\Delta \eta )}^{2}}=0.4\), where Δϕ and Δη are, respectively, the distance in the ϕ and η coordinates between the muon and the physics objects considered in the sum. Only charged particles within 2 mm of the muon track along the beam axis are considered in the isolation sum. The distance is evaluated between the points of closest approach to the beam line for each track. The same criteria are used to select charged particles used in the \({p}_{{\rm{T}}}^{{\rm{miss}}}\) calculation. Our definition differs from the standard CMS approach, where charged particles in the isolation and \({p}_{{\rm{T}}}^{{\rm{miss}}}\) sums are defined with respect to the vertex that maximizes the sum of \({p}_{{\rm{T}}}^{{\rm{2}}}\) of the associated physics objects72. This change of definition is needed to minimize the rate at which the wrong vertex is chosen, which is negligible in Z → μμ events but, with the standard CMS algorithm, ranges from 1% to 5% for W → μν events, depending on \({p}_{{\rm{T}}}^{{\rm{W}}}\). To ensure the validity of the isolation and \({p}_{{\rm{T}}}^{{\rm{miss}}}\) corrections measured with Z → μμ events and applied to W → μν events (as described in sections ‘Efficiency corrections’ and ‘Hadronic recoil calibration’), it is important to make sure that there are no differences in their dependence on the vertex selection.
Muons used in both the m Z and m W analyses are selected by the same trigger, requiring the presence of at least one muon with \({p}_{{\rm{T}}}^{{\rm{\mu }}} > 24\,\mathrm{GeV}\), to guarantee maximal consistency in terms of event selection and efficiency corrections. Events with electrons with p T > 10 GeV (or additional muons with p T > 15 GeV) or satisfying looser identification criteria are rejected25,26. In the m W analysis, the selected muon must have \(26 < {p}_{{\rm{T}}}^{{\rm{\mu }}} < 56\,\mathrm{GeV}\). The upper threshold is increased to 60 GeV for the W-like m Z measurement. These thresholds restrict the selected events to the \({p}_{{\rm{T}}}^{{\rm{\mu }}}\) range, in which the trigger and reconstruction efficiencies are measured most accurately. The selected muon must be geometrically matched to the object that triggered the event, within a cone of radius ΔR = 0.3. In the W-like analysis, in which two muons are reconstructed, the matching is required only for the muon used to form the \(({p}_{{\rm{T}}}^{{\rm{\mu }}},{\eta }^{{\rm{\mu }}})\) template. This choice avoids the need to evaluate correlations in the triggering efficiency in events in which both muons satisfy the trigger requirements. For consistency with the W boson selection, W-like events must satisfy m T > 45 GeV (about m V /2). In this case, m T is calculated from the selected muon and the \({{\bf{p}}}_{{\rm{T}}}^{{\rm{miss}}}\) value obtained by excluding the other muon from the vector sum.
Events are rejected if they contain electrons with p T > 10 GeV satisfying the identification criteria of the veto working point (which has 95% efficiency for genuine electrons26) or additional muons of p T > 15 GeV matching the loose criteria (with an efficiency of above 99% for real muons25). The electron veto rejects the residual contribution of events from top quark and boson pair production, and from Z →ττ decays with one τ lepton decaying to a muon and the other to an electron. The electron veto efficiency has a negligible impact on the analysis. The muon veto efficiency and the corresponding uncertainties are discussed in the next section.
The single-muon selection efficiency is 85%, evaluated from simulated W → μν and Z → μμ events. The fraction of W → μν events in the selected data sample is 89%. The signal purity of the selected dimuon sample is larger than 99.5%, given the stronger suppression of the backgrounds due to the double muon selection and invariant mass requirement. Although the W-like m Z analysis provides a stringent test of the analysis strategy in an almost background-free environment, the significant background from nonprompt muons in the m W analysis must be validated by other means, as discussed in section ‘Nonprompt-muon background determination’.
Efficiency corrections
The m W measurement is based on a fit to the measured \(({p}_{{\rm{T}}}^{{\rm{\mu }}},{\eta }^{{\rm{\mu }}},{q}^{{\rm{\mu }}})\) distribution using simulated templates for the signal and most background processes. Therefore, it is important that the simulation can accurately reproduce the efficiency of the event selection in the \(({p}_{{\rm{T}}}^{{\rm{\mu }}},{\eta }^{{\rm{\mu }}})\) bins used in the analysis. Corrections to the simulated muon efficiencies are determined from data with the tag-and-probe (T&P) method73, using events from the same Z → μμ sample that we use in the analysis, except that we apply a looser event selection.
The efficiencies are measured differentially in \(({p}_{{\rm{T}}}^{{\rm{\mu }}},{\eta }^{{\rm{\mu }}})\) for different stages of the muon selection, factorized as: reconstruction of a standalone track in the muon chambers; matching of a standalone muon with a track in the tracker to form a global muon candidate (tracking); impact parameter and identification quality criteria of the global muon track; trigger selection; and muon isolation. The efficiencies are evaluated in the measured and simulated event samples, for each of the five sequential stages, and their ratios are used as scale factors (SFs) to reweight the simulated events. Efficiencies are determined from the fraction of selected events in which the probe muon passes the selection whose efficiency is being evaluated. Background events with at least one nonprompt muon are subtracted when computing the efficiency in data. These background contributions are estimated by fitting the sum of a signal and a background model to the observed m μμ distribution. The Z → μμ contribution is modelled by a simulated template from the MINNLO PS sample, convolved with a Gaussian shape to account for differences in the momentum scale and resolution between data and simulation. An alternative signal model, defined by the convolution of a Breit–Wigner distribution and a resolution function that has a Gaussian core and asymmetric exponential tails, is used to assess the systematic uncertainty. The background component is modelled using an exponential function, except for the reconstruction and tracking steps in the failing probe samples, for which the background fraction is large and its shape at low m μμ is sculpted by the \({p}_{{\rm{T}}}^{{\rm{\mu }}}\) selection. For these steps, the background model is an exponential decay distribution that transitions to an error function for m μμ < m Z to capture threshold effects. Third- or fourth-order polynomials are tested as alternative background shapes.
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