A summary of systematic uncertainties for each source and processes is reported in Table II in the paper. -------------------------- The naming convention for nuisance parameters (NPs) and parameters of interest (POIs) is reported below. These names are used in the tables for covariance matrices (they include both NPs and POIs) and postfit pulls and constraints (these include only NPs). Whenever the source of uncertainty is uncorrelated between the muon and electron channel (thus different NPs are defined), this is indicated by "$\mu$" or "e" for the muon or electron channel, respectively. If none of them is reported, it means that the source of uncertainty is fully correlated between the two channels. In addition, if the source is further treated as uncorrelated between charges, the charge is specified in the name (for instance, with "e^+" to refer to electron channel with positive charge) Some NPs are defined in bins of lepton pseudorapidity and transverse momemtum. The boundaries for these bins may vary between the helicity and double-differential cross section measurements. -------------------------- -------------------------- NUISANCE PARAMETERS -------------------------- QCD bkg $\eta$-norm-chargeUncorr: normalization uncertainty in the QCD multijet background as a function of the lepton pseudorapidity, treated as uncorrelated between charges. NPs are defined for different ranges of lepton pseudorapidity (Sect. VII-A-1) QCD bkg $\eta$-norm: normalization uncertainty in the QCD multijet background as a function of the lepton pseudorapidity, treated as fully correlated between charges. NPs are defined for different ranges of lepton pseudorapidity (Sect. VII-A-1) QCD bkg $p_{T}$-norm: normalization uncertainty in the QCD multijet background as a function of the lepton transverse momentum, treated as fully correlated between charges. NPs are defined for different ranges of lepton transverse momentum (Sect. VII-A-1) QCD bkg $p_{T}$-shape: shape uncertainty in the QCD multijet background as a function of the lepton pseudorapidity, treated as fully correlated between charges. NPs are defined for different ranges of lepton transverse momentum (Sect. VII-A-1) $p_{T}$ scale stat.N: systematic uncertainty in the lepton momentum scale, related to the size of the data and simulated calibration samples. The number N represents each of the 99 (97) NPs defined for the muon (electron) channel. The uncertainty is fully correlated across lepton pseudorapidity and transverse momentum (Sect. VII-A-2). $p_{T}$ scale syst.N: systematic uncertainty in the lepton momentum scale. Different NPs, distinguished by the number N, are defined. N goes from 2 (0) to 5 (1) in the muon (electron) channel. In the electron channel, N = 0 (1) is related to changing the signal (background) model in the fit to the Z boson line shape when deriving the scale corrections. In the muon channel, the values of N from 2 to 5 respectively refers to: the modeling of the Z boson $p_{T}$, electroweak effects on the Z boson line shape, the effect of the acceptance on the dimuon invariant mass, and choice of electroweak parameters used to generate the calibration sample. In the electron channel, the uncertainties are treated as uncorrelated between charges. They are also decorrelated in 4 pseudorapidity bins, and in 2 bins of electron transverse momemtum. In the muon channel, the uncertainties are decorrelated in 2 bins of pseudorapidity, and, except for N = 3, between charges (Sect. VII-A-2). Eff.stat. param.N: statistical uncertainty for the lepton efficiency, as applied to W and Z events. A NP is defined for each bin of lepton pseudorapidity and each of the 3 parameters N of the error function used to model the efficiency versus lepton transverse momentum. The model is defined as [0]*Erf((x-[1])/[2]), where x represents the lepton transvers momentum, and [0], [1], and [2] represent the 3 parameters of the model. (Sect. VII-A-3) eff.syst. bkg: normalization uncertainty due to lepton efficiency, applied only to t quark, Dibosons, and charge flips backgrounds (Sect. VII-A-3) eff.syst.: systematic uncertainty for lepton efficiency, applied only to W (signal and $W\rightarrow\tau\nu$ background) and Z processes in different bins of lepton pseudorapidity (Sect. VII-A-3) L1-trigger electron eff.syst.: systematic uncertainty covering for the inefficiency of the L1-trigger in the electron channel (Sect. VII-A-3) second lepton veto: uncertainty related to the efficiency for the veto of a second lepton in the event (Sect. VII-A-4) X bkg norm.: background normalization for process X (Sect. VII-A-5 and VII-B-5 in paper) luminosity: uncertainty in integrated luminosity (Sect. VII-A-6 in paper) $\mu_{F}$, $\mu_{R}$, $\mu_{R}\mu_{F}$: theoretical uncertainty related to the QCD factorization and normalization scales. Different NPs are defined for the Z or $W\rightarrow\tau\nu$ backgrounds, and for W signal processes (name includes "Drell-Yan bkg","$W\rightarrow\tau\nu$ bkg", or "W signal", respectively). For all W processes, different NPs are defined for exclusive bins of W boson transverse momentum ($p_{T}^{W}$), and also decorrelated between the two charges. In addition, for the W signal process the uncertainties are also decorrelated among the helicity states, where applicable (Sect. VII-B-1 and VII-B-2). Hessian X: uncertainty in the parton distibution functions. 60 independent NPs are defined, with X going from 1 to 60 (Sect. VII-B-3) $\alpha_{S}$: uncertainty in the strong coupling constant $m_W$: uncertainty in the choice on the W boson mass in simulated samples (Sect. VII-B-6) QED final state radiation: uncertainty in the modeling of QED radiation. The uncertainty is decorrelated between the muon and electron channels (Sect. VII-B-7) norm.syst. X: normalization systematic uncertainty assigned to signal bin X (e.g. X = "$W^{+}_{L}$, $|y_{W}| \in$ [2.50,2.75]" for signal events with a W boson with positive charge, left polarization, and rapidity between 2.50 and 2.75). These uncertainties are only used for the helicity fit, and only on signal bins characterized by either $|y_{W}| >$ 2.5 or longitudinal polarization. For these bins the cross section is fixed to the theoretical prediction (Sect. VIII-A-2) -------------------------- PARAMETERS OF INTEREST -------------------------- fiducial X: quantity X (e.g. X = "cross section, $W\\rightarrow {l}\\nu$, $|\eta|$-$p_{{T}} \in$ [0.0,2.4]-[26.0,56.0]") as measured from the double-differential cross section fit by integrating all bins in the range of lepton $|\eta| < 2.4$ and lepton $p_{T}$ in [26, 56] GeV. These quantities are reported in Fig.19 of the paper. POI, X: parameter of interest (POI) for bin X. For example, X = "$W^{+}_{L}$, $|y_{W}| \in$ [0.00,0.25]" to denote positive W boson with left polarization, with rapidity between 0 and 0.25. The POI usually represents a cross section, absolute or normalized as appropriate, charge asymmetry, or angular coefficient, as detailed in the description of the table.