Measurements of inclusive $W$ and $Z$ boson production crosssections in $pp$ collisions at $\sqrt{s}=7$ TeV using final states containing muons are presented. The data sample corresponds to an integrated luminosity of 37 pb$^{1}$ collected with the LHCb detector. The $W$ and $Z$ bosons are reconstructed from muons with a transverse momentum above 20 GeV$/c$ and pseudorapidity between 2.0 and 4.5, and, in the case of the $Z$ crosssection, a dimuon invariant mass between 60 and 120 GeV$/c^2$. The crosssections are measured to be {$831\pm9\pm27\pm 29$ pb} for $W^+$, {$656\pm8\pm19\pm 23$ pb} for $W^$ and {$76.7\pm1.7\pm3.3\pm2.7$ pb} for $Z$, where the first uncertainty is statistical, the second is systematic and the third is due to the luminosity. Differential crosssections, $W$ and $Z$ crosssection ratios and the lepton charge asymmetry are also measured in the same kinematic region. The ratios are determined to be $\sigma_{W^+\rightarrow\mu^+\nu} / \sigma_{W^\rightarrow\mu^\bar{\nu}}= ${$1.27\pm0.02\pm0.01$}, and $\sigma_{W^+\rightarrow\mu^+\nu} + \sigma_{W^\rightarrow\mu^\bar{\nu}})/\sigma_{Z\rightarrow\mu\mu}= ${$19.4\pm0.5\pm0.9$}. The results are in general agreement with theoretical predictions, performed at nexttonexttoleading order in QCD using recently calculated parton distribution functions.
Invariant mass of the selected muon pairs. The fitted distribution to the data is shown as a solid line and the contribution from background and offresonance DrellYan production as a dashed line. 
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Distributions for $p_\mathrm{T}^\mathrm{cone}$ (top) and $E_\mathrm{T}^\mathrm{cone}$ (bottom). The points are for muons from pseudo$W$ data, the yellow (shaded) histograms are for $W$MC simulation, while the open histograms are for muons from QCD background with IP $>80$ $\,\upmu\rm m$ from data. All distributions are normalised to unity. 
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Muon IP distribution for pseudoW events as points, $W$MC as a yellow (shaded) histogram, and muons from simulated semileptonic decays of hadrons containing a $b$ quark in the full open histogram or a $c$ quark in the dashed open histogram. All distributions are normalised to unity. 
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Distribution of muon $p_\mathrm{T}$ for positively (left panel) and negatively (right panel) charged muons in $W$ candidate events, for the total fiducial crosssection (a). The plots (b) to (f) give the same information for the different $\eta^\mu $ bins. The data (points) are compared to the fitted contributions from $W^$ and $W^+$ (light shaded). The background contributions are, from top to bottom in the legend: decayinflight, $Z\rightarrow\mu\mu$ , $\tau$ decays of W and $Z$, and heavy flavour decays. 
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Measurements of the $Z$, $W^+$ and $W^$ crosssection and ratios, data are shown as bands which the statistical (dark shaded/orange) and total (light hatched/yellow) errors. The measurements are compared to NNLO and NLO predictions with different PDF sets for the proton, shown as points with error bars. The PDF uncertainty, evaluated at the $68$% confidence level, and the theoretical uncertainties are added in quadrature to obtain the uncertainties of the predictions. 
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Differential crosssection for $Z\rightarrow\mu\mu$ as a function of $y^Z$. The dark shaded (orange) bands correspond to the statistical uncertainties, the light hatched (yellow) band to the statistical and systematic uncertainties added in quadrature. Superimposed are NNLO (NLO) predictions with different parametrisations for the PDF as points with error bars; they are displaced horizontally for presentation. 
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Lepton charge asymmetry $A_\mu=(\sigma_{W^+\rightarrow\mu^+\nu} \sigma_{W^\rightarrow\mu^\bar{\nu}} )/(\sigma_{W^+\rightarrow\mu^+\nu} +\sigma_{W^\rightarrow\mu^\bar{\nu}} )$ in bins of muon pseudorapidity. The dark shaded (orange) bands correspond to the statistical uncertainties, the light hatched (yellow) band to the statistical and systematic uncertainties added in quadrature. Superimposed are NNLO (NLO) predictions as described in Fig 7. The MSTW08 values for $\eta^\mu <2$ represent the central value of the prediction. 
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$R_W=\sigma_{W^+\rightarrow\mu^+\nu} /\sigma_{W^\rightarrow\mu^\bar{\nu}} $ in bins of muon pseudorapidity. The dark shaded (orange) bands correspond to the statistical uncertainties, the light hatched (yellow) band to the statistical and systematic uncertainties added in quadrature. Superimposed are NNLO (NLO) predictions with different parametrisations as described in Fig 7. The MSTW08 values for $\eta^\mu <2$ represent the central value of the prediction. 
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Lepton charge asymmetry $A_\mu=(\sigma_{W^+\rightarrow\mu^+\nu} \sigma_{W^\rightarrow\mu^\bar{\nu}} )/(\sigma_{W^+\rightarrow\mu^+\nu} +\sigma_{W^\rightarrow\mu^\bar{\nu}} )$ for muons with $p^\mu_\mathrm{T} >$25 (top) and 30 $ {\mathrm{\,Ge V\!/}c}$ (bottom), respectively in bins of muon pseudorapidity. The dark shaded (orange) bands correspond to the statistical uncertainties, the light hatched (yellow) band to the statistical and systematic uncertainties added in quadrature. The statistical uncertainty is undistinguishable from the total uncertainty. Superimposed are the NNLO predictions with the MSTW08 parametrisation for the PDF.\vspace*{1.5cm} 
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Animated gif made out of all figures. 
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Contributions to the systematic uncertainty for the total $Z$ and $W$ crosssections. The different contributions are discussed in Sect. 4.6 
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Correlation coefficients between $W^+$, $W^$ and Z in the five bins considered. The luminosity uncertainty is not included. 
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Differential $Z\rightarrow \mu \mu$ crosssection, $d\sigma_{Z\rightarrow\mu\mu} /dy^Z$, in bins of boson rapidity. The first crosssection uncertainty is statistical, the second systematic, and the third due to the uncertainty on the luminosity determination. The correction factor $f^Z_{\mathrm{FSR}}$ which is used to correct for FSR is listed separately. 
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Lepton charge asymmetry, $A_\mu$, in bins of muon pseudorapidity for a $p^\mu_\mathrm{T} $ threshold at 20, 25 and 30 GeV/c. The first uncertainty is statistical and the second systematic. The effect of FSR is at the level of $10^{4}$ and is not listed. 
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Created on 20 April 2019.Citation count from INSPIRE on 20 April 2019.