A measurement of the production crosssection for $Z$ bosons that decay to muons is presented. The data were recorded by the LHCb detector during $pp$ collisions at a centreofmass energy of 7 TeV, and correspond to an integrated luminosity of 1.0 fb$^{1}$. The crosssection is measured for muons in the pseudorapidity range $2.0 < \eta < 4.5$ with transverse momenta $p_{T} > 20$ GeV/c. The dimuon mass is restricted to $60 < M_{\mu^{+}\mu^{}} < 120$ GeV/c$^{2}$. The measured crosssection is $$\sigma_{Z\rightarrow\mu^{+}\mu^{}} = (76.0 \pm 0.3 \pm 0.5 \pm 1.0 \pm 1.3) \text{pb}$$ where the uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. This result is in good agreement with theoretical predictions at nexttonexttoleading order in perturbative quantum chromodynamics. The crosssection is also measured differentially as a function of kinematic variables of the $Z$ boson. Ratios of the production crosssections of electroweak bosons are presented using updated LHCb measurements of $W$ boson production. A precise test of the Standard Model is provided by the measurement of the ratio $$\frac{\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}} + \sigma_{W^{}\rightarrow\mu^{}\bar{\nu}_{\mu}}}{\sigma_{Z\rightarrow\mu^{+}\mu^{}}} = 20.63\pm0.09\pm0.12\pm0.05,$$ where the uncertainty due to luminosity cancels.
Invariant mass of dimuon candidates. 
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(a) Differential crosssection as a function of $y_{Z}$ compared with the prediction of Fewz configured with various PDF sets. Different predictions are displaced horizontally for visibility. (b) Normalised differential crosssection as a function of $y_{Z}$ compared to the predictions of ResBos and Powheg + Herwig . The shaded (yellow) bands indicate the statistical and total uncertainties on the measurements, which are symmetric about the central value. 
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Normalised differential crosssection as a function of $p_{T,Z}$ on (a) logarithmic and (b) linear scales. The shaded (yellow) bands indicate the statistical and total uncertainties on the measurements, which are symmetric about the central value. The measurements are compared to the predictions of ResBos and Powheg + Herwig . 
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Normalised differential crosssection as a function of $\phi^{*}_{Z}$ on (a) logarithmic and (b) linear scales. The shaded (yellow) bands indicate the statistical and total uncertainties on the measurements, which are symmetric about the central value. The measurements are compared to the predictions of ResBos and Powheg + Herwig . 
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Normalised differential crosssection as a function of $p_{T,Z}$ on (a) logarithmic and (b) linear scales. The shaded (yellow) bands indicate the statistical and total uncertainties on the measurements, which are symmetric about the central value. The measurements are compared to MC@NLO + Herwig (HW) and MC@NLO + Herwiri (HERWIRI). Herwig is configured with two choices of the root meansquaredeviation of the intrinsic $k_{T}$ distribution, 0 and 2.2 $ {\mathrm{ Ge V /}c}$ . 
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Normalised differential crosssection as a function of $\phi^{*}_{Z}$ on (a) logarithmic and (b) linear scales. The shaded (yellow) bands indicate the statistical and total uncertainties on the measurements, which are symmetric about the central value. The measurements are compared to MC@NLO + Herwig (HW) and MC@NLO + Herwiri (HERWIRI). Herwig is configured with two choices of the root meansquaredeviation of the intrinsic $k_{T}$ distribution, 0 and 2.2 $ {\mathrm{ Ge V /}c}$ . 
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LHCb measurements of electroweak boson production crosssections compared to NNLO pQCD as implemented by the Fewz generator using various PDF sets. The shaded (yellow) bands indicate the statistical and total uncertainties on the measurements, which are symmetric about the central value. 
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Two dimensional plots of electroweak boson crosssections compared to NNLO predictions for various parameterisations of the PDFs. The outer, shaded (yellow) ellipse corresponds to the total uncertainty on the measurements. The inner, shaded (purple) ellipse excludes the beam energy and luminosity uncertainties. The uncertainty on the theoretical predictions corresponds to the PDF uncertainty only. All ellipses correspond to uncertainties at 68.3$\%$ confidence level. 
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Ratios of electroweak boson production $R_{\it W^{+}Z}$, $R_{\it W^{}Z}$, $R_{\it WZ}$, $R_{\it W}$, compared to various theoretical predictions. The shaded (yellow) bands indicate the statistical and total uncertainties on the measurements, which are symmetric about the central value. 
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Animated gif made out of all figures. 
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Contributions to the relative uncertainty on the total $ Z $ boson crosssection. 
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Contributions to the relative uncertainty on the electroweak boson crosssection ratios. 
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Inclusive differential crosssections for $ Z$ boson production as a function of $y_{Z}$. Uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. No candidates are observed in the 4.250  4.500 bin. 
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Inclusive differential crosssections for $ Z$ boson production as a function of $p_{T,Z}$. Uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. 
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Inclusive differential crosssections for $ Z$ boson production as a function of $\phi^{*}_{Z}$. Uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. 
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Inclusive differential crosssections for $ W ^+$ (left) and $ W ^$ (right) boson production as a function of muon $\eta$. Uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. These supersede the results in Ref. \cite{wmu}. 
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$ W ^+$ to $ W ^$ boson production crosssection ratios as a function of muon $\eta$. Uncertainties are due to the sample size, systematic effects and the beam energy. These supersede the results in Ref. \cite{wmu}. 
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Lepton charge asymmetries as a function of muon $\eta$. Uncertainties are due to the sample size, systematic effects and the beam energy. These supersede the results in Ref. \cite{wmu}. 
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Correlation coefficients of differential crosssection measurements as a function of $y_{Z}$. The beam energy and luminosity uncertainties, which are fully correlated between crosssection measurements, are excluded. 
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Correlation coefficients of differential crosssection measurements as a function of $p_{T,Z}$. The beam energy and luminosity uncertainties, which are fully correlated between crosssection measurements, are excluded. 
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Correlation coefficients of differential crosssection measurements as a function of $\phi^{*}_{Z}$. The beam energy and luminosity uncertainties, which are fully correlated between crosssection measurements, are excluded. 
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Correlation coefficients between differential crosssection measurements as a function of $ W$ boson muon $\eta$. The beam energy and luminosity uncertainties, which are fully correlated between crosssection measurements, are excluded. 
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Correlation coefficients between differential crosssection measurements as a function of $y_{Z}$ and $ W$ boson muon $\eta$. The LHC beam energy and luminosity uncertainties, which are fully correlated between crosssection measurements, are excluded. 
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Supplementary material full pdf 
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This ZIP file contains supplemetary material for the publication LHCbPAPER2015001. The files are: supplementary.pdf : An overview of the extra figures Fig*S.pdf, Fig*S.png, Fig*S.eps, Fig*S.C : The figures in various formats 
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Created on 20 February 2021.