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A measurement of the production cross-section for $Z$ bosons that decay tomuons is presented. The data were recorded by the LHCb detector during $pp$collisions at a centre-of-mass energy of 7 TeV, and correspond to an integratedluminosity of 1.0 fb$^{-1}$. The cross-section is measured for muons in thepseudorapidity 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 cross-section 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, systematiceffects, the beam energy and the luminosity. This result is in good agreementwith theoretical predictions at next-to-next-to-leading order in perturbativequantum chromodynamics. The cross-section is also measured differentially as afunction of kinematic variables of the $Z$ boson. Ratios of the productioncross-sections of electroweak bosons are presented using updated LHCbmeasurements of $W$ boson production. A precise test of the Standard Model isprovided 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 luminositycancels.

Measurement of the forward $Z$ boson production cross-section in $pp$ collisions at $\sqrt{s}$ = 7 TeV