A measurement of the production cross-section for Z bosons that decay to muons 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 integrated luminosity of 1.0 fb−1. The cross-section is measured for muons in the pseudorapidity range 2.0 < η < 4.5 with transverse momenta p T > 20 GeV/c. The dimuon mass is restricted to 60 < M μ + μ − < 120 GeV/c 2. The measured cross-section is
σZ→μ+μ−=(76.0±0.3±0.5±1.0±1.3)pb
σZ→μ+μ−=(76.0±0.3±0.5±1.0±1.3)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 next-to-next-to-leading order in perturbative quantum chromodynamics. The cross-section is also measured differentially as a function of kinematic variables of the Z boson. Ratios of the production cross-sections 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
σW+→μ+νμ+σW−→μ−ν¯¯¯μσZ→μ+μ−=20.63±0.09±0.12±0.05,
σW+→μ+νμ+σW−→μ−ν¯μσZ→μ+μ−=20.63±0.09±0.12±0.05,
where the uncertainty due to luminosity cancels.