Precision measurement of forward $Z$ boson production in proton-proton collisions at $\sqrt{s}=13$ TeV

A precision measurement of the $Z$ boson production cross-section at $\sqrt{s}=13$ TeV in the forward region is presented, using $pp$ collision data collected by the LHCb detector, corresponding to an integrated luminosity of 5.1 fb${}^{-1}$. The production cross-section is measured using $Z\to {\mu }^{+}{\mu }^{-}$ events within the fiducial region defined as pseudorapidity $2.0<\eta <4.5$ and transverse momentum $p_T>20$ GeV/$c$ for both muons and dimuon invariant mass $60<M_{\mu \mu }<120$ GeV/$c^2$. The integrated cross-section is determined to be \begin{equation*} \sigma(Z\rightarrow\mu^+\mu^-) = 196.4 \pm 0.2 \pm 1.6 \pm 3.9~pb, \end{equation*} where the first uncertainty is statistical, the second is systematic, and the third is due to the luminosity determination. The measured results are in agreement with theoretical predictions within uncertainties.