Measurement of the $Z\rightarrow\mu^{+}\mu^{-}$ production cross-section at forward rapidities in pp collisions at $\sqrt{s} = 13$ TeV

A measurement of the production cross-section for $Z$ bosons in pp collisions at $\sqrt{s} = 13$ TeV is presented using LHCb data, considering events in which the $Z$ boson decays to two muons. The cross-section is measured for muons with pseudorapidities between $2.0 < \eta < 4.5$, transverse momenta $p_\text{T}> 20$ GeV, and where the dimuon invariant mass is in the range $60 < M (\mu\mu) < 120\ \text{GeV}$. The integrated $Z$ boson cross-section is measured to be \begin{align*} \sigma_{Z\rightarrow\mu\mu} &= 198.4 \pm 1.0 \pm 4.7 \pm 7.7\text{ pb}, \end{align*} where the uncertainties are due to the sample size, systematic effects, and the luminosity determination, respectively. In addition, differential cross-sections are measured as functions of the $Z$ boson rapidity, transverse momentum and $\phi_\eta^{*}$, where the $\phi_\eta^{*}$ variable is precisely measured exclusively from the measured lepton directions, and probes similar physics to the boson transverse momentum. The $Z$ boson rapidity distribution is compared to theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. The predictions vary with the choice of parton distribution functions used, but the data are not yet precise enough to favour a specific selection. The $\phi_\eta^{*}$ and boson transverse momentum distributions are compared to the predictions of event generator programs which make use of parton-showers to model higher order effects. Predictions from Pythia~8 describe the LHCb data much better than predictions produced using Powheg + Pythia~8 with the default Powheg settings and the Monash 2013 tune of Pythia~8.