Updated measurements of $W$ and $Z$ production at $\sqrt{s}$ = 7 TeV with the LHCb experiment

We have measured the $W$ and $Z$ boson production cross-sections in proton-proton collisions at a centre-of-mass energy of 7~TeV, using 37.1$\pm 1.3$~pb$^{-1}$ of data. The $W$ and $Z$ bosons are reconstructed from muons with transverse momentum $p_{T\mu}$ exceeding 20 GeV, pseudorapidity $\eta_{\mu}$ within 2.0 - 4.5, and, in the case of the $Z$, a dimuon invariant mass $m_{Z}$ in the range 60 $\leq m_{Z} \leq$ 120 GeV. We obtain: \[ \sigma_{Z} (2.0 \leq \eta_{\mu} \leq4.5, p_{T\mu} \geq 20, 60 \leq m_{Z} \leq 120) = 74.9 \pm 1.6 \pm3.8 \pm 2.6 \textrm{ pb} ; \] \[ \sigma_{W+} (2.0 \leq \eta_{\mu} \leq 4.5, p_{T\mu} \geq 20) =808\pm7\pm28\pm28 \textrm{ pb} ; \] \[ \sigma_{W-} (2.0 \leq \eta_{\mu} \leq 4.5, p_{T\mu}\geq 20) = 634\pm7\pm21\pm22 \textrm{ pb,} \] where the first error is statistical, the second systematic, and the third due to luminosity. The $W$ and $W$ cross-section ratios ($\sigma_{W+}+\sigma_{W-}) / \sigma_{Z}$ and $\sigma_{W+} / \sigma_{W-}$, and the $W$ charge asymmetry, $A_W$, \[ {\sigma_{W+}- \sigma_{W-} \over \sigma_{W+}+ \sigma_{W-}}, \] have also been measured within the same kinematic region. and provide constraints to parton density functions in a new kinematic region. All results are consistent with next-to-next-to-leading order theoretical predictions.