Measurement of $W^{\pm }$-boson and $Z$-boson production cross-sections in $pp$ collisions at $\sqrt{s}=2.76$ TeV with the ATLAS detector

The production cross-sections for $W^{\pm }$ and $Z$ bosons are measured using ATLAS data corresponding to an integrated luminosity of 4.0 pb${}^{-1}$ collected at a centre-of-mass energy $\sqrt{s}=2.76$ TeV. The decay channels $W \rightarrow \ell \nu$and$Z \rightarrow \ell \ell $areused,where$\ell$ can be an electron or a muon. The cross-sections are presented for a fiducial region defined by the detector acceptance and are also extrapolated to the full phase space for the total inclusive production cross-section. The combined (average) total inclusive cross-sections for the electron and muon channels are: \begin{eqnarray} \sigma^{$\text{tot}$}{W^{+}\rightarrow \ell \nu}& = & 2312 \pm 26\ ($\text{stat.}$)\ \pm 27\ ($\text{syst.}$) \pm 72\ ($\text{lumi.}$) \pm 30
($\text{extr.}$)$\text{pb}$ \nonumber, \ \sigma^{$\text{tot}$}{W^{-}\rightarrow \ell \nu}& = & 1399 \pm 21\ ($\text{stat.}$)\ \pm 17\ ($\text{syst.}$) \pm 43
($\text{lumi.}$) \pm 21\ ($\text{extr.}$)$\text{pb}$ \nonumber, \ \sigma^{$\text{tot}$}_{Z \rightarrow \ell \ell}& = & 323.4 \pm 9.8
($\text{stat.}$) \pm 5.0\ ($\text{syst.}$) \pm 10.0\ ($\text{lumi.}$) \pm 5.5 ($\text{extr.}$) $\text{pb}$ \nonumber. \end{eqnarray} Measured ratios and asymmetries constructed using these cross-sections are also presented. These observables benefit from full or partial cancellation of many systematic uncertainties that are correlated between the different measurements.