Electroweak and QCD studies in the forward region with LHCb

Measurements of the $Z^{0}$ and $W$ production cross-sections constitute important tests of the Standard Model at the LHC energies. NLO predictions have relative errors of between a few percents and $\sim 10\%$, depending on rapidity, where the dominant uncertainty is due to the knowledge of the PDFs. The forward acceptance of the LHCb experiment can provide unique measurements to constrain the PDFs in previously unexplored regions of the $(x, Q^{2})$ space. Determinations of cross-sections and ratios of $Z^{0}$ and $W$ bosons using $\int\mathcal{L} = (16.5 \pm 1.7)$ pb$^{-1}$ of LHCb data at $\sqrt{s} = 7$ TeV collected during 2010 are reported.