Flavour tagging and mixing at LHCb

We report on the optimization and calibration of the flavour tagging algorithms using the decays $B^0 \to D^{*-} \mu^+ \nu_{\mu}$ , $B^+ \to J/\psi K^+$ and $B^0 \to J/\psi K^{*0}$ and $\sim 36 pb^{-1} $ of data from the LHCb 2010 physics run. After a data-driven optimization and calibration, the measured effective tagging efficiency $1.99\pm0.15$\% for the opposite-side tagger combination and $2.64\pm0.22$\% for the same-side pion and opposite-side tagger combination. The optimized flavour tagging was used to measure the $B^0_{d/s} - \bar B^0_{d/s}$ mixing frequencies using the decays $B^0_d \to D^- \pi^+$ and $B^0_s \to D_s^- (3)\pi^+$. The results are \dmd is $0.499\pm 0.032 \pm0.003 $~ps $^{-1}$ and \dms = $17.63\pm0.11 \pm0.04 $~ps$^{-1}$.