LHCb: Determination of $f_s / f_d$ for 7 TeV $pp$ collisions and a measurement of the branching ratio of the decay $B^{0} \to D^{⁻} K^{+}$

This poster presents an analysis measuring the relative abundance of the three decay modes $B^{0} \to D^{-} K^{+}$, $B^{0} \to D^{-} \pi^{+}$ and $B^{0}_{s} \to D^{-}_{s} \pi^{+}$ produced in 7 TeV $pp$ collisions at the LHC, from data corresponding to an integrated luminosity of 35 pb$^{-1}$. The branching fraction of $B^{0} \to D^{-} K^{+}$ is found to be $BR(B^{0}\to D^{-} K^{+}) = (2.01\pm 0.18^{stat}\pm 0.14^{syst}) 10^{-4}$. The ratio of fragmentation fractions $f_s/f_d$ is determined through the relative abundance of $B^{0}_{s} \to D^{-}_{s} \pi^{+}$ to $B^{0} \to D^{-} K^{+}$ and $B^{0} \to D^{-} \pi^{+}$, leading to $f_s/f_d = 0.253\pm 0.017\pm 0.017\pm 0.020$, where the uncertainties are statistical, systematic and theoretical respectively. A detailed presentation can be found in the paper, conference note and analysis note (LHCb-ANA-2010-010; LHCb-CONF-2011-013; CERN-LHCb-CONF-2011-013; latest paper draft: LHCB-B2DH-004; CERN-PH-EP-2011-075).