Measurement of the Ratio of Branching Fractions $\cal{B}\mathrm{(B^{\pm} \rightarrow J/\psi \pi^{\pm})/\cal{B}\mathrm{(B^{\pm} \rightarrow J/\psi K^{\pm})}}$ at $\sqrt{\mathrm{s}}=7~\mathrm{TeV}$ with the LHCb Detector

The ratio of the branching fractions of the decays $\mathrm{B^{\pm} \rightarrow J/\psi \pi^{\pm}}$ and $\mathrm{B^{\pm} \rightarrow J/\psi K^{\pm}}$ has been measured with the LHCb detector in proton-proton collisions at a centre-of-mass energy of $\sqrt{\mathrm{s}}=7~\mathrm{TeV}$. The analysis is based on a data sample of 37~pb$^{-1}$ collected between April and November 2010 at the Large Hadron Collider. We observe $175 \pm 19 $ $\mathrm{B^{\pm} \rightarrow J/\psi \pi^{\pm}}$ events and $5026 \pm 73$ $\mathrm{B^{\pm} \rightarrow J/\psi K^{\pm}}$ events. The ratio of the branching fractions is measured to be $\cal{B}\mathrm{(B^{\pm} \rightarrow J/\psi \pi^{\pm})}/\cal{B}\mathrm{(B^{\pm} \rightarrow J/\psi K^{\pm})} = \mathrm{(3.94 \pm 0.39(stat.) \pm 0.17(syst.)) \times 10^{-2}}$.