Measurement of the ratio of $B_c^{+}$ branching fractions to $J\mathrm{/}\psi {\pi }^{+}$ and $J\mathrm{/}\psi {\mu }^{+}{\nu }_{\mu }$

The first measurement that relates semileptonic and hadronic decay rates of the $B_c^{+}$ meson is performed using proton-proton collision data corresponding to 1.0 fb${}^{-1}$ of integrated luminosity collected with the LHCb detector. The measured value of the ratio of branching fractions, ${\cal B}(B_c^+ \to J/\psi \pi^+)/{\cal B}(B_c^+\to J/\psi\mu^+\nu_\mu)=0.0469 \pm 0.0028 (stat.) \pm 0.0046 (syst.)$, is at the lower end of available theoretical predictions.