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Measurements of $B_c^+$ production and mass are performed with the decay mode$B_c^+ \to J/\psi \pi^+$ using 0.37 fb$^{-1}$ of data collected in $pp$collisions at $\sqrt{s}=7$ TeV by the LHCb experiment. The ratio of theproduction cross-section times branching fraction between the $B_c^+ \to J/\psi\pi^+$ and the $B^+ \to J/\psi K^+$ decays is measured to be $(0.68 \pm0.10\,({\rm stat.}) \pm 0.03\,({\rm syst.}) \pm 0.05\,({\rm lifetime}))$% for$B_c^+$ and $B^+$ mesons with transverse momenta $p_{\rm T}>4 $GeV/$c$ andpseudorapidities $2.5<\eta<4.5$. The $B_c^+$ mass is directly measured to be$6273.7 \pm 1.3\,({\rm stat.}) \pm 1.6 \,({\rm syst.})$ MeV/$c^2$, and themeasured mass difference with respect to the $B^+$ meson is $M(B_c^+)-M(B^+) =994.6 \pm 1.3\,({\rm stat.}) \pm 0.6\,({\rm syst.})$ MeV/$c^2$.

Measurements of $B_c^+$ production and mass with the $B_c^+ \to J/\psi \pi^+$ decay