$J/\psi$ and $B_c^\pm$ production at LHCb

Measurements of the $J/\psi$ and $B_c^+$ production cross-sections at $\sqrt{s}=7$ TeV with the LHCb detector are presented. The analysis of $J/\psi$ production is based on an integrated luminosity of 5.2 pb$^{-1}$ of data. The double differential cross-section of both prompt $J/\psi$ and $J/\psi$ from $b$ is measured, as a function of the $J/\psi$ transverse momentum $p_{\rm T}$ and of the rapidity $y$ in the fiducial region $p_{\rm T} \in [0,14]$ GeV/$c$ and $y \in [2.0,4.5]$. The integrated cross-section for prompt $J/\psi$ production in this fiducial region is measured to be $\sigma\left({\rm prompt}\,\, J/\psi,\, p_{\rm T} <14\,\mbox{GeV}/c,\,2.0<y<4.5\right) \, = \, 10.52 \pm 0.04 (\rm stat.) \pm 1.40 (\rm syst.)^{+1.64}_{-2.20}(\rm polarisation)\,\,\mu{\rm b}$. The integrated cross-section for the production of $J/\psi$ from $b$ in the same fiducial region is measured to be $\sigma\left(J/\psi\, \mbox{from } b,\, p_{\rm T} <14\,\mbox{GeV}/c,\,2.0<y<4.5\right) \, = \, 1.14 \pm 0.01(\rm stat.)\pm 0.16(\rm syst.)\,\mu{\rm b}$. The $B_c^+$ production measurement is based on an integrated luminosity of 32 pb$^{-1}$. We present a preliminary measurement of the ratio of production cross-section times branching ratio for $B_c^+\to J/\psi \pi^+$ relative to that of $B^+ \to J/\psi K^+$, $\frac{\sigma(B_c^+) \times BR(B_c^+ \rightarrow J/\psi \pi^+)} {\sigma(B^+) \times BR(B^+ \rightarrow J/\psi K^+)} =\left(2.2 \pm 0.8 ({\rm stat.}) \pm 0.2 ({\rm syst.}) \right)\%$.