We describe a measurement of the ratio of the cross sections times branching fractions of the $B_c^{+}$ meson in the decay mode $B_c^{+}\to J/\psi {\mu }^{+}\nu$ to the $B^{+}$ meson in the decay mode $B^{+}\to J/\psi K^{+}$ in proton-antiproton collisions at center-of-mass energy $\sqrt{s}=1.96\mathrm{TeV}$. The measurement is based on the complete CDF Run II data set, which comes from an integrated luminosity of $8.7{\mathrm{fb}}^{-1}$. The ratio of the production cross sections times branching fractions for $B_c^{+}$ and $B^{+}$ mesons with momentum transverse to the beam greater than $6\mathrm{GeV}/c$ and rapidity magnitude smaller than 0.6 is $0.211\pm 0.012{(\mathrm{stat})}_{-0.020}^{+0.021}(\mathrm{syst})$. Using the known $B^{+}\to J/\psi K^{+}$ branching fraction, the known $B^{+}$ production cross section, and a selection of the predicted $B_c^{+}\to J/\psi {\mu }^{+}\nu$ branching fractions, the range for the total $B_c^{+}$ production cross section is estimated.

• Received 17 January 2016

DOI:https://doi.org/10.1103/PhysRevD.93.052001