Summary
We describe a measurement of the ratio of the cross sections times branching fractions of the ${B}_{c}^{+}$ meson in the decay mode ${B}_{c}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\mu}}^{+}\ensuremath{\nu}$ to the ${B}^{+}$ meson in the decay mode ${B}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}$ in proton-antiproton collisions at center-of-mass energy $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$. The measurement is based on the complete CDF Run II data set, which comes from an integrated luminosity of $8.7\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. The ratio of the production cross sections times branching fractions for ${B}_{c}^{+}$ and ${B}^{+}$ mesons with momentum transverse to the beam greater than $6\text{ }\text{ }\mathrm{GeV}/c$ and rapidity magn
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