Ratios of bottom meson branching fractions involvingJψmesons and determination ofbquark fragmentation fractions

We report a measurement of the ratios of the decay rates of the ${B}^{+}$, ${B}^{0}$, and ${B}_{s}^{0}$ mesons into exclusive final states containing a $\frac{J}{\ensuremath{\psi}}$ meson. The final states were selected from 19.6 pb-1 of $p\overline{p}$ collisions recorded by the Collider Detector at Fermilab. These data are interpreted to determine the $b$ quark fragmentation fractions ${f}_{u}$, ${f}_{d}$, and ${f}_{s}$. We also determine the branching fractions for the decay modes ${B}^{+}\ensuremath{\rightarrow}\frac{J}{\ensuremath{\psi}{K}^{+}}$, ${B}^{+}\ensuremath{\rightarrow}\frac{J}{\ensuremath{\psi}{K}^{*}{(892)}^{+}}$, ${B}^{0}\ensuremath{\rightarrow}\frac{J}{\ensuremath{\psi}{K}^{0}}$, ${B}^{0}\ensuremath{\rightarrow}\frac{J}{\ensuremath{\psi}{K}^{*}{(892)}^{0}}$, and ${B}_{s}^{0}\ensuremath{\rightarrow}\frac{J}{\ensuremath{\psi}\ensuremath{\varphi}(1020)}$. We discuss the implications of these measurements to $B$ meson decay models.