Inclusive charm production in χ b decays

We calculate the inclusive decay rate of the spin-triplet bottomonium states ${\ensuremath{\chi}}_{bJ}$ into charm hadrons, including the leading-order color-singlet and color-octet $b\overline{b}$ annihilation mechanisms. We also calculate the momentum distribution of the charm quark from the decay of ${\ensuremath{\chi}}_{bJ}$. The infrared divergences from the color-singlet process $b\overline{b}\ensuremath{\rightarrow}c\overline{c}g$ are factored into the probability density at the origin for a $b\overline{b}$ pair in a color-octet state. That probability density can be determined phenomenologically from the fraction of decays of ${\ensuremath{\chi}}_{bJ}$ that include charm hadrons. It can then be used to predict the partial widths into light hadrons for all four states in the $P$-wave bottomonium multiplet.