Inclusive charm production inΥ(nS)decay

Abstract

Based on the nonrelativistic QCD (NRQCD) factorization formalism, we calculate the inclusive charm production rate in $\ensuremath{\Upsilon}(nS)$ decay at leading order in the strong coupling constant ${\ensuremath{\alpha}}_{s}$ and the relative velocity $v$ of the $b$ quark in the quarkonium rest frame. The branching fractions for $\ensuremath{\Upsilon}(nS)$ to charm for $n=1$, 2, and 3 are all around 7%--9%. About 60% of the branching fraction into charm is from annihilation of the color-singlet $b\overline{b}$ pair into ${\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}c\overline{c}$. Most of the remaining branching fraction is from annihilation of the color-singlet $b\overline{b}$ pair decaying into $c\overline{c}gg$. We also compute the momentum distributions of the charm quark and charmed hadrons in the decays. The virtual-photon contribution to the charm-quark momentum distribution is concentrated at the end point while the $c\overline{c}gg$ contribution is broad. The momentum distributions for charmed hadrons are obtained by convolving the charm-quark momentum distribution with charm fragmentation functions. This makes the momentum distributions for charmed hadrons softer than that for the charm quark. This effect is particularly significant in the virtual-photon contribution.