Perturbative QCD Fragmentation Functions for $B_c$ and $B_c^{\ast }$ Production

Abstract

The dominant production mechanism for $\bar{b}c$ bound states in high energy processes is the production of a high energy $\bar{b}$ or $c$ quark, followed by its fragmentation into the $\bar{b}c$ state. We calculate the fragmentation functions for the production of the S-wave states $B_c$ and $B_c^{\ast }$ to leading order in the QCD coupling constant. The fragmentation probabilities for $\bar{b}\to B_c$ and $\bar{b}\to B_c^{\ast }$ are approximately $2.2\times 10^{-4}$ and $3.1\times 10^{-4}$, while those for $c\to B_c$ and $c\to B_c^{\ast }$ are smaller by almost two orders of magnitude.

Comments: Latex, 12 pages, 3 figures available upon request, NUHEP-TH-93-6