How to calculate the heavy-quark fragmentation function: An application of cut vertices

Abstract

I show that the heavy-quark fragmentation function is calculable to leading order in the inverse heavy mass. This implies that the production of a heavy particle (with one heavy quark) with a given momentum is calculable. In first approximation the function is $\delta \mathrm{}(1-x)\mathrm{}$. The peak at $x=1\mathrm{}$ is, however, not of zero width, but has a width on the order of the inverse mass. I determine the shape of the function for $x$ near 1. Lastly, I show that the spin of the heavy quark does not flip during its fragmentation. This paper extends the work of Mueller, Sterman, and others.