Relativistic corrections to heavy quark fragmentation to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-wave heavy mesons

Abstract

The relativistic corrections of order ${v}^{2}$ to the fragmentation functions for the heavy quark to $S$-wave heavy quarkonia are calculated in the framework of the nonrelativistic quantum chromodynamics factorization formula. We derive the fragmentation functions by using the Collins-Soper definition in both the Feynman gauge and the axial gauge. We also extract them through the process ${Z}^{0}\ensuremath{\rightarrow}Hq\overline{q}$ in the limit ${M}_{Z}/m\ensuremath{\rightarrow}\ensuremath{\infty}$. We find that all results obtained by these two different methods and in different gauges are the same. We estimate the relative size of the relativistic corrections to the fragmentation functions.