Next-to-leading order Calculation of a Fragmentation Function in a Light-Cone Gauge

Abstract

Next-to-leading order corrections to fragmentation functions in a light-cone gauge are discussed. This gauge simplifies the calculation by eliminating many Feynman diagrams at the expense of introducing spurious poles in loop integrals. As an application, the short-distance coefficients for the color-octet $^3S_1$ term in the fragmentation function for a gluon to split into polarized heavy quarkonium states are re-calculated to order $α_s^2$. We show that the ill-defined spurious poles cancel and the appropriate prescriptions for the remaining spurious poles can be determined by calculating a subset of the diagrams in the Feynman gauge. Our answer agrees with the recent calculation of Braaten and Lee in the Feynman gauge, but disagrees with another previous calculation.