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 ${}^3{S}_1$ term in the fragmentation function for a gluon to split into polarized heavy quarkonium states are re-calculated to order ${\alpha }_s^2$. 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.

20 pages, 4 figures