Dimensional Regularization in Quarkonium Calculations

TL;DR

The paper addresses the incompatibility of dimensional regularization with the standard covariant projection method in NRQCD factorization for heavy quarkonium production and decay. It generalizes the threshold expansion to N spatial dimensions and uses perturbative matching to derive short-distance coefficients, systematically handling infrared and ultraviolet poles through NRQCD operator renormalization. The authors compute the leading color-octet $\alpha_s$ and leading color-singlet $\alpha_s^2$ contributions to gluon fragmentation functions for arbitrary quarkonium states, providing explicit results for $\eta_c$, $J/\psi$, and $\chi_{cJ}$, and resolve a discrepancy in spin-triplet P-wave calculations. This framework offers a robust, extensible approach for higher-order quarkonium calculations and the associated renormalization-group evolution of NRQCD matrix elements.

Abstract

Dimensional regularization is incompatible with the standard covariant projection methods that are used to calculate the short-distance coefficients in inclusive heavy quarkonium production and annihilation rates. A new method is developed that allows dimensional regularization to be used consistently to regularize the infrared and ultraviolet divergences that arise in these perturbative calculations. We illustrate the method by calculating the leading color-octet terms and the leading color-singlet terms in the gluon fragmentation functions for arbitrary quarkonium states. We resolve a discrepancy between two previous calculations of the gluon fragmentation functions for the spin-triplet P-wave quarkonium states.