Resummation of threshold double logarithms in quarkonium fragmentation functions

TL;DR

This paper introduces a formalism to resum threshold double logarithms in quarkonium fragmentation functions, improving their physical behavior and ensuring positive, finite cross sections in heavy quarkonium production.

Contribution

The authors develop a novel resummation method for threshold logarithms in quarkonium fragmentation functions within the nonrelativistic QCD framework, avoiding nonperturbative models.

Findings

Resummation renders fragmentation functions finite and positive.

The formalism allows perturbative calculation of resummed functions.

Addresses unphysical negative cross sections in fixed-order calculations.

Abstract

We develop a formalism for resumming threshold double logarithms that appear in fragmentation functions for production of heavy quarkonia. Threshold singularities appear in fixed-order calculations of quarkonium fragmentation functions in the nonrelativistic QCD factorization formalism due to radiation of soft gluons. Because of this, fixed-order quarkonium fragmentation functions are not positive definite, and can lead to unphysically negative cross sections. This problem can be resolved by resumming threshold logarithms to all orders in perturbation theory, which renders the fragmentation functions finite and ensures the positivity of cross sections. We present a detailed derivation of the resummation formalism and derive the formula for resummed quarkonium fragmentation functions, which can be computed entirely within perturbation theory without the need for nonperturbative model functions.