Collinear Singularities and Running Coupling Corrections to Gluon Production in CGC

TL;DR

This paper investigates how running coupling corrections introduce collinear singularities in gluon production within the CGC framework, affecting the infrared safety of the cross section and requiring regularization.

Contribution

It demonstrates that collinear singularities in gluon production are unaffected by CGC resummations and must be regularized with an infrared cutoff, impacting theoretical calculations.

Findings

Collinear singularities are unaffected by CGC resummations.

Infrared cutoff enters the cross section via alpha_s(Lambda_coll^2).

Singularities do not affect the energy density of produced matter.

Abstract

We analyze the structure of running coupling corrections to the gluon production cross section in the projectile-nucleus collisions calculated in the Color Glass Condensate (CGC) framework. We argue that for the gluon production cross section (and for gluon transverse momentum spectra and multiplicity) the inclusion of running coupling corrections brings in collinear singularities due to final state splittings completely unaffected by CGC resummations. Hence, despite the saturation/CGC dynamics, the gluon production cross section is not infrared-safe. As usual, regularizing the singularities requires an infrared cutoff Lambda_coll that defines a resolution scale for gluons. We specifically show that the cutoff enters the gluon production cross section in the argument of the strong coupling constant alpha_s(Lambda_coll^2). We argue that for hadron production calculations one should be able to absorb the collinear divergence into a fragmentation function. The singular collinear terms in the gluon production cross section are shown not to contribute to the energy density of the produced matter, which is indeed an infrared-finite quantity.