Comment on "Nonuniversality of Transverse Momentum Dependent Parton Distributions at Small x"

TL;DR

This paper clarifies that the analysis in arXiv:1003.0482 actually confirms the universality of transverse momentum dependent quark distributions at small x, supporting earlier findings and enabling experimental constraints through $pp$ and $pA$ collisions.

Contribution

It demonstrates that the analysis verifies universality of TMD quark distributions at small x and connects infrared divergences to Wilson line operators for $k_T$ factorization.

Findings

Universality of TMD quark distributions at small x is confirmed.

Infrared divergences are factorized into Wilson line operators.

Exponential factors can be constrained by $pp$ collision data.

Abstract

We point out that the analysis in arXiv:1003.0482 actually verifies the universality of transverse momentum dependent quark distributions at small $x$, which supports the observation in our earlier work arXiv:0904.4150. Once the gluon exchanges responsible for the additional infrared divergences are factorized and summed into an exponential factor, it can be expressed as a matrix element of Wilson line operators, and treated as a nonperturbative input to the $k_T$ factorization of $pA$ collisions. The same exponential factor has been extracted from $pp$ collisions in arXiv:0904.4150, rendering possible experimental constraints on its behavior from $pp$ processes, and predictions for $pA$ processes.