One-loop Factorization for Inclusive Hadron Production in $pA$ Collisions in the Saturation Formalism

TL;DR

This paper establishes one-loop QCD factorization for inclusive hadron production in proton-nucleus collisions within the saturation formalism, explicitly calculating gluon radiation diagrams and demonstrating divergence factorization.

Contribution

It provides the first explicit one-loop calculation of the hard coefficient function in the saturation formalism for $pA$ collisions, confirming factorization at this order.

Findings

Successful factorization of divergences into parton distributions and dipole gluon evolution.

Explicit one-loop calculation of the hard coefficient function without divergences.

Validation of the saturation formalism at next-to-leading order for hadron production.

Abstract

We demonstrate the QCD factorization for inclusive hadron production in $pA$ collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final state hadron, as well as the rapidity divergence with small-$x$ dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.