Inclusive Hadron Productions in pA Collisions

TL;DR

This paper advances the theoretical understanding of inclusive hadron production in proton-nucleus collisions by calculating the cross section at one-loop order within the small-x saturation formalism, incorporating factorization and evolution equations.

Contribution

It introduces a next-to-leading order factorization framework in coordinate space, connecting small-x evolution with DGLAP evolution for the first time in this context.

Findings

Derived a one-loop order hard coefficient function.

Demonstrated factorization of divergences into evolution equations.

Confirmed consistency with known evolution equations.

Abstract

We calculate inclusive hadron productions in pA collisions in the small-x saturation formalism at one-loop order. The differential cross section is written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The rapidity divergence with small-x dipole gluon distribution of the nucleus is factorized into the energy evolution of the dipole gluon distribution function, which is known as the Balitsky-Kovchegov equation. Furthermore, the collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final state hadron are factorized into the splittings of the associated parton distribution and fragmentation functions, which allows us to reproduce the well-known DGLAP equation. The hard coefficient function, which is finite and free of divergence of any kind, is evaluated at one-loop order.