# On the implementation of NLO high energy factorization in single inclusive forward hadron production

## TL;DR

This paper investigates the implementation of NLO high energy factorization in single inclusive forward hadron production, demonstrating stability and positivity of the cross section with fixed and running coupling, and addressing issues in previous calculations.

## Contribution

It introduces a new rapidity factorization procedure for NLO calculations, ensuring physically meaningful and stable cross sections in forward hadron production.

## Key findings

- Fixed coupling yields positive, stable cross sections.
- Running coupling results are stable but differ from previous coordinate space approaches.
- The approach improves theoretical consistency in high energy QCD calculations.

## Abstract

Single inclusive particle production cross sections in high energy hadron collisions at forward rapidity are an important benchmark process for the CGC picture of small x QCD. Recent calculations of this process have not led to a stable perturbative expansion for this quantity at high transverse momenta. We consider the quark channel production cross section using the new rapidity factorization procedure proposed by Iancu et al. We show that for fixed coupling one does indeed obtain a physically meaningful cross section which is positive and reduces in a controlled way to previous leading order calculations. We also consider a running coupling that depends on the transverse momentum of the produced particle. This gives a stable result which, however, is not fully consistent with previous leading order calculations that use a coordinate space running coupling.