# Soft-gluon resolution scale in QCD evolution equations

## TL;DR

This paper introduces a new numerical method for solving QCD evolution equations through parton branching, enabling detailed analysis of infrared contributions and momentum-dependent distributions.

## Contribution

A novel numerical solution for QCD evolution equations using parton branching, applicable to infrared analysis and momentum-dependent distributions.

## Key findings

- Effective analysis of infrared contributions order-by-order in α_s
- Application to transverse-momentum and angular ordering cases
- Capability to handle distributions depending on longitudinal and transverse momenta

## Abstract

QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution, order-by-order in the strong coupling $\alpha_s$, as a function of the soft-gluon resolution scale parameter. We examine the cases of transverse-momentum ordering and angular ordering. We illustrate that this approach can be used to treat distributions which depend both on longitudinal and on transverse momenta.