Monte Carlo study of NLO correction to QCD evolution kernel induced by the change of the factorization scale

TL;DR

This paper demonstrates that changing the factorization scale in QCD evolution can be exactly represented by NLO corrections to the leading-order kernel within a Monte Carlo framework, providing insights for practical simulations.

Contribution

It shows how the redefinition of the factorization scale corresponds precisely to NLO corrections in a Markovian Monte Carlo parton shower, linking theoretical and computational approaches.

Findings

Exact equivalence between scale change and NLO correction demonstrated

Implementation within Monte Carlo simulations shown to be feasible

Potential impact on improving QCD evolution modeling in MC tools

Abstract

The aim of the present study is to show that: the redefinition of the factorization scale $Q_i\to z_i Q_i$ in the ladder can be traded exactly for the NLO correction to the LO evolution kernel, $P(z)\to P(z)+(2C_F \alpha_S/\pi)\Delta(z)$ The above observation was done/exploited in the literature, but the present study demonstrates how this phenomenon is realized within the Markovian Monte Carlo parton shower - hence it might be relevant in MC practice.