Markovian Monte Carlo solutions of the NLO QCD evolution equations

TL;DR

This paper introduces a precise Monte Carlo method using Markovian algorithms to solve NLO QCD evolution equations, validated against existing non-MC programs, enabling high-accuracy QCD computations.

Contribution

It presents a new Markovian Monte Carlo approach for NLO QCD evolution, with detailed algorithms and a dedicated program, achieving high precision and benchmarking against other methods.

Findings

Monte Carlo solutions agree with non-MC programs at 0.1% level

The FMC algorithms provide rigorous solutions to NLO QCD evolution

The approach enables high-precision QCD calculations

Abstract

We present precision Monte Carlo calculations solving the QCD evolution equations up to the next-to-leading-order (NLO) level. They employ forward Markovian Monte Carlo (FMC) algorithms, which provide the rigorous solutions of the QCD evolution equations. Appropriate Monte Carlo algorithms are described in detail. They are implemented in the form of the Monte Carlo program EvolFMC, which features the NLO kernels for the QCD evolution. The presented numerical results agree with those from independent, non-MC, programs (QCDNum16, APCheb33) at the level of 0.1%. In this way we have demonstrated the feasibility of the precision MC calculations for the QCD evolution and provided very useful numerical tests (benchmarks) for other, non-Markovian, MC algorithms developed recently.