Hierarchical Markovian algorithm in QCD evolution

TL;DR

This paper introduces a hierarchical Markovian algorithm for QCD evolution equations, specifically the DGLAP equation, enabling efficient Monte Carlo simulations by separating different emission types.

Contribution

It presents a novel hierarchical formalism for QCD evolution that distinguishes emission types and demonstrates its implementation and validation against standard algorithms.

Findings

Hierarchical solution effectively separates emission processes.

Algorithm is compatible with Monte Carlo methods.

Validated against existing Markovian algorithms.

Abstract

A general formalism was introduced for reorganization of QCD evolution equations and derivation of hierarchical solution to DGLAP equation. The hierarchical solution separates two types of parton emissions: the flavour changing emissions and the diagonal ones (bremsstrahlung). It has been shown that both of the achieved processes are of the Markovian type, what gives a nice possibility of Monte Carlo implementation. Hierarchical algorithm has been implemented and crosschecked with standard Markovian algorithm implemented in program EvolFMC.