Commuting Matrix Solutions of PQCD Evolution Equations

TL;DR

This paper presents a method for solving PQCD evolution equations using commuting matrix solutions in x space, enabling direct data-driven parton distribution extraction and potential non-parametric analysis.

Contribution

It introduces well-developed commuting matrix solutions for PQCD evolution equations, matching standard results and facilitating direct, non-parametric data analysis.

Findings

Finite LO evolution results match standard LO sets

Commuting matrix solutions are effective for PQCD evolution

Potential for non-parametric data analysis in parton distributions

Abstract

A method of obtaining parton distributions directly from data is revealed in this series. In the process, the first step would be developing appropriate matrix solutions of the evolution equations in $x$ space. A division into commuting and non-commuting matrix solutions has been made. Here, well-developed commuting matrix solutions are presented. Results for finite LO evolution match those of standard LO sets. There is a real potential of doing non-parametric data analysis.