Extracting the parton distribution functions evolution equations using the stochastic modeling in the non-equilibrium statistical mechanics

TL;DR

This paper introduces a stochastic modeling approach from non-equilibrium statistical mechanics to derive the evolution equations of parton distribution functions, offering a simpler mathematical framework compared to traditional methods.

Contribution

It presents a novel stochastic modeling method to derive DGLAP equations using non-equilibrium statistical mechanics, simplifying the mathematical process.

Findings

Derived DGLAP equations via stochastic modeling

Established equivalence with traditional evolution equations

Proposed a more straightforward mathematical approach

Abstract

In this paper, using the stochastic modeling of the non-equilibrium statistical mechanics in the momentum space, the evolution equations of the parton distribution functions (PDF) usually used in the hadrons phenomenology are generated. These stochastic modeling PDF evolution equations are the same as those of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) ones, but they can be obtained by a more simplistic mathematical procedure based on the non-equilibrium statistical mechanics and the theory of Markov processes.