Partonic Entropy of the Proton from DGLAP Evolution

TL;DR

This paper explores how the entropy of partons inside the proton evolves with energy scale, emphasizing the role of saturation effects and proposing entanglement entropy as an observable.

Contribution

It introduces the concept of partonic entropy within DGLAP evolution, demonstrates its monotonic increase, and proposes entanglement entropy as a measurable quantity.

Findings

Partonic entropy increases monotonically with the evolution scale.

Saturation effects at small x regulate the growth of entropy.

Entanglement entropy is proposed as an experimentally testable observable.

Abstract

We investigate the concept of partonic entropy of the proton within the Dokshitzer--Gribov--Lipatov--Altarelli--Parisi (DGLAP) evolution scheme of collinear parton distributions. We show that such entropy increases monotonically with the evolution scale. The mechanism underlying this growth is illustrated using a simplified model of DGLAP evolution, highlighting the importance of including saturation effects at small x in the evolution of parton distributions, which tame the otherwise unbounded growth of partonic entropy. Based on existing literature, we present two simplified models of parton saturation at small x. In one of these models, partonic entropy is identified with entanglement entropy and proposed as an experimentally testable observable.