Shannon entropy of fragmentation functions and their Kullback-Leibler divergence to parton pdfs

TL;DR

This paper explores the entropy of fragmentation functions and their divergence from parton distribution functions, proposing entropy as a measure of extraction progress and analyzing their relationships through Kullback-Leibler divergence.

Contribution

It introduces the entropy of fragmentation functions as a new metric for their analysis and applies Kullback-Leibler divergence to study their relation to parton distribution functions.

Findings

Fragmentation function entropy can characterize extraction progress.

Kullback-Leibler divergence reveals relations between FFs and PDFs.

Entropy measures provide new insights into high-energy collision information flow.

Abstract

The flow of information in high-energy collisions has been recently investigated by various groups: this includes the entanglement entropy of the proton becoming classical information entropy of pdfs, jet splitting affecting entropy, or the entropy distribution in hadron decays. Here we examine fragmentation functions in this context, including their entropy as probability distributions, and propose it as one convenient number to characterize progress in their extraction. We also use the Kullback-Leibler divergence to examine relations between FFs and pdfs such as that of Barone, Drago and Ma.