Information entropy and fragmentation functions

TL;DR

This paper explores the information entropy of fragmentation functions in high-energy physics, proposing it as a key measure for future research and assessing relations between FFs and PDFs using divergence metrics.

Contribution

It introduces the concept of entropy for fragmentation functions and evaluates existing theoretical relations between FFs and PDFs using Kullback-Leibler divergence.

Findings

Fragmentation function entropy is a useful characterization tool.

Current FF parametrizations do not support the proposed relation with PDFs.

FFs and PDFs may share similar power-law behaviors near x=1.

Abstract

Several groups have recently investigated the flow of information in high-energy collisions, from the entanglement entropy of the proton yielding classical Shannon entropy of its parton distribution functions (pdfs), through jet splitting generating entropy, to the entropy distribution in hadron decays. Lacking in the literature is a discussion of the information entropy of fragmentation functions (FFs) in the instances where they can be considered as probability distributions, and we here provide it. We find that this entropy is a single, convenient number to characterize future progress in the extraction of fragmentation functions. We also deploy the related Kullback-Leibler divergence between two distributions to assess existing relations among FFs and parton distribution functions (pdfs) such as that of Barone, Drago and Ma. From a couple of current parametrizations of FFs, we do not find supporting empirical evidence for the relation, although it is possible that FFs and pdfs have similar power-laws near the $x=1$ endpoint.