Do fragmentation functions in factorization theorems correctly treat non-perturbative effects?

TL;DR

This paper critically examines the treatment of non-perturbative effects in the factorization theorems' fragmentation functions, highlighting missing elements related to hadronization models and the filling of rapidity gaps.

Contribution

It identifies gaps in existing proofs of factorization, emphasizing the need to incorporate non-perturbative effects like hadronization more accurately.

Findings

Current proofs omit non-perturbative effects in fragmentation functions.

Large rapidity gaps are filled in reality, contrary to assumptions in proofs.

Missing elements are related to string and cluster models of hadronization.

Abstract

Current all-orders proofs of factorization of hard processes are made by extracting the leading power behavior of Feynman graphs, i.e., by extracting asymptotics strictly order-by-order in perturbation theory. The resulting parton densities and fragmentation functions include non-perturbative effects. I show how there are missing elements in the proofs; these are related to and exemplified by string and cluster models of hadronization. The proofs rely on large rapidity differences between different parts of graphs for the process; but in reality large rapidity gaps are filled in