No Generalized TMD-Factorization in the Hadro-Production of High Transverse Momentum Hadrons

TL;DR

This paper demonstrates that generalized TMD factorization fails in high transverse momentum hadro-production due to process-dependent Wilson lines, using a counter-example in a non-Abelian gauge theory.

Contribution

It provides a direct counter-example showing the impossibility of a universal generalized TMD factorization in non-Abelian gauge theories.

Findings

Counter-example disproves generalized TMD factorization in non-Abelian theories.

Breakdown of universality in transverse momentum dependent PDFs.

Challenges the use of separate correlation functions for each hadron.

Abstract

It has by now been established that standard QCD factorization using transverse momentum dependent parton distribution functions fails in hadro-production of nearly back-to-back hadrons with high transverse momentum. The essential problem is that gauge invariant transverse momentum dependent parton distribution functions cannot be defined with process-independent Wilson line operators, thus implying a breakdown of universality. This has led naturally to proposals that a correct approach is to instead use a type of "generalized" transverse momentum dependent factorization in which the basic factorized structure is assumed to remain valid, but with transverse momentum dependent parton distribution functions that contain non-standard, process dependent Wilson line structures. In other words, to recover a factorization formula, it has become common to assume that it is sufficient to simply modify the Wilson lines in the parton correlation functions for each separate hadron. In this paper, we will illustrate by direct counter-example that this is not possible in a non-Abelian gauge theory. Since a proof of generalized transverse momentum dependent factorization should apply generally to any hard hadro-production process, a single counter-example suffices to show that a general proof does not exist. Therefore, to make the counter-argument clear and explicit, we illustrate with a specific calculation for a double spin asymmetry in a spectator model with a non-Abelian gauge field. The observed breakdown of generalized transverse momentum dependent factorization challenges the notion that the role of parton transverse momentum in such processes can be described using separate correlation functions for each external hadron.