Transverse moments of TMD parton densities and ultraviolet divergences

TL;DR

This paper discusses the ultraviolet divergences in transverse moments of TMD parton densities, highlighting that violations of integral relations are not perturbatively suppressed and emphasizing the need for more precise definitions.

Contribution

It reviews open questions about large transverse momentum divergences in TMDs and presents recent findings on violations of integral relations not being perturbatively suppressed.

Findings

Violations of integral relations are not perturbatively suppressed.

Ultraviolet divergences affect the definitions of transverse moments.

More precise correlation function definitions are needed.

Abstract

I review some open questions relating to the large transverse momentum divergences in transverse moments of transverse momentum dependent (TMD) parton correlation func- tions. I also explain, in an abbreviated and summarized form, recent work that shows that the resulting violations of a commonly used integral relation are not perturbatively suppressed. I argue that this implies a need for more precise definitions for the correlation functions used to describe transverse moments.