Gauge links, TMD-factorization, and TMD-factorization breaking

TL;DR

This paper analyzes transverse momentum dependent (TMD) parton distributions and the gauge-link structures mandated by factorization. It explains how Wilson lines, rapidity regularization, and soft factors shape TMD definitions and their evolution, highlighting Collins-Soper-Sterman (CSS) formalism. A central finding is that TMD-factorization can break in hadroproduction due to complex color flow and nonuniversal gauge-link structures, with Ward-identity arguments failing in certain scenarios. The authors emphasize the need for experimental tests to distinguish factorization from factorization-breaking dynamics and outline ongoing theoretical work on TMD evolution and universality.

Abstract

In this section, we discuss some basic features of transverse momentum dependent, or unintegrated, parton distribution functions. In particular, when these correlation functions are combined in a factorization formulae with hard processes beyond the simplest cases, there are basic problems with universality and factorization. We discuss some of these problems as well as the opportunities that they offer.

Figures (6)

• Figure 1: (a) Target-collinear gluons in a graph for SIDIS. (b) Factorization of extra gluons into gauge link contributions.
• Figure 2: (a) Simple light-like gauge link structure in integrated the PDF. (b) First try at a gauge link structure for the TMD PDF. In both of these diagrams, the thick red arrows represent the main light-like legs of the gauge link. In (b), the then dotted link at connecting the main legs at light-cone minus infinity points in the transverse direction, which is perpendicular to the page.
• Figure 3: Gauge link structure for the TMD PDF tilted away from the exactly light-like direction.
• Figure 4: A single collinear gluon attachment (a) after the hard scattering in SIDIS and (b) before the hard scattering in DY.
• Figure 5: Graphs with extra collinear gluons attaching at the "wrong" side of the graph for them to be identified with the standard universal gauge link contributions in the lower proton PDF.