Generalized universality of higher transverse moments of quark transverse momentum dependent correlators

TL;DR

This paper demonstrates the universality of higher transverse moments of quark TMD correlators, showing how process dependence can be factored into universal distributions and gluonic pole factors across different target spins.

Contribution

It introduces a generalized framework for universal TMD correlators and their transverse moments, including specific results for double weighting and various target spins.

Findings

Universal TMD correlators can be parametrized in universal distribution functions.

Process dependence is contained in gluonic pole factors determined by gauge links.

Results are generalized for any rank of TMD correlators and different target spins.

Abstract

The color gauge-invariant transverse momentum dependent (TMD) quark correlators contain process dependent gauge links in the bilocal matrix elements. In this paper, we split these process dependent correlators into universal TMD correlators, which in turn can be parametrized in universal TMD distribution functions. The process dependence is contained in gluonic pole factors, of which the value is determined by the gauge link. The operator structures of the universal TMD correlators are identified using transverse moments. In this paper, specific results for double transverse weighting of quark TMDs are given. In particular, we show that for a spin 1/2 target one has three universal time-reversal even leading `pretzelocity distributions', two of which involve double gluonic pole matrix elements and come with process dependent gluonic pole factors. We generalize the results for single and double weighting to TMD correlators of any specific rank, illustrating it for unpolarized, spin 1/2 and spin 1 targets.