TMD Soft Function from Large-Momentum Effective Theory

TL;DR

This paper explores Euclidean formulations of the TMD soft function in QCD, relating it to form factors and wave functions, enabling nonperturbative calculations for processes like SIDIS and Drell-Yan.

Contribution

It introduces a novel Euclidean approach to compute the TMD soft function using large-momentum effective theory, linking it to form factors and wave functions.

Findings

Relates TMD soft function to form factors of nearly-lightlike color sources.

Shows how to extract TMD soft function from meson form factors and wave functions.

Provides a framework for nonperturbative calculations of TMD quantities.

Abstract

We study Euclidean formulations of the transverse-momentum-dependent (TMD) soft function, which is a cross section for soft gluon radiations involving color charges moving in two conjugate lightcone directions in quantum chromodynamics. We show it is related to a special form factor of a pair of color sources traveling with nearly-lightlike velocities, which can be matched to TMD physical observables in semi-inclusive deep-inelastic scattering and Drell-Yan process in the framework of large momentum effective theory. It can also be extracted by combining a large-momentum form factor of light meson and its leading TMD wave function. These formulations are useful for initiating nonperturbative calculations of this useful quantity.