Lattice-QCD Calculations of TMD Soft Function Through Large-Momentum Effective Theory

TL;DR

This paper uses lattice QCD and large-momentum effective theory to compute the TMD soft function, including its rapidity-independent and dependent parts, crucial for understanding small transverse momentum processes in QCD.

Contribution

It presents the first lattice QCD calculation of the TMD soft function using large-momentum effective theory, including the extraction of the Collins-Soper evolution kernel.

Findings

Successful extraction of the rapidity-independent soft function component.

Determination of the Collins-Soper evolution kernel from lattice data.

Validation of large-momentum effective theory methods for TMD studies.

Abstract

The transverse-momentum-dependent (TMD) soft function is a key ingredient in QCD factorization of Drell-Yan and other processes with relatively small transverse momentum. We present a lattice QCD study of this function at moderately large rapidity on a 2+1 flavor CLS dynamic ensemble with $a=0.098$ fm. We extract the rapidity-independent (or intrinsic) part of the soft function through a large-momentum-transfer pseudo-scalar meson form factor and its quasi-TMD wave function using leading-order factorization in large-momentum effective theory. We also investigate the rapidity-dependent part of the soft function---the Collins-Soper evolution kernel---based on the large-momentum evolution of the quasi-TMD wave function.