Lattice QCD Study of Transverse-Momentum Dependent Soft Function

TL;DR

This paper presents a lattice QCD calculation of the soft function relevant for small transverse momentum processes, using large momentum effective theory and nonperturbative techniques, providing insights into TMD factorization.

Contribution

The study introduces a first-principles lattice QCD computation of the intrinsic soft function and Collins-Soper kernel within the large momentum effective theory framework.

Findings

Soft function consistent with one-loop perturbative results at high momentum

Nonperturbative soft function determined after renormalization and higher-twist removal

Collins-Soper kernel calculated from quasi-TMD wave functions

Abstract

In this work, we perform a lattice QCD study of the intrinsic, rapidity-independent soft function within the framework of large momentum effective theory. The computation is carried out using a gauge ensemble of $N_f=2+1+1$ clover-improved twisted mass fermion. After applying an appropriate renormalization procedure and the removal of significant higher-twist contamination, we obtain the intrinsic soft function that is comparable to the one-loop perturbative result at large external momentum. The determination of the nonperturbative soft function from first principles is crucial to sharpen our understanding of the processes with small transverse momentum such as the Drell-Yan production and the semi-inclusive deep inelastic scattering. Additionally, we calculate the Collins-Soper evolution kernel using the quasi-transverse-momentum-dependent wave function as input.