Transverse-Momentum-Dependent Parton Distribution Functions from Large-Momentum Effective Theory

TL;DR

This paper demonstrates how to extract transverse-momentum-dependent parton distribution functions (TMDPDFs) from Euclidean QCD calculations using large-momentum effective theory (LaMET), enabling non-perturbative studies relevant for high-energy scattering.

Contribution

It introduces a LaMET-based factorization framework for calculating TMDPDFs from lattice QCD, including perturbative matching and renormalization group properties.

Findings

Derived LaMET factorization for quasi-TMDPDFs

Established perturbative matching coefficients with RG evolution

Discussed lattice implementation with finite-length gauge links

Abstract

We show that transverse-momentum-dependent parton distribution functions (TMDPDFs), important non-perturbative quantities for describing the properties of hadrons in high-energy scattering processes such as Drell-Yan and semi-inclusive deep-inelastic scattering with observed small transverse momentum, can be obtained from Euclidean QCD calculations in the framework of large-momentum effective theory (LaMET). We present a LaMET factorization of the Euclidean quasi-TMDPDFs in terms of the physical TMDPDFs and off-light-cone soft function at leading order in $1/P^z$ expansion, with the perturbative matching coefficient satisfying a renormalization group equation. We also discuss the implementation in lattice QCD with finite-length gauge links as well as the rapidity-regularization-independent factorization for Drell-Yan cross section.