Soft Factor Subtraction and Transverse Momentum Dependent Parton Distributions on Lattice

TL;DR

This paper introduces a method to compute transverse momentum dependent parton distributions on the lattice using a soft factor subtraction within the quasi-distribution framework, enabling insights into nucleon structure.

Contribution

It demonstrates the necessity of soft factor subtraction for lattice-calculable TMDs and extends the quasi-distribution approach to TMDs, GPDs, and Wigner distributions.

Findings

Soft factor subtraction is essential for lattice TMD calculations.

Quasi-TMDs can be applied to processes like Drell-Yan.

Framework enables lattice-based nucleon tomography.

Abstract

We study the transverse momentum dependent (TMD) parton distributions in the newly proposed quasi-parton distribution function framework in Euclidean space. A soft factor subtraction is found to be essential to make the TMDs calculable on lattice. We show that the quasi-TMDs with the associated soft factor subtraction can be applied in hard QCD scattering processes such as Drell-Yan lepton pair production in hadronic collisions. This allows future lattice calculations to provide information on the non-perturbative inputs and energy evolutions for the TMDs. Extension to the generalized parton distributions and quantum phase space Wigner distributions will lead to a complete nucleon tomography on lattice.