Nonperturbative Evolution of Parton Quasi-Distributions

TL;DR

This paper establishes a formal connection between TMDs and quasi-distributions using VDFs, revealing strong nonperturbative evolution of PQDs at moderate Pz, which offers new insights into 3D hadron structure via lattice QCD.

Contribution

It introduces a VDF-based formalism linking TMDs and quasi-distributions, enabling analysis of nonperturbative evolution of PQDs in lattice QCD studies.

Findings

Strong nonperturbative evolution of PQDs at moderate Pz

Models show Pz dependence reflecting TMD transverse momentum effects

Provides a new perspective for 3D hadron structure investigation

Abstract

Using our formalism of parton virtuality distribution functions (VDFs) we establish a connection between the transverse momentum dependent distributions (TMDs) ${\cal F} (x, k_\perp^2)$ and quasi-distributions $Q(y,P_z)$ introduced recently by X. Ji for lattice QCD extraction of parton distributions $f(x)$. We build models for PQDs from the VDF-based models for soft TMDs, and analyze the $P_z$ dependence of the resulting PQDs. We observe a strong nonperturbative evolution of PQDs for small and moderately large values of $P_z$ reflecting the transverse momentum dependence of TMDs. Thus, the study of PQDs on the lattice in the domain of strong nonperturbative effects opens a new perspective for investigation of the 3-dimensional hadron structure.