Partonic quasi-distributions of the pion in chiral quark models

TL;DR

This paper non-perturbatively evaluates the pion's quark quasi-distribution amplitude using chiral quark models, providing explicit analytic expressions and comparing evolved results with lattice data.

Contribution

It introduces a non-perturbative method to compute pion quasi-distributions within chiral quark models, including explicit analytic formulas and QCD evolution to lattice scales.

Findings

Derived simple analytic expressions for pion quasi-distributions.

Successfully evolved model results to lattice scales and compared with LaMET data.

Demonstrated the dependence of distributions on longitudinal momentum and transverse momentum.

Abstract

The evaluation of partonic distributions presents a challenge for QCD, and in particular for its Euclidean lattice realization. Recently, objects called quasi-distributions (which become standard distributions in a limit of the longitudinal momentum of the target hadron going to infinity) have been proposed. We present a non-perturbative, dynamical evaluation of the quark quasi-distribution amplitude (QDA) of the pion in the framework of chiral quark models (the Nambu--Jona-Lasinio model and the spectral quark model). We arrive at simple but nontrivial analytic expressions, where the dependence on the longitudinal momentum, the momentum fraction, or the transverse-momentum (for the unintegrated objects) can be explicitly assessed. For the parton distribution amplitude (PDA), we carry out the necessary QCD evolution from the constituent quark model scale to higher scales accessible on the lattice, and compare favorably to the LaMET data.