Quasi parton distributions of pions at large longitudinal momentum

TL;DR

This paper develops a method using the functional renormalization group to calculate quasi-parton distributions of pions at high momentum, aligning with lattice QCD and Dyson-Schwinger results, advancing first-principles QCD studies.

Contribution

It introduces a novel fRG-based approach to compute pion quasi-PDA and quasi-PDF at large momentum, including a new contour deformation technique for accurate integrals.

Findings

Quasi-PDA extrapolated from large momentum agrees with lattice QCD.

The method accurately captures the complex structure of quasi-PDA.

Demonstrates the feasibility of fRG for first-principles QCD calculations.

Abstract

In this paper, we develop an approach to calculate the valence-quark quasi parton distribution amplitude (quasi-PDA) and quasi parton distribution function (quasi-PDF) for the pion with a large longitudinal momentum with the functional renormalization group (fRG). This is demonstrated in a low energy effective theory (LEFT) with four-quark scatterings. In the study of the complex structure of quasi-PDA, we introduce a deformed integration contour in the calculations of quasi-PDA or quasi-PDF, which allows us to obtain correct integrals for all momentum fractions. It is found that the pion light-front PDA extrapolated from quasi-PDA based on the large momentum effective theory (LaMET) in the LEFT is comparable with lattice QCD and Dyson-Schwinger equation. This work paves the way to study the PDA and PDF within the fRG approach to first-principles QCD.