Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass

TL;DR

This paper presents a novel lattice QCD calculation of the pion distribution amplitude at physical pion mass, incorporating threshold resummation and comparing results from different fermion discretizations, providing new insights into pion structure.

Contribution

It introduces the first inclusion of threshold resummation in lattice QCD calculation of the pion DA and compares results from domain-wall and staggered fermions at physical masses.

Findings

Resummed results show controlled uncertainties within x∈[0.25,0.75] at high pion momentum.

The DA from chiral fermions is flatter and lower near x=0.5 compared to staggered fermions.

First lattice QCD calculation of the pion DA with threshold resummation at physical pion mass.

Abstract

We present a direct lattice QCD calculation of the $x$-dependence of the pion distribution amplitude (DA), which is performed using the quasi-DA in large momentum effective theory on a domain-wall fermion ensemble at physical quark masses and spacing $a\approx 0.084$ fm. The bare quais-DA matrix elements are renormalized in the hybrid scheme and matched to $\overline{\rm MS}$ with a subtraction of the leading renormalon in the Wilson-line mass. For the first time, we include threshold resummation in the perturbative matching onto the light-cone DA, which resums the large logarithms in the soft gluon limit at next-to-next-to-leading log. The resummed results show controlled scale-variation uncertainty within the range of momentum fraction $x\in[0.25,0.75]$ at the largest pion momentum $P_z\approx 1.85$~GeV. In addition, we apply the same analysis to quasi-DAs from a highly-improved-staggered-quark ensemble at physical pion mass and $a=0.076$ fm. By comparison we find with $2\sigma$ confidence level that the DA obtained from chiral fermions is flatter and lower near $x=0.5$.