Lattice QCD Calculation of $x$-dependent Meson Distribution Amplitudes at Physical Pion Mass with Threshold Logarithm Resummation

TL;DR

This paper reports a lattice QCD calculation of the pion and kaon distribution amplitudes at physical pion mass, incorporating threshold logarithm resummation to improve the perturbative matching and extend the reliable x-range.

Contribution

It introduces a novel lattice QCD approach with threshold logarithm resummation for calculating x-dependent meson distribution amplitudes at physical pion mass.

Findings

Kaon distribution amplitude is slightly skewed and narrower than pion's.

The calculation reliably covers x in [0.25, 0.75] for pion and [0.2, 0.8] for kaon.

Systematic errors are controlled within the specified x-range.

Abstract

We present a lattice quantum chromodynamics (QCD) calculation of the $x$-dependent pion and kaon distribution amplitudes (DA) in the framework of large momentum effective theory. This calculation is performed on a fine lattice of $a=0.076$ fm at physical pion mass, with the pion boosted to $1.8$ GeV and kaon boosted to $2.3$ GeV. We renormalize the matrix elements in the hybrid scheme and match to $\overline{\rm MS }$ with a subtraction of the leading renormalon in the Wilson-line mass. The perturbative matching is improved by resumming the large logarithms related to the small quark and gluon momenta in the soft-gluon limit. After resummation, we demonstrate that we are able to calculate a range of $x\in[x_0,1-x_0]$ with $x_0=0.25$ for pion and $x_0=0.2$ for kaon with theoretical systematic errors under control. The kaon DA is shown to be slighted skewed, and narrower than pion DA. Although the $x$-dependence cannot be direct calculated beyond these ranges, we estimate higher moments of the pion and kaon DAs by complementing our calculation with short-distance factorization.