Precision Control in Lattice Calculation of $x$-dependent Pion Distribution Amplitude

TL;DR

This paper introduces a refined lattice QCD analysis of the pion distribution amplitude's x-dependence, employing advanced resummation techniques and large momentum expansion to improve accuracy across the entire x-range.

Contribution

It develops a novel combination of renormalon resummation, perturbative matching, and momentum log resummation within a large momentum framework for precise pion distribution amplitude extraction.

Findings

Enhanced x-dependence determination across the full range.

Improved accuracy in the middle and endpoint regions.

Consistent results across multiple lattice spacings.

Abstract

We present a new Bjorken $x$-dependence analysis of a previous lattice quantum chromodynamics data for the pion distribution amplitude from MILC configurations with three lattice spacing $a=0.06,0.09, 0.12$~fm. A leading renormalon resummation in renormalization as well as the perturbative matching kernel in the framework of large momentum expansion generates the power accuracy of the matching to the light-cone amplitude. Meanwhile, a small momentum log resummation is implemented for both the quark momentum $xP_z$ and the antiquark momentum $(1-x)P_z$ inside a meson of boost momentum $P_z$ up to 1.72 GeV along the $z$ direction, allowing us to have more accurate determination of the $x$-dependence in the middle range. Finally, we use the complementarity between the short-distance factorization and the large momentum expansion to constrain the endpoint regions $x\sim 0, 1$, thus obtaining the full-range $x$-dependence of the amplitude.