Pion distribution amplitude from lattice-QCD

TL;DR

This paper introduces a method to accurately approximate the pion's valence-quark distribution amplitude from limited lattice QCD data, revealing its broad shape persists at high energies and challenging previous asymptotic assumptions.

Contribution

A novel approach to derive the pion's PDA from limited lattice QCD moments, aligning with Dyson-Schwinger predictions and highlighting the importance of nonperturbative effects.

Findings

PDA remains broad at energies above 100 GeV.

Asymptotic distribution is a poor approximation at accessible energies.

Method provides a pointwise accurate PDA consistent with nonperturbative QCD.

Abstract

A method is explained through which a pointwise accurate approximation to the pion's valence-quark distribution amplitude (PDA) may be obtained from a limited number of moments. In connection with the single nontrivial moment accessible in contemporary simulations of lattice-regularised quantum chromodynamics (QCD), the method yields a PDA that is a broad concave function whose pointwise form agrees with that predicted by Dyson-Schwinger equation analyses of the pion. Under leading-order evolution, the PDA remains broad to energy scales in excess of 100 GeV, a feature which signals persistence of the influence of dynamical chiral symmetry breaking. Consequently, the asymptotic distribution, \phi_\pi^asy(x), is a poor approximation to the pion's PDA at all such scales that are either currently accessible or foreseeable in experiments on pion elastic and transition form factors. Thus, related expectations based on \phi_\pi^asy(x) should be revised.