Moments of pseudoscalar meson distribution amplitudes from the lattice

TL;DR

This paper presents lattice QCD calculations of the first two moments of pseudoscalar meson distribution amplitudes, providing key nonperturbative inputs for understanding meson structure and decay processes.

Contribution

It offers the first lattice-based determinations of these moments at physical quark masses, including nonperturbative renormalisation in the MSbar scheme.

Findings

Second moment of pion distribution amplitude: a_2^pi=0.201(114)

First and second moments of kaon distribution amplitude: a_1^K=0.0453(9)(29), a_2^K=0.175(18)(47)

Results are obtained at a scale of 4 GeV^2.

Abstract

Based on lattice simulations with two flavours of dynamical, O(a)-improved Wilson fermions we present results for the first two moments of the distribution amplitudes of pseudoscalar mesons at several values of the valence quark masses. By extrapolating our results to the physical masses of up/down and strange quarks, we find the first two moments of the K^+ distribution amplitude and the second moment of the pi^+ distribution amplitude. We use nonperturbatively determined renormalisation coefficients to obtain results in the MSbar scheme. At a scale of 4 GeV^2 we find a_2^pi=0.201(114) for the second Gegenbauer moment of the pion's distribution amplitude, while for the kaon, a_1^K=0.0453(9)(29) and a_2^K=0.175(18)(47).