The distribution amplitude of the $\eta_c$-meson at leading twist from Lattice QCD

TL;DR

This paper presents the first lattice QCD calculation of the $ ext{η}_c$-meson distribution amplitude at leading twist, providing a relativistic, non-perturbative insight into its structure and comparing it with other theoretical approaches.

Contribution

It introduces a novel lattice QCD method to compute the $ ext{η}_c$-meson distribution amplitude at leading twist, addressing systematic uncertainties and connecting Euclidean lattice results to Minkowski space.

Findings

Significant deviations from Dyson-Schwinger results at small Ioffe times.

First relativistic lattice determination of the $ ext{η}_c$ distribution amplitude.

Comparison with non-relativistic QCD highlights differences in meson structure.

Abstract

Distribution amplitudes are functions of non-perturbative matrix elements describing the hadronization of quarks and gluons. Thanks to factorization theorems, they can be used to compute the scattering amplitude of high-energy processes. Recently, new ideas have allowed their computation using lattice QCD, which should provide us with a general, fully relativistic determination. We present the first lattice calculation of the $\eta_c$-meson distribution amplitude at leading twist. Starting from the relevant matrix element in discrete Euclidean space on a set of $N_f=2$ CLS ensembles, we explain the method to connect to continuum Minkowski spacetime. After addressing several sources of systematic uncertainty, we compare to Dyson-Schwinger and non-relativistic QCD determinations of this quantity. We find significant deviations between the latter and our result even at small Ioffe times.