Distribution amplitudes of radially-excited pi- and K-mesons

TL;DR

This paper computes the leading-twist parton distribution amplitudes for radially-excited pi- and K-mesons using a symmetry-preserving approach, revealing how dynamical chiral symmetry breaking influences their structure and decay constants.

Contribution

It introduces a novel calculation of PDAs for radially-excited pseudoscalar mesons, demonstrating the effects of dynamical chiral symmetry breaking on their properties.

Findings

PDAs are dilated compared to conformal-limit forms.

PDAs are skewed toward the heavier valence-quark in asymmetric systems.

PDAs of radially-excited pseudoscalars are not positive definite.

Abstract

A symmetry-preserving truncation of the two-body bound-state problem in relativistic quantum field theory is used to compute the leading-twist parton distribution amplitudes (PDAs) for the first radial excitations of the $\pi$- and $K$-mesons. In common with ground states in these channels, the PDAs are found to be dilated with respect to the relevant conformal-limit form and skewed toward the heavier valence-quark in asymmetric systems. In addition, the PDAs of radially-excited pseudoscalar mesons are not positive definite, owing to the fact that dynamical chiral symmetry breaking (DCSB) forces the leptonic decay constant of such states to vanish in the chiral limit. These results highlight that DCSB is expressed visibly in every pseudoscalar meson constituted from light-quarks. Hence, so long as its impact is empirically evident in the pseudoscalar members of a given spectrum level, it is unlikely that chiral symmetry is restored in any of the hadrons that populate this level.