QED interaction effects on heavy meson masses from lattice QCD+QED

TL;DR

This study calculates QED effects on heavy meson masses using lattice QCD+QED, isolating Coulomb interactions to improve phenomenological models and derive effective meson sizes.

Contribution

It introduces a method to isolate QED interaction terms in heavy mesons and provides new estimates of their effective sizes using lattice QCD+QED simulations.

Findings

QED effects on meson masses are dominated by Coulomb interactions.

Derived effective sizes for $ ext{η}_c$, $J/ψ$, and $D_s$ mesons.

Results can enhance phenomenological models of meson structure.

Abstract

Hadron masses are subject to few MeV corrections arising from QED interactions, almost entirely arising from the electric charge of the valence quarks. The QED effects include both self-energy contributions and interactions between the valence quarks/anti-quarks. By combining results from different signs of the valence quark electric charge we are able to isolate the interaction term which is dominated by the Coulomb piece, $\langle \alpha_{\mathrm{QED}}e_{q_1}e_{\overline{q}_2}/r \rangle$, in the nonrelativistic limit. We study this for $D_s$, $\eta_c$ and $J/\psi$ mesons, working in lattice QCD plus quenched QED. We use gluon field configurations that include up, down, strange and charm quarks in the sea at multiple values of the lattice spacing. Our results, including also values for mesons with quarks heavier than charm, can be used to improve phenomenological models for the QED contributions. The QED interaction term carries information about meson structure; we derive effective sizes $\langle 1/r_{\mathrm{eff}} \rangle^{-1}$ for $\eta_c$, $J/\psi$ and $D_s$ of 0.206(8) fm, 0.321(14) fm and 0.307(31) fm respectively.