QED effects in the pseudoscalar meson sector

TL;DR

This paper reports on lattice QCD+QED simulations to analyze isospin symmetry violations in pseudoscalar meson masses, detailing techniques and the impact of different renormalization schemes on electromagnetic self-energies.

Contribution

It provides a detailed methodology for separating QCD and QED contributions to isospin breaking in meson masses, including a proposed renormalization scheme respecting Dashen's theorem.

Findings

Quantified $C6^+$-$C6^0$ mass splitting due to QED and QCD effects.

Analyzed the scheme dependence of electromagnetic self-energies.

Discussed the implications of different renormalization schemes on isospin violation.

Abstract

We present results on the pseudoscalar meson masses from a fully dynamical simulation of QCD+QED. We concentrate particularly on violations of isospin symmetry. We calculate the $\pi^+$-$\pi^0$ splitting and also look at other isospin violating mass differences. We have presented results for these isospin splittings in arXiv:1508.06401 [hep-lat]. In this paper we give more details of the techniques employed, discussing in particular the question of how much of the symmetry violation is due to QCD, arising from the different masses of the $u$ and $d$ quarks, and how much is due to QED, arising from the different charges of the quarks. This decomposition is not unique, it depends on the renormalisation scheme and scale. We suggest a renormalisation scheme in which Dashen's theorem for neutral mesons holds, so that the electromagnetic self-energies of the neutral mesons are zero, and discuss how the self-energies change when we transform to a scheme such as $\bar{MS}$, in which Dashen's theorem for neutral mesons is violated.