Electromagnetic and strong isospin breaking in light meson masses

TL;DR

This paper investigates electromagnetic and strong isospin breaking effects on light meson mass splittings using a coupled Dyson-Schwinger and Bethe-Salpeter framework, revealing complex interactions and non-linear contributions.

Contribution

It introduces a comprehensive approach combining gluon, pion, and photon exchanges to analyze isospin breaking in mesons, highlighting non-linear effects from different sources.

Findings

Different patterns of mass splittings for pion, kaon, and rho mesons.

Evidence that quark mass and charge effects do not sum linearly.

Quantitative insights into electromagnetic and strong isospin breaking contributions.

Abstract

We study electromagnetic as well as strong isospin breaking effects in the isospin mass splittings of light pseudoscalar and vector mesons. To this end we employ a coupled system of quark Dyson-Schwinger and meson Bethe-Salpeter equations whose interaction kernels contain gluon, pion and photon exchange interactions. In bound states, QCD-induced isospin breaking is manifest on different levels. On the one hand, a different explicit up- and down-quark mass directly affects the propagators of the constituent quarks. On the other hand, it leads to different interaction kernels within the isospin multiplets. In addition, electromagnetic isospin breaking is induced via a photon exchange diagram. Using the kaon iso-doublet and the charged pion masses as input to determine the up, down and strange quark masses we find for the pion, kaon and rho meson mass splittings different patterns each. In particular, our results provide evidence that the effects from two sources of mass splittings, the different quark masses and the different quark charges, do not add up linearly.