Isospin splittings of meson and baryon masses from three-flavor lattice QCD + QED

TL;DR

This paper extends lattice QCD simulations to include QED effects, providing precise calculations of isospin splittings in mesons and baryons, including nucleon mass differences and pion mass splitting, with a novel separation of strong and electromagnetic contributions.

Contribution

It introduces a systematic approach to incorporate QED into lattice QCD for isospin splitting analysis, offering first results on electromagnetic effects and separation in the $ar{MS}$ scheme.

Findings

Nucleon mass difference of 1.35(18)(8) MeV

Electromagnetic pion splitting of 4.60(20) MeV

First separation of strong and electromagnetic contributions in $ar{MS}$ scheme

Abstract

Lattice QCD simulations are now reaching a precision where isospin breaking effects become important. Previously, we have developed a program to systematically investigate the pattern of flavor symmetry beaking within QCD and successfully applied it to meson and baryon masses involving up, down and strange quarks. In this Letter we extend the calculations to QCD + QED and present our first results on isospin splittings in the pseudoscalar meson and baryon octets. In particular, we obtain the nucleon mass difference of $M_n-M_p=1.35(18)(8)\,\mbox{MeV}$ and the electromagnetic contribution to the pion splitting $M_{\pi^+}-M_{\pi^0}=4.60(20)\,\mbox{MeV}$. Further we report first determination of the separation between strong and electromagnetic contributions in the $\bar{MS}$ scheme.