Towards leading isospin breaking effects in mesonic masses with $O(a)$ improved Wilson fermions

TL;DR

This paper investigates the leading isospin breaking effects on mesonic masses using $O(a)$ improved Wilson fermions, employing reweighting techniques and perturbative expansion in QCD+QED.

Contribution

It introduces a method to study isospin breaking effects with existing isosymmetric QCD ensembles by combining reweighting and perturbative expansion in QED and quark mass differences.

Findings

Demonstrates the feasibility of calculating isospin breaking effects with improved Wilson fermions.

Employs QED$_{ ext{L}}$ for finite volume electromagnetic effects.

Provides a framework for future precise determinations of mesonic mass splittings.

Abstract

We present an exploratory study of leading isospin breaking effects in mesonic masses using $O(a)$ improved Wilson fermions. Isospin symmetry is explicitly broken by distinct masses and electric charges of the up and down quarks. In order to be able to make use of existing isosymmetric QCD gauge ensembles we apply reweighting techniques. The path integral describing QCD+QED is expanded perturbatively in powers of the light quarks' mass deviations and the electromagnetic coupling. We employ QED$_{\mathrm{L}}$ as a finite volume formulation of QED.