# Electromagnetic Splittings and Light Quark Masses in Lattice QCD

## TL;DR

This paper introduces a lattice QCD method to compute electromagnetic effects on hadron masses, providing preliminary results on meson mass splittings and light quark mass ratios.

## Contribution

It presents a novel approach to incorporate electromagnetic fields dynamically in lattice QCD and calculates electromagnetic mass splittings and quark mass ratios.

## Key findings

- π^+-π^0$ splitting of 4.9(3) MeV
- Determined $m_u/m_d$ ratio as 0.512(6)
- Discussed systematic errors in the method

## Abstract

A method for computing electromagnetic properties of hadrons in lattice QCD is described and preliminary numerical results are presented. The electromagnetic field is introduced dynamically, using a noncompact formulation. Employing enhanced electric charges, the dependence of the pseudoscalar meson mass on the (anti)quark charges and masses can be accurately calculated. At $\beta=5.7$ with Wilson action, the $\pi^+-\pi^0$ splitting is found to be $4.9(3)$ MeV. Using the measured $K^0-K^+$ splitting, we also find $m_u/m_d = .512(6)$. Systematic errors are discussed.