# Electromagnetic and strong isospin-breaking corrections to the muon $g - 2$ from Lattice QCD+QED

## TL;DR

This paper presents a lattice QCD calculation of electromagnetic and isospin-breaking corrections to the muon g-2, providing the most accurate estimate to date of these effects on the hadronic vacuum polarization contribution.

## Contribution

The study introduces a precise lattice QCD+QED computation of isospin-breaking corrections to muon g-2, using the RM123 approach with quenched QED and multiple lattice configurations.

## Key findings

- Calculated corrections for light, strange, and charm quarks with uncertainties.
- Provided the most accurate estimate of isospin-breaking effects on muon g-2.
- Results support refined theoretical predictions for muon anomalous magnetic moment.

## Abstract

We present a lattice calculation of the leading-order electromagnetic and strong isospin-breaking corrections to the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses between $\simeq 210$ and $\simeq 450$ MeV. The results are obtained adopting the RM123 approach in the quenched-QED approximation, which neglects the charges of the sea quarks. Quark disconnected diagrams are not included. After the extrapolations to the physical pion mass and to the continuum and infinite-volume limits the contributions of the light, strange and charm quarks are respectively equal to $\delta a_\mu^{\rm HVP}(ud) = 7.1 ~ (2.5) \cdot 10^{-10}$, $\delta a_\mu^{\rm HVP}(s) = -0.0053 ~ (33) \cdot 10^{-10}$ and $\delta a_\mu^{\rm HVP}(c) = 0.0182 ~ (36) \cdot 10^{-10}$. At leading order in $\alpha_{em}$ and $(m_d - m_u) / \Lambda_{QCD}$ we obtain $\delta a_\mu^{\rm HVP}(udsc) = 7.1 ~ (2.9) \cdot 10^{-10}$, which is currently the most accurate determination of the isospin-breaking corrections to $a_\mu^{\rm HVP}$.