A ChPT estimate of the strong-isospin-breaking contribution to the anomalous magnetic moment of the muon

TL;DR

This paper estimates the strong isospin-breaking contribution to the muon's anomalous magnetic moment using chiral perturbation theory, providing a key correction for precise Standard Model predictions.

Contribution

It offers the first continuum estimate of the strong isospin-breaking effect on the muon g-2 using $SU(3)$ chiral perturbation theory and resonance-region contributions.

Findings

The strong isospin-breaking contribution is dominated by resonance-region effects.

The result is linked to a low-energy constant from flavor-breaking hadronic tau decay sum rules.

Implications for lattice QCD calculations of $a_rac{SIB}$ are discussed.

Abstract

First-principles lattice determinations of the Standard Model expectation for the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon have become sufficiently precise that further improvement requires including strong and electromagnetic isospin-breaking effects. We provide a continuum estimate of the strong isospin-breaking contribution, $a_\mu^{SIB}$, using $SU(3)$ chiral perturbation theory. The result is shown to be dominated by resonance-region contributions encoded in a single low-energy constant whose value is known from flavor-breaking hadronic $\tau$ decay sum rules. Implications of the form of the result for lattice determinations of $a_\mu^{SIB}$ are also discussed.