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

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