  All lattice-QCD calculations of the hadronic-vacuum-polarization contribution
to the muon's anomalous magnetic moment to-date have been performed with
degenerate up- and down-quark masses. Here we calculate directly the
strong-isospin-breaking correction to $a_\mu^{\rm HVP}$ for the first time with
physical values of $m_u$ and $m_d$ and dynamical $u$, $d$, $s$, and $c$ quarks,
thereby removing this important source of systematic uncertainty. We obtain a
relative shift to be applied to lattice-QCD results obtained with degenerate
light-quark masses of $\delta a_\mu^{{\rm HVP,} m_u \neq m_d}$= +1.5(7)%, in
agreement with estimates from phenomenology and a recent lattice-QCD
calculation with unphysically heavy pions.

High Energy Physics - Lattice;High Energy Physics - Phenomenology