Strong-isospin-breaking correction to the muon anomalous magnetic moment from lattice QCD at the physical point

Abstract

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(4)\%, in agreement with estimates from phenomenology and a recent lattice-QCD calculation with unphysically heavy pions.