Isospin-breaking corrections to the muon magnetic anomaly in Lattice QCD

Abstract

In this contribution we present a lattice calculation of the leading-order electromagnetic and strong isospin-breaking (IB) corrections to the quark-connected hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon. The results are obtained adopting the RM123 approach in the quenched-QED approximation and using the QCD gauge configurations generated by the ETM Collaboration with $N_f=2+1+1$ dynamical quarks, at three values of the lattice spacing ($a\simeq 0.062,0.082,0.089$ fm), at several lattice volumes and with pion masses between $\simeq 210$ and $\simeq 450$ MeV. 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 $\hat{I}´a_{\hat{I}}{¼}^{\mathrm{HVP}}(ud)=7.1(2.5)\cdot 10^{-10}$, $\hat{I}´a_{\hat{I}}{¼}^{\mathrm{HVP}}(s)=-0.0053(33)\cdot 10^{-10}$ and $\hat{I}´a_{\hat{I}}{¼}^{\mathrm{HVP}}(c)=0.0182(36)\cdot 10^{-10}$. At leading order in $\hat{I}{\pm }_{em}$ and $(m_d-m_u)/\hat{I}{›}_{QCD}$ we obtain $\hat{I}´a_{\hat{I}}{¼}^{\mathrm{HVP}}(udsc)=7.1(2.9)\cdot 10^{-10}$, which is currently the most accurate determination of the IB corrections to $a_{\hat{I}}{¼}^{\mathrm{HVP}}$.

Invited talk at the 9th International Workshop on Chiral Dynamics (CD18), Durham, North Carolina (USA), 17-21 September 2018. 11 pages, 4 figures