Calculation of the Hadronic Vacuum Polarization Contribution to the Muon Anomalous Magnetic Moment.

We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is a_{µ}^{HVP LO}=715.4(18.7)×10^{-10}. By supplementing lattice data for very short and long distances with R-ratio data, we significantly improve the precision to a_{µ}^{HVP LO}=692.5(2.7)×10^{-10}. This is the currently most precise determination of a_{µ}^{HVP LO}.