The Strong Isospin-Breaking Correction to the Leading-Order Hadronic Vacuum Polarisation Contribution to the Anomalous Magnetic Moment of the Muon

The contribution of strong isospin-breaking (SIB) effects to the value of the anomalous magnetic moment of the muon is studied using the leading-order SIB component of the photon vacuum polarisation function, calculated in Chiral Perturbation Theory (ChPT) in the low Euclidean momentum-squared regime. At two-loop order in ChPT the result is found to be aSIB= 0.82(12)1010, approximately 1 order of magnitude less than recent determinations using Lattice Quantum Chromodynamics (QCD) and also phenomenology. It is shown that the inclusion of a tree-level term from next-to-next-to-next-to leading order (NNNLO) raises the ChPT prediction to aSIB= 3.61(98)1010. This result is consistent with the most precise result from Lattice QCD. The dominant NNNLO contribution is interpreted as parameterising the SIB physics of the lightest resonances which are predicted to be the most significant processes at low momentum.