Chiral extrapolation of hadronic vacuum polarization

Abstract

We study the pion-mass dependence of the two-pion channel in the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon $a_{\hat{I}}{¼}^{\text{HVP}}$, by using an Omnès representation for the pion vector form factor with the phase shift derived from the inverse-amplitude method (IAM). Our results constrain the dominant isospin-$1$ part of the isospin-symmetric light-quark contribution, and should thus allow one to better control the chiral extrapolation of $a_{\hat{I}}{¼}^{\text{HVP}}$, required for lattice-QCD calculations performed at larger-than-physical pion masses. In particular, the comparison of the one- and two-loop IAM allows us to estimate the associated systematic uncertainties and show that these are under good control.

9 pages, 4 figures; journal version; Mathematica implementation included as supplemental material