Chiral extrapolation of hadronic vacuum polarization

TL;DR

This paper investigates how the pion mass affects the two-pion contribution to the muon's anomalous magnetic moment, using a theoretical model to improve the chiral extrapolation relevant for lattice QCD calculations.

Contribution

It introduces a method using the Omnès representation and inverse-amplitude method to better understand pion-mass dependence in HVP contributions, aiding lattice QCD extrapolations.

Findings

The phase shift derived from IAM constrains the isospin-1 contribution.

Comparison of one- and two-loop IAM estimates systematic uncertainties.

Results help control chiral extrapolation in lattice QCD calculations.

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 $a_\mu^\text{HVP}$, by using an Omn\`es 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 $a_\mu^\text{HVP}$, 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.