Pion mass dependence of the HVP contribution to muon $g-2$

TL;DR

This paper examines the challenges of accurately extrapolating lattice QCD results for the hadronic vacuum polarization contribution to muon g-2 from unphysical pion masses, highlighting potential systematic errors exceeding 1%.

Contribution

It provides a detailed analysis using two-loop chiral perturbation theory showing the limitations of current extrapolation methods for pion masses between 220 and 440 MeV.

Findings

Extrapolation errors may exceed 1% at physical pion mass.

Two-loop chiral perturbation theory indicates current methods are insufficient.

Proposed tricks do not significantly improve extrapolation accuracy.

Abstract

One of the systematic errors in some of the current lattice computations of the HVP contribution to the muon anomalous magnetic moment $g-2$ is that associated with the extrapolation to the physical pion mass. We investigate this extrapolation assuming lattice pion masses in the range of 220 to 440 MeV with the help of two-loop chiral perturbation theory, and find that such an extrapolation is unlikely to lead to control of this systematic error at the 1% level. This remains true even if various proposed tricks to improve the chiral extrapolation are taken into account.