# Pion form factor and low-energy hadronic contribution to muon $g-2$ by analytic extrapolation: consistency and sensitivity tests

## TL;DR

This paper assesses the accuracy and sensitivity of an analytic continuation method for determining the low-energy hadronic contribution to muon g-2, comparing it with experimental and lattice QCD data.

## Contribution

It introduces a consistency and sensitivity analysis of a model-independent analytic extrapolation technique for the pion form factor in muon g-2 calculations.

## Key findings

- The analytic continuation results agree with experimental and lattice data within uncertainties.
- Sensitivity to input data is significant when extending the energy range up to 0.76 GeV.
- The method provides a reliable cross-check for low-energy hadronic contributions.

## Abstract

The largest error in the theoretical determination of the muon anomalous magnetic moment is due to the low-energy hadronic vacuum polarization, which cannot be calculated by perturbative QCD and requires nonperturbative techniques. Recently, an accurate determination of the low-energy two-pion contribution to muon $g-2$ has been obtained by a parametrization-free analytic continuation of the pion vector form factor from other kinematical regions. In this work we compare the results of the analytic continuation with direct determinations at low momenta from experiment and lattice QCD. We also explore the sensitivity of the method to the timelike data on the modulus of the form factor used as input, by extending the input region to energies up to 0.76 GeV.