The Muon Anomalous Magnetic Moment and the Pion Polarizability

TL;DR

This paper calculates the pion loop contribution to the muon g-2, incorporating pion polarizability effects, and finds it increases the discrepancy between experimental and theoretical values, highlighting the importance of precise polarizability measurements.

Contribution

It introduces two models consistent with chiral symmetry and QCD to evaluate pion polarizability effects on muon g-2, enhancing the understanding of theoretical uncertainties.

Findings

The contribution increases the muon g-2 discrepancy by up to 60×10^{-11}.

Planned measurements will reduce parametric uncertainties.

Model uncertainties remain significant for future precision tests.

Abstract

We compute the charged pion loop contribution to the muon anomalous magnetic moment $a_\mu$, taking into account the effect of the charged pion polarizability, $(\alpha_1-\beta_1)_{\pi^+}$. We evaluate this contribution using two different models that are consistent with the requirements of chiral symmetry in the low-momentum regime and perturbative quantum chromodynamics in the asymptotic region. The result increases the disagreement between the present experimental value for $a_\mu$ and the theoretical, Standard Model prediction by as much as $\sim 60\times 10^{-11}$, depending on the value of $(\alpha_1-\beta_1)_{\pi^+}$ and the choice of the model. The planned determination of $(\alpha_1-\beta_1)_{\pi^+}$ at Jefferson Laboratory will eliminate the dominant parametric error, leaving a theoretical model uncertainty commensurate with the error expected from planned Fermilab measurement of $a_\mu$.