Hadronic Light-by-Light and the Pion Polarizability

TL;DR

This paper calculates the charged pion loop contribution to light-by-light scattering in chiral perturbation theory, revealing the importance of NLO effects and the impact of pion polarizability on muon g-2 predictions.

Contribution

It introduces the first NLO calculation of the charged pion loop contribution to light-by-light scattering, highlighting the significance of pion polarizability effects.

Findings

NLO contributions are more significant than LO due to numerical suppression of LO terms.

Current models omit pion polarizability, leading to potential inaccuracies in muon g-2 estimates.

Models consistent with QCD low-momentum behavior are necessary for reliable predictions.

Abstract

We compute the charged pion loop contribution to the light-by-light scattering amplitude for off-shell photons in chiral perturbation theory through next-to-leading order (NLO). We show that NLO contributions are relatively more important due to a fortuitous numerical suppression of the leading-order (LO) terms. Consequently, one expects theoretical predictions for the hadronic light-by-light (HLBL) contribution to the muon anomalous magnetic moment, $a_\mu^{HLBL}$, to be sensitive to the choice of model for the higher momentum-dependence of the LBL amplitude. We show that models employed thus far for the charged pion loop contribution to $a_\mu^{HLBL}$ are not consistent with low-momentum behavior implied by quantum chromodynamics, having omitted potentially significant contributions from the pion polarizability.