Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$

TL;DR

This paper presents a comprehensive dispersive approach to evaluate the hadronic light-by-light contribution to the muon g-2, achieving a precise theoretical estimate aligned with recent experimental measurements.

Contribution

It introduces a complete dispersive formalism for HLbL scattering, utilizing experimental data and recent theoretical constraints to improve the accuracy of the muon g-2 prediction.

Findings

Calculated $a_\mu^{\text{HLbL}}=101.9(7.9)\times 10^{-11}$

Achieved precision compatible with Fermilab results

Enhanced understanding of hadronic contributions to muon g-2

Abstract

Hadronic light-by-light (HLbL) scattering defines one of the critical contributions in the Standard-Model prediction of the anomalous magnetic moment of the muon. In this Letter, we present a complete evaluation using a dispersive formalism, in which the HLbL tensor is reconstructed from its discontinuities, expressed in terms of simpler hadronic matrix elements that can be extracted from experiment. Profiting from recent developments in the determination of axial-vector transition form factors, short-distance constraints for the HLbL tensor, and the vector-vector-axial-vector correlator, we obtain $a_\mu^\text{HLbL}=101.9(7.9)\times 10^{-11}$, which meets the precision requirements set by the final result of the Fermilab experiment.