Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon

TL;DR

This paper provides a precise, data-driven calculation of the pion-pole contribution to the muon's anomalous magnetic moment, crucial for understanding hadronic effects in particle physics.

Contribution

It introduces a novel dispersive approach to reconstruct the doubly-virtual pion transition form factor using existing experimental data, enabling a complete and accurate estimate of the pion-pole contribution.

Findings

The pion-pole contribution to (g-2)_mu is quantified as 62.6^{+3.0}_{-2.5} x 10^{-11}.

The method allows for uncertainty reduction with improved measurements.

A comprehensive, data-driven framework for evaluating the pion-pole contribution is established.

Abstract

The $\pi^0$ pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLbL) tensor, and thus provides the leading contribution in a dispersive approach to HLbL scattering in the anomalous magnetic moment of the muon $(g-2)_\mu$. It is unambiguously defined in terms of the doubly-virtual pion transition form factor, which in principle can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full space-like doubly-virtual form factor can be reconstructed very accurately based on existing data for $e^+e^-\to 3\pi$, $e^+e^-\to e^+e^-\pi^0$, and the $\pi^0\to\gamma\gamma$ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the $(g-2)_\mu$ loop integral. The resulting value, $a_\mu^{\pi^0\text{-pole}}=62.6^{+3.0}_{-2.5}\times 10^{-11}$, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly-virtual measurements alone would allow one to further reduce the uncertainty in $a_\mu^{\pi^0\text{-pole}}$.