On dispersion relations and hadronic light-by-light scattering contribution to the muon anomalous magnetic moment

TL;DR

This paper examines the use of dispersion relations to evaluate the hadronic light-by-light scattering contribution to the muon g-2, highlighting ambiguities and the need for additional theoretical input in the absence of experimental data.

Contribution

It critically analyzes the dispersive approach for calculating the muon g-2 hadronic light-by-light contribution, emphasizing its limitations and the necessity of extra theoretical assumptions.

Findings

Dispersion relation methods face ambiguities without experimental data.

Additional theoretical input is required, making the approach similar to phenomenological models.

Recent dispersive proposals may violate chiral limit constraints.

Abstract

We discuss the use of dispersion relations for the evaluation of the pseudoscalar contributions to the muon anomalous magnetic moment. We point out that, in the absence of experimental data, reconstruction of light-by-light scattering amplitudes from their absorptive parts is ambiguous and requires additional theoretical input. The need for an additional input makes dispersive computations of the hadronic light-by-light scattering contribution to g-2 akin to phenomenological models, in spite of pretense to the contrary. In particular, we argue that the recent proposal [1], based on the dispersive approach, satisfies short distance constraints at the expense of unjustifiably large deviations from the chiral limit.