Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon

TL;DR

This paper refines the calculation of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment by implementing QCD short-distance constraints through a Regge sum, resulting in a smaller estimated correction.

Contribution

It introduces an efficient method to incorporate longitudinal short-distance constraints using a Regge sum constrained by phenomenological data, reducing previous overestimations.

Findings

The longitudinal SDC correction is estimated at 13(6)×10^{-11}.

The correction is significantly smaller than previous ad-hoc estimates.

Transversal SDC corrections are expected to be even smaller.

Abstract

A key ingredient in the evaluation of hadronic light-by-light (HLbL) scattering in the anomalous magnetic moment of the muon $(g-2)_\mu$ concerns short-distance constraints (SDCs) that follow from QCD by means of the operator product expansion. Here we concentrate on the most important such constraint, in the longitudinal amplitudes, and show that it can be implemented efficiently in terms of a Regge sum over excited pseudoscalar states, constrained by phenomenological input on masses, two-photon couplings, as well as SDCs on HLbL scattering and the pseudoscalar transition form factors (TFFs). Our estimate of the effect of the longitudinal SDCs on the HLbL contribution is: $\Delta a_\mu^\text{LSDC}=13(6)\times 10^{-11}$. This is significantly smaller than previous estimates, which mostly relied on an ad-hoc modification of the pseudoscalar poles and led to up to a $40\%$ increase with respect to the nominal pseudoscalar-pole contributions, when evaluated with modern input for the relevant TFFs. We also comment on the status of the transversal SDCs and, by matching to perturbative QCD, argue that the corresponding correction will be significantly smaller than its longitudinal counterpart.