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

Abstract

A key ingredient in the evaluation of hadronic light-by-light (HLBL) scattering in the anomalous magnetic moment of the muon $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ concerns short-distance constraints 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 short-distance constraints on HLBL scattering and the pseudoscalar transition form factors. Our estimate of the effect of the longitudinal short-distance constraints on the HLBL contribution is $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}^{\mathrm{LSDC}}=13(6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$. 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 transition form factors. We also comment on the status of the transversal short-distance constraints and, by matching to perturbative QCD, argue that the corresponding correction will be significantly smaller than its longitudinal counterpart.