Dispersion relation for hadronic light-by-light scattering: subleading contributions

TL;DR

This paper evaluates subleading effects in the hadronic light-by-light scattering contribution to the muon's magnetic moment, incorporating axial-vector, pseudoscalar, and tensor meson effects with a new matching strategy.

Contribution

It introduces a novel matching approach to include subleading hadronic effects in the light-by-light scattering contribution to the muon g-2.

Findings

Subleading contributions amount to 33.2(7.2)×10^{-11} in the muon g-2.

Total hadronic light-by-light contribution is 101.9(7.9)×10^{-11}.

Tensor mesons and tails of pseudoscalar poles significantly influence results.

Abstract

In this work, we present an evaluation of subleading effects in the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Using a recently derived optimized basis, we first study the matching of axial-vector contributions to short-distance constraints at the level of the scalar basis functions, finding that also the tails of the pseudoscalar poles and tensor mesons play a role. We then develop a matching strategy that allows for a combined evaluation of axial-vector and short-distance constraints, supplemented by an estimate of tensor-meson contributions based on simplified assumptions for their transition form factors. Uncertainties are primarily propagated from the axial-vector transition form factors and the variation of the matching scale, but we also consider estimates of the low-energy effect of hadronic states not explicitly included. In total, we obtain $a_\mu^\text{HLbL}\big|_\text{subleading}=33.2(7.2)\times 10^{-11}$, which in combination with previously evaluated contributions in the dispersive approach leads to $a_\mu^\text{HLbL}\big|_\text{total}=101.9(7.9)\times 10^{-11}$.