Hadronic light-by-light scattering in the anomalous magnetic moments of electron and τ

Abstract

In Refs. [1], [2] we provided a complete dispersive evaluation of the hadronic light-by-light (HLbL) contribution to the anomalous magnetic moment of the muon. While the evaluation strategy was developed for the kinematic situation determined by the muon mass, a similar approach also applies to the HLbL corrections to the anomalous magnetic moments of the electron and τ lepton, shifting the sensitivity in the loop integrals to smaller and larger momenta, respectively. In this Letter, we propagate the corresponding uncertainties of the various contributions, obtaining $a_e^{\text{HLbL}}=3.51\left(23\right)\times {10}^{-14}$ and $a_{\tau }^{\text{HLbL}}=3.77\left(29\right)\times {10}^{-8}$.