Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$

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 $\tau$ 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 $a_e^\text{HLbL}= 3.51(23)\times 10^{-14}$ and $a_\tau^\text{HLbL}= 3.77(29)\times 10^{-8}$.