Hadronic light-by-light contribution to the muon g-2

Abstract

We have computed the hadronic light-by-light (LbL) contribution to the muon anomalous magnetic moment $a_\mu$ in the frame of Chiral Perturbation Theory with the inclusion of the lightest resonance multiplets as dynamical fields (R$\chi$T). It is essential to give a more accurate prediction of this hadronic contribution due to the future projects of J-Parc and FNAL on reducing the uncertainty in this observable. We, therefore, computed the pseudoscalar transition form factor and proposed the measurement of the $e^+e^-\to\mu^+\mu^-\pi^0$ cross section and dimuon invariant mass spectrum to determine more accurately its parameters. Then, we evaluated the pion exchange contribution to $a_\mu$, obtaining $(6.66\pm0.21)\cdot10^{-10}$. By comparing the pion exchange contribution and the pion-pole approximation to the corresponding transition form factor ($\pi$TFF) we recalled that the latter underestimates the complete $\pi$TFF by (15-20)\%. Then, we obtained the $\eta^({}'^)$ TFF, obtaining a total contribution of the lightest pseudoscalar exchanges of $(10.47\pm0.54)\cdot10^{-10}$, in agreement with previous results and with smaller error.