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 $(6.66\pm 0.21)\cdot 10^{-10}$. 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 ${\eta }^{(}{}^{\prime )}$ TFF, obtaining a total contribution of the lightest pseudoscalar exchanges of $(10.47\pm 0.54)\cdot 10^{-10}$, in agreement with previous results and with smaller error.

arXiv comment6 pages, 8figures, 30th Reunion Anual de la Division de Particulas y Campos de la SMF (DPC-SMF2016)

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