Pseudoscalar pole contribution to the hadronic light-by-light piece of a_μ

¹ Departamento de Física Teórica and UPARCOS, Universidad Complutense de Madrid, Plaza de las Ciencias 1, 28040 Madrid, Spain
² Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000, Ciudad de México, Mexico

^* e-mail: adguevar@ucm.es
^** e-mail: proig@fis.cinvestav.mx
^*** e-mail: jjsanzcillero@ucm.es

Published online: 14 November 2018

Abstract

We have studied the P → γ^⋆ γ^⋆ form factor in Resonance Chiral Theory, with P = π⁰; η, η', to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading U(3) chiral symmetry breaking terms, obtaining the most general expression for the form factor of order O(m²_P). The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike momentum region of the virtual photon. Chiral symmetry relations among the transition form factors for π⁰, η and η' allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar π⁰ data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of a^P,HLbL_η = (8:47 ± 0:16) · 10^-10 for our best fit (neglecting the BaBar π⁰ data). Also, a preliminary rough estimate of the impact of NLO in 1=NC corrections and higher vector multiplets (asym) enlarges the uncertainty up to a^P,HLbL_η = (8:47 ± 0:16_stat ± 0:09_NC ^+0:5 _-0:0asym).