$\pi^0, \eta, \eta^\prime$ two-photon transition form factors in the holographic soft-wall model and contributions to $(g-2)_\mu$

Abstract

We compute the two-photon transition form factors of the light pseudoscalar $\pi^0$, $\eta$ and $\eta^\prime$ mesons in a soft-wall holographic model of QCD with a solution of the $U(1)_A$ problem. We compare the results with the experimental data in different ranges of photon virtualities. The obtained transition form factors are used to determine the $\pi^0$, $\eta$ and $\eta^\prime$ pole terms in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon.