Scalar resonances in the hadronic light-by-light contribution to the muon $(g-2)$

Abstract

We evaluate the contribution of scalar mesons to the hadronic light-by-light piece of the muon anomalous magnetic moment, using a warped five-dimensional model and holographic methods. We assess the contribution of the lightest, sub-GeV scalars $\sigma(500)$, $a_0(980)$ and $f_0(980)$ together with their associated towers of excited states, which the model generates automatically. Our results point at a clearly negative contribution, overwhelmingly dominated by the $\sigma(500)$ meson, that we estimate at $a_\mu^{\rm{HLbL,S}}=-9(2)\cdot 10^{-11}$. This number is in very good agreement with the most recent determinations from dispersive analyses.