Scalar meson contributions to aμ from hadronic light-by-light scattering

Using an effective $\sigma /f_0\left(500\right)$ resonance, which describes the $\pi \pi \to \pi \pi$ and $\gamma \gamma \to \pi \pi$ scattering data, we evaluate its contribution and the ones of the other scalar mesons to the hadronic light-by-light (HLbL) scattering component of the anomalous magnetic moment $a_{\mu }$ of the muon. We obtain the conservative range of values: ${\sum }_S{a}_{\mu }^{lbl}{|}_S\simeq -(4.51\pm 4.12)\times {10}^{-11}$, which is dominated by the $\sigma /f_0\left(500\right)$ contribution ($50\text{\%}\sim 98\text{\%}$), and where the large error is due to the uncertainties on the parametrisation of the form factors. Considering our new result, we update the sum of the different theoretical contributions to $a_{\mu }$ within the standard model, which we then compare to experiment. This comparison gives $(a_{\mu }^{\exp }-a_{\mu }^{\mathrm{SM}})=+(312.1\pm 64.6)\times {10}^{-11}$, where the theoretical errors from HLbL are dominated by the scalar meson contributions.