Scalar Meson Contributions to a_\mu from Hadronic Light-by-Light Scattering

TL;DR

This paper evaluates the scalar meson contributions to the hadronic light-by-light scattering part of the muon's anomalous magnetic moment, providing updated estimates and their impact on the Standard Model prediction versus experimental results.

Contribution

It introduces an effective \sigma/f_0(500) resonance model to estimate scalar meson effects on a_L, updating the theoretical contributions to a_ and comparing with experimental data.

Findings

Scalar meson contributions to a_L are estimated as -(4.51 b1 4.12) ^{-11}.

The \sigma/f_0(500) dominates the scalar meson effects, accounting for 50-98%.

Updated the Standard Model prediction for a_ and its deviation from experiment.

Abstract

Using an effective \sigma/f_0(500) resonance, which describes the \pi\pi-->\pi\pi and \gamma\gamma-->\pi\pi scattering data, we evaluate its contribution and the ones of the other scalar mesons to the 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}\vert_S = -(4.51+- 4.12) 10^{-11}, which is dominated by the \sigma/f_0(500) contribution ( 50%~98%), 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^{\rm exp} - a_\mu^{SM})= +(312.1+- 64.3) 10^{-11}, where the theoretical errors from HLbL are dominated by the scalar meson contributions.