Scalar Meson Contributions to a_μfrom Hadronic Light-by-Light Scattering

Abstract

Using an effective σ/f_0(500) resonance, which describes the ππ-->ππand γγ-->ππscattering 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_μof the muon. We obtain the conservative range of values: \sum_S~a_μ^{lbl}\vert_S = -(4.51+- 4.12) 10^{-11}, which is dominated by the σ/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_μwithin the standard model, which we then compare to experiment. This comparison gives (a_μ^{\rm exp} - a_μ^{SM})= +(312.1+- 64.3) 10^{-11}, where the theoretical errors from HLbL are dominated by the scalar meson contributions.

15 pages, 7 figures, 8 tables, some misprints corrected in Eq. 4.5 which modifies the results in Table 4 and slightly changes the final result