Abstract
Using an effective σ/f0(500) resonance, which describes the ππ→ππ and γγ→ππ 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 aμ of the muon. We obtain the conservative range of values: ∑Saμlbl|S≃−(4.51±4.12)×10−11, which is dominated by the σ/f0(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 aμ within the standard model, which we then compare to experiment. This comparison gives (aμexp−aμSM)=+(312.1±64.6)×10−11, where the theoretical errors from HLbL are dominated by the scalar meson contributions.
Highlights
The anomalous magnetic moments a ( ≡ e, μ) of the light charged leptons, electron and muon, are among the most accurately measured observables in particle physics
An ongoing experiment at Fermilab [4,5,6], and a planned experiment at J-PARC [7], aim at reducing the experimental uncertainty on aμ to the level of 0.14 ppm, and there is room for future improvements on the precision of ae. The confrontation of these very accurate measurements with precise predictions from the standard model provides a stringent test of the latter, and, as the experimental precision is further increasing, opens up the possibility of indirectly revealing physics degrees of freedom that even go beyond it. From this last point of view, the present situation remains unconclusive in the case of the muon
We have systematically studied the light scalar meson contributions to the anomalous magnetic moment of the muon aμ from hadronic light-by-light scattering (HLbL)
Summary
The anomalous magnetic moments a ( ≡ e, μ) of the light charged leptons, electron and muon, are among the most accurately measured observables in particle physics. [10] provides a recent overview, as well as references to the literature; see Section 10 at the end of this article) reveal a discrepancy between theory and experiment, which is at the level of ∼ 3.5 standard deviations only It is therefores mandatory, as the experimental precision increases, to reduce the theoretical uncertainties in the evaluation of aμ. The approach considered here for the treatment of the contribution from scalar states to HLbL has, to some extent, overlaps with both of the last two of these more recent approaches It rests on a set of coupled-channel dispersion relations for the processes γγ → ππ, KK , where the strong S-matrix amplitudes for ππ → ππ, KKare represented by an analytic K-matrix model, first introduced in Ref. We summarize the present experimental and theoretical situation concerning the standard-model evaluation of the anomalous magnetic moment of the muon (Section 11) and end this article by giving our conclusions (Section 12)
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