A dispersive estimate of scalar contributions to hadronic light-by-light scattering

Danilkin, Igor; Hoferichter, Martin; Stoffer, Peter (2021). A dispersive estimate of scalar contributions to hadronic light-by-light scattering. Physics letters. B, 820, p. 136502. Elsevier 10.1016/j.physletb.2021.136502

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We consider the contribution of scalar resonances to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. While the f0(500)has already been addressed in previous work using dispersion relations, heavier scalar resonances have only been estimated in hadronic models so far. Here, we compare an implementation of the f0(980)resonance in terms of the coupled-channel S-waves for γ∗γ∗→ππ/ ̄KKto a narrow-width approximation, which indicates aHLbLμ[f0(980)] =−0.2(2) ×10−11. With a similar estimate for the a0(980), the combined effect is thus well below 1 ×10−11in absolute value. We also estimate the contribution of heavier scalar resonances. In view of the very uncertain situation concerning their two-photon couplings we suggest to treat them together with other resonances of similar mass when imposing the matching to short-distance constraints. Our final result is a refined estimate of the S-wave rescattering effects in the ππand ̄KKchannel up to about 1.3GeV and including a narrow-width evaluation of the a0(980): aHLbLμ[scalars] =−9(1) ×10−11.

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