The π η interaction and a₀ resonances in photon–photon scattering

We revisit the information on the two lightest a₀ a0 resonances and S -wave π η πη scattering that can be extracted from photon–photon scattering experiments. For this purpose we construct a model for the S -wave photon–photon amplitudes which satisfies analyticity properties, two-channel unitarity and obeys the soft photon as well as the soft pion constraints. The underlying I=1 hadronic T -matrix involves six phenomenological parameters and is able to account for two resonances below 1.5 GeV. We perform a combined fit of the γ γ → π η γγ→πη and γ γ → KSKS γγ→KSKS high statistics experimental data from the Belle collaboration. Minimisation of the χ ² χ2 is found to have two distinct solutions with approximately equal χ ² χ2 . One of these exhibits a light and narrow excited a₀ a0 resonance analogous to the one found in the Belle analysis. This however requires a peculiar coincidence between the $$J=0$$ J=0 and $$J=2$$ J=2 resonance effects which is likely to be unphysical. In both solutions the a₀(980) a0(980) resonance appears as a pole on the second Riemann sheet. The location of this pole in the physical solution is determined to be m-i /2=1000.7+12.9-0.7 -i\,36.6+12.7-2.6 m-iΓ/2=1000.7-0.7+12.9-i36.6-2.6+12.7 MeV. The solutions are also compared to experimental data in the kinematical region of the decay η → π ⁰γ γ η→π0γγ . In this region an isospin violating contribution associated with π ⁺π ⁻ π+π- rescattering must be added for which we provide a dispersive evaluation.