The $$\pi \eta $$ πη interaction and $$a_0$$ a0 resonances in photon–photon scattering

Abstract

Abstract We revisit the information on the two lightest $$a_0$$ a0 resonances and S-wave $$\pi \eta $$ 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 $$\gamma \gamma \rightarrow \pi \eta $$ γγ→πη and $$\gamma \gamma \rightarrow K_SK_S$$ γγ→KSKS high statistics experimental data from the Belle collaboration. Minimisation of the $$\chi ^2$$ χ2 is found to have two distinct solutions with approximately equal $$\chi ^2$$ χ2 . One of these exhibits a light and narrow excited $$a_0$$ 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 $$a_0(980)$$ 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 $$m-i\varGamma /2=1000.7^{+12.9}_{-0.7} -i\,36.6^{+12.7}_{-2.6}$$ 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 $$\eta \rightarrow \pi ^0\gamma \gamma $$ η→π0γγ . In this region an isospin violating contribution associated with $${\pi ^+}{\pi ^-}$$ π+π- rescattering must be added for which we provide a dispersive evaluation.