Abstract
We revisit the information on the two lightest a_0 resonances and S-wave pi eta 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 and gamma gamma rightarrow K_SK_S high statistics experimental data from the Belle collaboration. Minimisation of the chi ^2 is found to have two distinct solutions with approximately equal chi ^2. One of these exhibits a light and narrow excited a_0 resonance analogous to the one found in the Belle analysis. This however requires a peculiar coincidence between the J=0 and J=2 resonance effects which is likely to be unphysical. In both solutions the a_0(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-ivarGamma /2=1000.7^{+12.9}_{-0.7} -i,36.6^{+12.7}_{-2.6} MeV. The solutions are also compared to experimental data in the kinematical region of the decay eta rightarrow pi ^0gamma gamma . In this region an isospin violating contribution associated with {pi ^+}{pi ^-} rescattering must be added for which we provide a dispersive evaluation.
Highlights
Tion experiments using an η beam, analogous to those which have allowed to determine the π π or π K phase shifts, are not feasible
Measurements with much higher statistics were recently performed by the Belle collaboration [13]
There are two puzzling aspects in the data analysis performed by the Belle collaboration which we wish to reconsider: a) they find that the a0(980) peak seems to be best described by an ordinary Breit-Wigner function and b) they find an excited a0, which could correspond to the a0(1450), but has a width, Γ = 65+−25
Summary
A theoretically motivated treatment of final-state interactions becomes prohibitively difficult for multiparticle final states. MeV, much smaller than the PDG average as well as a significantly smaller mass These data have been re-analysed recently [18] based on a specific mesonmeson T -matrix model [19] applied to the π η S-wave, from which the corresponding γ γ amplitude is deduced from a Muskhelishvili-Omnès (MO) construction [20,21]. The S-wave photon–photon amplitudes are deduced from a general MO representation involving two subtraction constants and implementing a simple description of the left-hand cut from cross-channel vector-meson exchanges. The comparison with the experimental data on photon–photon scattering is performed in Sect. 5 and the information that can be deduced on the a0 resonances are discussed
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