Two Photon Decays Ofσ (600), α₀(980) And F₀(980) In A Quark-level Linear Sigma Model

It is a long-standing problem that if light scalars exist and what are their quark structures and properties, especially several scalar resonances with masses below 1GeV:σ(600),a₀ (980),f₀ (980)andκ(700). Among them, a₀ (980)and f₀ (980)were confirmed in 1960's, and they were assigned to convenient scalar mesons then; whileσ(600) appeared and disappeared several times in particle data table compiled by Particle Data Group since 1960's;κ(700) was confirmed only recently. At the same time, more convincing analysis confirmed the existence ofσ(600). In a word, their existence is confirmed more or less. However, their structures are still very controversial. They may form a convenient scalar meson nonet, but it seems that its mass spectrum does not support this. They may have more complicated structures, such as four-quark structures, meson-molecule structures, they may be the mixing of these too. Therefore, it is important to identify their quark structures.To decide the quark structure of a resonance, investigating their radiative decays is very helpful because quarks are sensitive to electromagnetic interaction. So investigating the structures of scalars through their radiative decays is an effectual approach. Usually, phenomenological models are built to do this.In this paper, we investigate two photon decays of the neutralσ(600),a0 (980)and f₀ (980)by a quark-level U (3)×U(3)linear sigma model. This model is a generalization of the original SU (2)×SU(2) linear sigma model. In this model, in addition to quarks and pseudosca -lars in a U (3) nonet, a scalar nonet which containsσ(600),a₀ (980) and f₀(980) is intro -duced. That is to say, these scalars are assumed to have convenient qq structures. The two photon decays of these particles process through quark triangle graphs. The linear sigma model has the advantage that only a few free parameters are involved: in two photon decay processes, only the mass of the u quark is involved, all other parameters can be decided by experiments. We calculate these decay widths and discuss if linear sigma model support their qq structures.