σ and f0(980) substructures from γγ→ππ, J/ψ,ϕ radiative and Ds semi-leptonic decays

Using an improved “analytic K-matrix model”, we reconsider the extraction of the σ≡f0(600) and f0(980)γγ widths from γγ→ππ scatterings data of Crystal Ball and Belle. Our main results are summarized in Tables 3 and 4. The averaged σ “direct width” to γγ is 0.16(3) keV which confirms a previous result of Mennessier et al. (2007, 2008) [1] and which does neither favour a large four-quark/molecule nor a pure q¯q components. The “direct width” of the f0(980) of 0.28(2) keV is much larger than the four-quark expectation but can be compatible with a s¯s or a gluonium component. We also found that the rescattering part of each amplitude is relatively large indicating an important contribution of the meson loops in the determinations of the σ and f0(980)γγ total widths. This is mainly due to the large couplings of the σ and f0(980) to ππ and/or K¯K, which can also be due to a light scalar gluonium with large OZI violating couplings but not necessary to a four-quark or molecule state. Our average results for the total (direct + rescattering) γγ widths: Γσtot=3.08(82) keV, Γf0tot=0.16(1) keV are comparable with the ones from dispersion relations and PDG values. Using the parameters from QCD spectral sum rules, we complete our analysis by showing that the production rates of unmixed scalar gluonia σB(1) and G(1.5-1.6) agree with the data from J/ψ, ϕ radiative and Ds semi-leptonic decays.