Lightest scalar and tensor resonances in $γγ\toππ$ after the Belle experiment
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New high statistics Belle data on the $γγ\toπ^+π^-$ reaction cross section measured in the range of pion-pair invariant masses $\sqrt{s}$ between 0.8 GeV and 1.5 GeV are analyzed to clarify the current situation around the $σ(600)$, $f_0(980)$, and $f_2(1270)$ resonances in $γγ$ collisions. The present analysis shows that the direct coupling constants of the $σ(600)$ and $f_0(980)$ resonances to $γγ$ are small, and the $σ(600)\toγγ$ and $f_0(980)\toγγ$ decays are four-quark transitions caused by the $π^+π^-$ and $K^+K^-$ loop mechanisms, respectively. The chiral shielding of the $σ(600)$ resonance takes place in the reactions $γγ\toππ$ as well as in $ππ$ scattering. Some results of a simultaneous description of the $γγ\toπ^+π^-$ and $γγ\toπ^0π^0$ Belle data are also presented. In particular, the following tentative estimate of the $f_2(1270)\toγγ$ decay width is obtained: $Γ_{f_2\toγγ}(m^2_{f_2})\approx 3.68$ keV.
14 pages, 5 figures. Fitted for the publication in Physical Review D
14 pages, 5 figures. Fitted for the publication in Physical Review D