Radiative decays with scalar mesons and in Resonance Chiral Theory

Abstract

The φ(1020) radiative decays form a good playground for study of the low-lying a0(980) and f0(980) scalar mesons. The complicated interplay of kaon loop mechanism, isoscalar meson mixing and momentum dependence of the effective couplings manifests itself in the invariant mass distributions in the φ(1020) → π 0 π 0 γ and πηγ spectra. These distributions are fitted in framework of Resonance Chiral Theory.

e+e- annihilation to (pi0 pi0 gamma) and (pi0 eta gamma) as a source of information on scalar and vector mesons

“…For discussion of momentumdependent couplings G SP P (p 2 ) and constant SP P couplings of other models (e.g., [10]) see Ref. [26]. The finite-width effects for scalar resonances are very important and expressions (B9), (B10) do not have physical meaning of decay width, when evaluated at the resonance peak value of p 2 .…”

“…Nevertheless, in several papers, e.g., [12,20,39], the tree-level expressions of a similar form were used to find the model parameters (c d , c m and θ) from measured widths. It was observed [24,26,40] that the coupling constants could be better determined from fitting the ππ and πη invariant mass distributions in e + e − → φ → γππ and e + e − → φ → γπη reactions. The fit results [24] are shown in Table 4 and these values are used in our numerical calculations.…”

On modeling the scalar meson dynamics with Resonance Chiral Theory

“…Ref. [9]) fitted (A): M a 0 to πη spectrum, M f 0 , θ to π 0 π 0 spectrum, m ππ > 700 MeV (separate fits); fitted (B): M a 0 to πη spectrum, M f 0 , M σ , θ to π 0 π 0 spectrum (separate fits);…”

On modeling the scalar meson dynamics with RChT

“…[6,7]) have been proposed to describe these decays. In our previous consideration [9] we performed the separate fits (π 0 π 0 and πη) for the mass-parameters of scalar mesons and the angle θ , while 4c d c m = F 2 and c d = c m relations of Ref. [21] were imposed.…”

“…Improvements on this way were initiated in Ref. [9] and this paper is aimed to this analysis as well. Section 4 is devoted to the fits of the invariant mass distributions in the radiative decays of the φ (1020) meson: φ → (γa 0 →)γπη and φ → (γ f 0 /σ →)γππ.…”