Analysis of the nature of the φ → γπη and φ → γπ
AbstractWe study interference patterns in the φ → (γa 0 + π 0 ρ) → γπη and φ → (γf 0 + π 0 ρ) → γπ 0 π 0 reactions. Taking into account the interference, we fit the experimental data and show that the background reaction does not distort the π 0 η spectrum in the decay φ → γπη everywhere over the energy region and does not distort the π 0 π 0 spectrum in the decay φ → γπ 0 π 0 in the wide region of the π 0 π 0 system invariant mass, m ππ > 670 MeV, or when the photon energy is less than 300 MeV. We discuss the details of the scalar meson production in the radiative decays and note that there are reasonable arguments in favor of the one-loop mechanism φ → K + K − → γa 0 and φ → K + K − → γf 0 . We discuss also distinctions between the four-quark, molecular, and two-quark models and argue that the Novosibirsk data give evidence in favor of the four-quark nature of the scalar a 0 (980) and f 0 (980) mesons.12.39.-x, 13.40.Hq, 13.65.+i
It is shown that the reactions e ϩ e Ϫ →␥ 0 0 () give a good chance for observing the scalar a 0 and f 0 mesons. In the photon energy region less than 100 MeV the vector meson contributions e ϩ e Ϫ →V 0 → 0 VЈ 0 →␥ 0 0 () are negligible in comparison with the scalar meson e ϩ e Ϫ → →␥ f 0 (a 0 )→␥ 0 0 () for B"→␥ f 0 (a 0 )→␥ 0 0 ()… greater than 5ϫ10 Ϫ6 (10 Ϫ5 ). Using the twochannel treatment of the scattering the predictions for B"→␥( f 0 ϩ)→␥… are derived. The fourquark model, the model of the KK molecule, and the ss model of scalar f 0 and a 0 mesons are discussed. ͓S0556-2821͑97͒00919-3͔ PACS number͑s͒: 12.39. Ϫx, 13.40.Hq. 13.65.ϩi In the case when f 0 ϭss the suppression by the OZI rule is absent and the evaluation gives ͓9͔ *Electronic address: achasov@math.nsc.ru † Electronic address: gubin@math.nsc.ru PHYSICAL
The potentialities of the production of the scalar KK molecules in the φ radiative decays are considered beyond the narrow resonance width ap-The mass spectra in the ππ , πη , K + K − , K 0K 0 channels are calculated. The imaginary part of the amplitude φ → γf 0 (a 0 ) is calculated analytically. It is obtained the phase of the scalar resonance production amplitude that causes the interference patterns in the reaction e + e − → γπ + π − in the φ meson mass region.12.39.-x, 13.40.Hq.
We describe the interference between amplitudes e ϩ e Ϫ →→␥ ϩ Ϫ and e ϩ e Ϫ →→␥ f 0 →␥ ϩ Ϫ , where the f 0 meson is considered in the framework of the four-quark model and the model of the scalar KK molecule. The general expressions for the differential cross section with the radiative corrections and two angle cuts are given. The interference patterns are obtained in the spectrum of the differential cross section by the energy of the photon and in the full cross section by the energy of the beams. ͓S0556-2821͑97͒01803-1͔
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