Scalar $f_0(980)$ and $\sigma (500)$ meson exchange in $\phi$ decays into $\pi^0\pi^0\gamma$

A. Bramon; R. Escribano; J.L. Lucio M.; M. Napsuciale; G. Pancheri

doi:doi:10.1140/epjc/s2002-01051-0

2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 26, 253-160 (2002)
DOI: 10.1140/epjc/s2002-01051-0

Scalar f₀(980) and $\sigma (500)$ meson exchange in $\phi$ decays into $\pi^0\pi^0\gamma$

A. Bramon¹, R. Escribano^{1, 2}, J.L. Lucio M.³, M. Napsuciale³ and G. Pancheri⁴

¹ Grup de Física Teòrica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
² IFAE, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
³ Instituto de Física, Universidad de Guanajuato, Lomas del Bosque #103, Lomas del Campestre, 37150 León, Guanajuato, Mexico
⁴ INFN-Laboratori Nazionali di Frascati, P.O. Box 13, 00044 Frascati, Italy

(Received: 14 May 2002 / Revised version: 25 July 2002 / Published online: 18 October 2002 )

Abstract
The complementarity between chiral perturbation theory and the linear sigma model is exploited to study $\pi^0\pi^0$ production in $\phi$ radiative decays, where the effects of the f₀(980) scalar resonance, and those of its more controversial $\sigma (500)$ partner, should become manifest via the $\phi\rightarrow K^+ K^- (\gamma)\rightarrow\pi^0\pi^0\gamma$ decay chain. The recently reported data on $\phi\rightarrow\pi^0\pi^0\gamma$ coming from the VEPP-2M e⁺ e^- collider in Novosibirsk and the DA $\Phi$ NE $\phi$ -factory in Frascati can be reasonably described in our approach, which we propose as a promising first step towards more detailed analyses. The f₀(980) contribution, which appears as a moderately narrow peak at the high part of the dipion mass spectrum, can be interpreted as the isoscalar member of the scalar nonet with a large $f_0 K\bar{K}$ coupling and an $f_0\pi\pi$ coupling suppressed by almost ideal $\sigma$ - f₀ mixing. Indeed, the mixing angle in the flavor basis is found to be $\phi_{S}\approx - 6^\circ$ , if the f₀ propagator is approximated by a simple Breit-Wigner expression, or $\phi_{S}\approx -9^\circ$ , if an improved two-channel analysis is performed. The $\sigma (500)$ resonance, which is then strongly coupled to pion pairs, yields a tiny contribution because, in our approach, its coupling to kaon pairs is proportional to $m^2_\sigma-m^2_K$ and thus quite small.