Radiative Decays Involving $f_0(980)$ and $a_0(980)$ and Mixing Between Low and High Mass Scalar Mesons

Abstract

We analyze the experimental data for $ϕ\to f_0(980)γ$, $ϕ\to a_0(980)γ$, $f_0(980)\toγγ$ and $a_0(980)\toγγ$ decay widths in a framework where $f_0(980)$ and $a_0(980)$ are assumed to be mainly $qq\bar{q}\bar{q}$ low mass scalar mesons and mixed with $q\bar{q}$ high mass scalar mesons. Applied the vector meson dominance model (VDM), these decays amplitudes are expressed by coupling parameters $B$ describing the S ($qq\bar{q}\bar{q}$ scalar meson)-V(vector meson)- V(vector meson) coupling and $B'$ describing the S' ($q\bar{q}$ scalar meson)-V-V coupling. Adopting the magnitudes for $B$ and $B'$ as $2.8{GeV^{-1}}$ and $12{GeV^{-1}}$, respectively, the mixing angle between $a_0(980)$ and $a_0(1450)$ as 9 degrees, and the mixing parameter $λ_{01}$ causing the mixing between I=0 $qq\bar{q}\bar{q}$ state and $q\bar{q}$ state as $0.24{GeV}^2$, we can interpret these experimental data, consistently.