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 $\varphi \to f_0(980)\gamma$, $\varphi \to a_0(980)\gamma$, $f_0(980)\to \gamma \gamma$ and $a_0(980)\to \gamma \gamma$ 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 $B^{\prime }$ describing the S' ($q\bar{q}$ scalar meson)-V-V coupling. Adopting the magnitudes for $B$ and $B^{\prime }$ as $2.8Ge{V}^{-1}$ and $12Ge{V}^{-1}$, respectively, the mixing angle between $a_0(980)$ and $a_0(1450)$ as 9 degrees, and the mixing parameter ${\lambda }_{01}$ 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.

Comments: 15 pages, 6 figures