Decay of the scalar charmonium state $\chi_{c0}(IP)$ in the extended Linear Sigma Model

Abstract

We study the hadronic decays of the ground-state scalar charmonium $\chi_{c0}(IP)$, $J^{PC}=0^{++}$, in the framework of a $U(4)_r \times U(4)_l$ symmetric linear sigma model with (pseudo)scalar and (axial-)vector mesons. The model fairly succeeds to describe the masses of charmed mesons and the (OZI-dominant) strong decays of open charmed mesons. Here we compute the (OZI-suppressed) decays of charmonium state $\chi_{c0}(1P)$. We calculate also the decay widths of this state into the scalar-isoscalar resonances $f_0(1370),\, f_0(1500)$ and a predominantly scalar glueball $f_0(1710)$. The results of measured decay widths are in good agreement with experiments. The unmeasured states and channels are interesting for the ongoing BESIII, Belle and BaBar experiments as well as the upcoming PANDA experiment at FAIR facility.