Decay of charmonium states into a scalar and a pseudoscalar glueball

In the framework of a chiral symmetric model, we expand a U(4)(R) x U(4)(L) symmetric linear sigma model with (axial-)vector mesons by including a dilaton field, a scalar glueball, and the pseudoscalar glueball. We compute the decay width of the scalar charmonium state chi(C0)(IP) into a predominantly scalar glueball f(0)(1710). We calculate the decay width of the pseudoscalar charmonium states eta(C)(IS) into a predominantly scalar glueball f(0)(1710) as well as into a pseudoscalar glueball with a mass of 2.6 GeV (as predicted by Lattice-QCD simulations) and with a mass of 2.37 GeV (corresponding to the mass of the resonance X(2370)). This study is interesting for the upcoming PANDA experiment at the FAIR facility and BESIII experiment. Moreover, we obtain the mixing angle between a pseudoscalar glueball, with a mass of 2.6 GeV, and the charmonium state eta(C).