K-Matrix Analysis of the (${IJ}^{PC}=00^{++}$) Amplitude in the Mass Region up to 1550 MeV

Abstract

K-matrix analysis of the $00^{++}$ wave is performed in the channels $ππ,~K\bar K,~ηη$ and $4π$ in the mass region up to 1550 MeV. The fit is based on the following data: $p\bar p ~(at~rest)\to π^0π^0π^0$, $π^0π^0η,~π^0ηη$ [1,2], $πN\to ππN$ [3,4], $πN\to K\bar K N$ [5] and the inelastic cross section of the $ππ$ interaction [6]. Simultaneous analysis of these data confirms the existence of the scalar resonances: $f_0(980),~f_0(1300)$ and $f_0(1500)$, the poles of the amplitude being at the following complex masses (in MeV): $(1008\pm 10)- i(43\pm 5)$, $(1290\pm 25)-i(120\pm 15)$, and $(1497\pm 6)-i(61\pm 5)$. The fourth pole has sunk deeply into the complex plane: $(1430 \pm 150) - i(600\pm 100)$. Positions of the K-matrix poles (which are referred to the masses of bare states) are at $750\pm 120$ MeV, $1240\pm 30$ MeV, $1280\pm 30$ MeV and $1615\pm 40$ MeV. Coupling constants of the K-matrix poles to the $ππ$, $ηη$ and $K\bar K$ channels are found that allow us to analyze the quark and gluonic content of bare states. It is shown that $f_0^{bare}(1240)$ and $f_0^{bare}(1615)$ (which are strongly related to $f_0(1500)$) can be considered as good candidates for scalar glueball.