From the $P_{\psi }^N$/$P_{\psi s}^{\Lambda }$ to ${\bar{T}}_{cc}^f$: symmetry analysis to the interactions of the $(\bar{c}q)(\bar{c}q)$/$(ccq)(\bar{c}q)$/$(ccq)(ccq)$ di-hadron systems

Abstract

We investigate the interactions of the $(\bar{c}q)(\bar{c}q)$/$(ccq)(\bar{c}q)$/$(ccq)(ccq)$ di-hadron systems based on a contact lagrangian possessing the SU(3) flavor and SU(2) spin symmetries. Under the assumptions of two scenarios for the $J^P$ quantum numbers of the $P_{\psi }^N(4440)$ and $P_{\psi }^N(4457)$ states, we obtain the parameters (${\tilde{g}}_s$, ${\tilde{g}}_a$) introduced from this contact lagrangian. Then we include the SU(3) breaking effect by introducing a factor $g_x$, this quantity can be further constrained by the experimental mass of the $P_{\psi s}^{\Lambda }(4338)$ state. We can reproduce the mass of the $T_{cc}^f(3875)$ state with the parameters extracted from the observed $P_{\psi }^N$ states, this consistency indicates a unified description of the di-hadron molecular states composed of two heavy-light hadrons. With the same parameters, we discuss the possible mass spectra of the ${\bar{T}}_{cc}^f$/$P_{\psi c}^{\Lambda }$/$H_{{\Omega }_{ccc}c}^{\Lambda }$ systems. Then we proceed to discuss the existences of the ${\bar{T}}_{cc\bar{s}}^{\theta }$/$P_{\psi cs}^N$/$H_{{\Omega }_{ccc}cs}^N$ states by investigating the SU(3) breaking effects. Our results show that the states in the ${\bar{T}}_{cc\bar{s}}^{\theta }$/$P_{\psi cs}^N$ systems can hardly form bound states, while the states in the $H_{{\Omega }_{ccc}cs}^N$ system can form bound states due to their larger reduced masses.

Comments: 12 pages, 4 figures, 4 Tables