From the $P^{N}_ψ$/$P^Λ_{ψs}$ to $\bar{T}^f_{cc}$: 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 $T^f_{cc}(3875)$ 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.