From the PNψ/PΛψ s to T̄ᶠcc: symmetry analysis to the interactions of the (c̄q)(c̄q)/(ccq)(c̄q)/$(ccq)(ccq)$ di-hadron systems

We investigate the interactions of the (c̄q)(c̄q)/(ccq)(c̄q)/$(ccq)(ccq)$ 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 JP quantum numbers of the PψN(4440) and PψN(4457) states, we obtain the parameters (g̃ₛ, g̃ₐ) introduced from this contact lagrangian. Then we include the SU(3) breaking effect by introducing a factor gₓ, this quantity can be further constrained by the experimental mass of the Pψ s^Λ(4338) state. We can reproduce the mass of the Tᶠcc(3875) state with the parameters extracted from the observed PψN 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 T̄ccᶠ/Pψ c^Λ/H_Ωcccc^Λ systems. Then we proceed to discuss the existences of the T̄ccs̄^θ/Pψ csN/H_ΩccccsN states by investigating the SU(3) breaking effects. Our results show that the states in the T̄ccs̄^θ/Pψ csN systems can hardly form bound states, while the states in the H_ΩccccsN system can form bound states due to their larger reduced masses.