S-wave QQqq state in the constituent quark model

Many proposals have been put forward to explore four-quark states QQqq (Q=s, c, b; q=u, d) by experiment, so a systematic study of QQqq spectrum with different constituent quark models by a high precision, few-body method, the Gaussian expression method, is useful. Three quark models: the Bhaduri, Cohler, Nogami quark model, the chiral quark model (ChQM), and the quark delocalization color screening model are all employed for a systematic calculation of the S-wave QQqq spectrum with different color structures, using the Gaussian expression method. The results show that only the bbqq state with (I,J)=(0,1) is bound in different color structures within the different quark models. The binding energy varies from several MeV for a di-meson structure to over 100 MeV for a diquark-antidiquark structure. For the ccqq system, the state with (I,J)=(0,1) is bound in a di-meson structure, and also bound in a diquark-antidiquark structure if pseudoscalar meson exchanges are accounted for. All are weakly bound states. The mixture of diquark-antidiquark and molecular structures is discussed in the framework of quark models for the first time; ccqq with (I,J)=(0,1) is below the threshold in addition to bbqq in both the ChQM and the Bhaduri, Cohler, Nogami quark model. In the same channel, ssqq is also a possible bound state with mass around 1.4 GeV in ChQM.