The scalar exotic resonances

The scalar resonances $$X(3915), X(3960), X_0(4140)$$ are considered as exotic four-quark states: $$cq\bar{c} \bar{q}, cs\bar{c} \bar{s}, cs\bar{c}\bar{s}$$, while the X(3863) is proved to be the $$c\bar{c}, 2\,^3P_0$$ state. The masses and the widths of these resonances are calculated in the framework of the Extended Recoupling Model, where a four-quark system is formed inside the bag and has relatively small size ($$\lesssim 1.0$$ fm). Then the resonance X(3915) appears due to the transitions: $$J/\psi \omega $$ into $$D^{*+}D^{*-}$$ (or $$D^{*0}\bar{D}^{*0})$$ and back, while the X(3960) is created due to the transitions $$D_s^+D_s^-$$ into $$J/\psi \phi $$ and back, and the $$X_0(4140)$$ is formed in the transitions $$J/\psi \phi $$ into $$D_s^{*+}D_s^{*-}$$ and back. The characteristic feature of the recoupling mechanism is that this type of resonances can be predominantly in the S-wave decay channels and has $$J^P=0^+$$. In two-channel case the resonance occurs to be just near the lower threshold, while due to coupling to third channel (like the $$c\bar{c}$$ channel) it is shifted up and lies by (20–30) MeV above the lower threshold. The following masses and widths are calculated: $$M(X(3915))=3920$$ MeV, $$\Gamma (X(3915))=20$$ MeV; $$M(X(3960))=3970$$ MeV, $$\Gamma (X(3960)=45(5)$$ MeV, $$M(X_0(4140))= 4120(20)$$ MeV, $$\Gamma (X_0(4140))=100$$ MeV, which are in good agreement with experiment