The scalar exotic resonances X(3915),X(3960),X0(4140)

Abstract

The scalar resonances $X(3915),X(3960),X_0(4140)$ are considered as exotic four-quark states: $cq\overline{c}\overline{q},cs\overline{c}\overline{s},cs\overline{c}\overline{s}$, while the X(3863) is proved to be the $c\overline{c},2{}^3{P}_0$ 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 $D^{\ast +}{D}^{\ast -}$ (or $D^{\ast 0}{\overline{D}}^{\ast 0})$ and back, while the X(3960) is created due to the transitions $D_s^{+}{D}_s^{-}$ into $J/\psi \varphi$ and back, and the $X_0(4140)$ is formed in the transitions $J/\psi \varphi$ into $D_s^{\ast +}{D}_s^{\ast -}$ 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 $c\overline{c}$ 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, $\mathrm{\Gamma }(X(3915))=20$ MeV; $M(X(3960))=3970$ MeV, $\mathrm{\Gamma }(X(3960)=45(5)$ MeV, $M(X_0(4140))=4120(20)$ MeV, $\mathrm{\Gamma }(X_0(4140))=100$ MeV, which are in good agreement with experiment.