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

Abstract

The scalar resonances $X(3915),X(3960),X(4140)$ 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 $c\bar{c},2{}^3{P}_0$ 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 ($\text{la}1.0$~fm). Then the resonance $X(3915)$ appears due to the transitions: $J/\psi \omega$ into $D^{\ast +}{D}^{\ast -}$ (or $D^{\ast 0}{\bar{D}}^{\ast 0})$ and back, while the $X(3960)$ is created due to the transitions $D_s^{+}{D}_s^{-}$ into $J/\psi \varphi$ and back, and the $X(4140)$ 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 $c\bar{c}$ 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, $M(X(4140))=4120(20)$~MeV, $\Gamma (X(4140))=100$~MeV, which are in good agreement with experiment.

Comments: 16 pages