The scalar exotic resonances $$X(3915), X(3960), X_0(4140)$$

Abstract

AbstractThe scalar resonances $$X(3915), X(3960), X_0(4140)$$ X ( 3915 ) , X ( 3960 ) , X 0 ( 4140 ) are considered as exotic four-quark states: $$cq\bar{c} \bar{q}, cs\bar{c} \bar{s}, cs\bar{c}\bar{s}$$ c q c ¯ q ¯ , c s c ¯ s ¯ , c s c ¯ s ¯ , while the X(3863) is proved to be the $$c\bar{c}, 2\,^3P_0$$ c 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 ($$\lesssim 1.0$$ ≲ 1.0  fm). Then the resonance X(3915) appears due to the transitions: $$J/\psi \omega $$ J / ψ ω into $$D^{*+}D^{*-}$$ D ∗ + D ∗ - (or $$D^{*0}\bar{D}^{*0})$$ D ∗ 0 D ¯ ∗ 0 ) and back, while the X(3960) is created due to the transitions $$D_s^+D_s^-$$ D s + D s - into $$J/\psi \phi $$ J / ψ ϕ and back, and the $$X_0(4140)$$ X 0 ( 4140 ) is formed in the transitions $$J/\psi \phi $$ J / ψ ϕ into $$D_s^{*+}D_s^{*-}$$ 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 $$J^P=0^+$$ 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 $$c\bar{c}$$ c c ¯ channel) it is shifted up and lies by (20–30) MeV above the lower threshold. The following masses and widths are calculated: $$M(X(3915))=3920$$ M ( X ( 3915 ) ) = 3920  MeV, $$\Gamma (X(3915))=20$$ Γ ( X ( 3915 ) ) = 20  MeV; $$M(X(3960))=3970$$ M ( X ( 3960 ) ) = 3970  MeV, $$\Gamma (X(3960)=45(5)$$ Γ ( X ( 3960 ) = 45 ( 5 )  MeV, $$M(X_0(4140))= 4120(20)$$ M ( X 0 ( 4140 ) ) = 4120 ( 20 )  MeV, $$\Gamma (X_0(4140))=100$$ Γ ( X 0 ( 4140 ) ) = 100  MeV, which are in good agreement with experiment.