From $J/\psi$ to LHCb pentaquarks

Abstract

The two exotic $P_c^{+}(4380)$ and $P_c^{+}(4450)$ discovered in $2015$ by the LHCb Collaboration, together with the four resonances $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$, reported in $2016$ by the same collaboration, are described in a constituent quark model which has been able to explain the properties of charmonium states from the $J/\psi$ to the $X(3872)$. Using this model we found a $\bar{D}{\Sigma }_c^{\ast }$ bound state with $J^P={\frac{3}{2}}^{-}$ that may be identified with the $P_c^{+}(4380)$. In the ${\bar{D}}^{\ast }{\Sigma }_c$ channel we found three possible candidates for the $P_c^{+}(4450)$ with $J^P={\frac{1}{2}}^{-}$, ${\frac{3}{2}}^{-}$ and ${\frac{3}{2}}^{+}$ with almost degenerated energies. The $X(4140)$ resonance appears as a cusp in the $J/\psi \varphi$ channel due to the near coincidence of the $D_s^{\pm }{D}_s^{\ast \pm }$ and $J/\psi \varphi$ mass thresholds. The remaining three $X(4274)$, $X(4500)$ and $X(4700)$ resonances appear as conventional charmonium states with quantum numbers $3^3{P}_1$, $4^3{P}_0$ and $5^3{P}_0$, respectively; and whose masses and widths are slightly modified due to their coupling with the corresponding closest meson-meson thresholds.

Comments: Contribution to the proceedings of the VIII International Workshop on Charm Physics (CHARM2016). September 5-9, 2016. Bologna, Italy