From $J/ψ$ 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 $\bar D\Sigma_c^*$ bound state with $J^P=\frac{3}{2}^-$ that may be identified with the $P_c^+(4380)$. In the $\bar D^*\Sigma_c$ 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 $J/\psi\phi$ channel due to the near coincidence of the $D_{s}^{\pm}D_{s}^{\ast\pm}$ and $J/\psi\phi$ 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.