Canonical description of the new LHCb resonances

Abstract

The LHCb Collaboration has recently observed four $J/\psi\phi$ structures called $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$ in the $B^{+}\to J/\psi\phi K^{+}$ decays. We study them herein using a nonrelativistic constituent quark model in which the degrees of freedom are quark-antiquark and meson-meson components. 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 $X(4700)$ 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. A particular feature of our quark model is a lattice-based screened linear confining interaction that has been constrained in the light quark sector and usually produces higher excited heavy-quark states with lower masses than standard quark model predictions.