$X(3872)$ and hidden charmed tetraquarks

TL;DR

This paper uses a constituent quark model with Semay-Silvestre-Brac potentials to predict masses of hidden charmed tetraquarks and tentatively assign observed XYZ states to these tetraquark configurations.

Contribution

It provides systematic mass calculations for hidden charmed tetraquarks including excitations and offers possible assignments for experimental XYZ states based on these predictions.

Findings

Predicted diquark masses around 2175 MeV (spin-0) and 2220 MeV (spin-1).

Mass splittings between states are smaller than those of normal charmonium.

Some XYZ states are tentatively identified as specific tetraquark states.

Abstract

In a constituent quark model, a hidden charmed tetraquark is assumed consisting of a $cq$ diquark and an $\bar c\bar q$ antidiquark or vice versa. The Semay-Silvestre-Brac potentials are employed to calculate the masses of $cq$ (q=u, d) diquarks. The mass of the $cq$ diquark or $\bar c\bar q$ antidiquark with spin-$0$ is predicted with $\sim 2175$ MeV, and the spin-$1$ one is predicted with $\sim 2220$ MeV. The masses of hidden charmed tetraquarks from $1S$ to $2P$ excitations are systemically calculated in terms of the same potentials. It is found that the mass of hidden charmed tetraquark without radial excitation grows higher in $1^{+-},~1^{++},~1^{--},~0^{-+},~0^{--},~1^{-+},~\cdots$ sequence, and the tetraquarks with exotic $J^{PC}=0^{--},~1^{-+}$ have higher masses. The hidden charmed tetraquarks with radial excitations have masses larger than $4300$ MeV. The $1S-1P$ and $1S-2S$ mass splittings of the hidden charmed tetraquarks are about $390-400$ MeV and $550-570$ MeV, respectively, which are about $70$ MeV and $50$ MeV smaller than those of normal charmonium. The $1P-2P$ and $2S-2P$ mass splittings are similar to those for conventional $c\bar c$ charmonium mesons. Based on our predicted masses for hidden charmed tetraquarks, some XYZ exotics are analyzed and tentatively assigned. $X^*(3860)$ is possibly the $0^{++}$ tetraquark. $Z_c(3900)$ and $X(3940)$ are possibly the $1^{+-}$ tetraquarks, and $X(3872)$ is possibly a $1^{++}$ tetraquark. $X(4250)$ may be a $0^{-+}$, $0^{++}$ or $1^{-+}$ tetraquark, $X(4240)$ may be a $0^{--}$ tetraquark. With radial excitations, $X(4350)$ may be a $0^{++}$ tetraquark, $Z_c(4430)$ may be a $1^{+-}$ tetraquark, $X(4630)$ may be a $0^{-+}$ or $1^{-+}$ tetraquark, and $X(Y)(4660)$ may be the $1^{--}$ tetraquark. $Y(4008)$ or $Y(4390)$ seems impossibly the $1^{--}$ tetraquark.