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$X (3872)$ and hidden charmed tetraquarks

You-You Lin, Ji-Ying Wang, and Ailin Zhang ^*

Department of Physics, Shanghai University, Shanghai 200444, China

^*Contact author: zhangal@shu.edu.cn

Phys. Rev. D 112, 034036 – Published 28 August, 2025

DOI: https://doi.org/10.1103/3vbj-jmfn

Abstract

In a constituent quark model, a hidden charmed tetraquark is assumed consisting of a $c q$ diquark and an $\bar{c} \bar{q}$ antidiquark or vice versa. The Semay-Silvestre-Brac potentials are employed to calculate the masses of $c q$ ( $q = u$ , d) diquarks. The mass of the $c q$ 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 $1 S$ to $2 P$ excitations are systematically calculated in terms of the same potentials. It is found that the mass of hidden charmed tetraquarks without radial excitation grows higher in $1^{+ -}, 1^{+ +}, 1^{- -}, 0^{- +}, 0^{- -}, 1^{- +}, \dots$ sequence, and the tetraquarks with exotic $J^{P C} = 0^{- -}, 1^{- +}$ have higher masses. The hidden charmed tetraquarks with radial excitations have masses greater than 4300 MeV. The $1 S - 1 P$ and $1 S - 2 S$ mass splittings of the hidden charmed tetraquarks are about 390–400 and 550–570 MeV, respectively, which are about 50 and 40 MeV smaller than those of normal charmoniums. The $1 P - 2 P$ and $2 S - 2 P$ 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 impossible to be the $1^{- -}$ tetraquark. In experiments, for the identification of a normal charmonium or a charmonium-like exotic, it is also important to take into account the mixing of normal charmoniums with hidden-flavor charmonium-like exotics.

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Phys. Rev. D 112, 034036– Published 28 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 30 June 2025
Accepted 8 August 2025

DOI: https://doi.org/10.1103/3vbj-jmfn

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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$X (3872)$ and hidden charmed tetraquarks

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X(3872) and hidden charmed tetraquarks

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References (108)

$X (3872)$ and hidden charmed tetraquarks