Eur. Phys. J. C (2023) 83: 810
https://doi.org/10.1140/epjc/s10052-023-11956-3

Regular Article - Theoretical Physics

Mass spectra of hidden heavy-flavor tetraquarks with two and four heavy quarks

¹ Institute of Theoretical Physics, College of Physics and Electronic Engineering, Northwest Normal University, 730070, Lanzhou, China
² Lanzhou Center for Theoretical Physics, Lanzhou University, 730000, Lanzhou, China

^c jiadj@nwnu.edu.cn

Received: 4 April 2023
Accepted: 24 August 2023
Published online: 11 September 2023

Abstract

Inspired by the observation of the X(6900) by LHCb and the X(6600) (with mass $6552\pm 10\pm 12$ MeV) recently by CMS and ATLAS experiments of the LHC in the di-$J/\Psi$ invariant mass spectrum, we systemically study masses of all ground-state configurations of the hidden heavy-flavor tetraquarks $q_1{Q}_2{\overline{q}}_3{\overline{Q}}_4$ and $Q_1{Q}_2{\overline{Q}}_3{\overline{Q}}_4$$(Q=c,b$; $q=u,d,s)$ containing two and four heavy quarks in the MIT bag model with chromomagnetic interaction and enhanced binding energy. Considering color-spin mixing due to chromomagnetic interaction, our mass computation indicates that the observed X(6600) is likely to be the $0^{++}$ ground states of hidden-charm tetraquark $cc\overline{c}\overline{c}$ with computed masses 6572 MeV, which has a $0^{++}$ color partner around 6469 MeV. The fully bottom system of tetraquark $bb\overline{b}\overline{b}$ has masses of 19685 MeV and 19717 MeV for the $0^{++}$ ground states. Further calculation of the tetraquark systems $sc\overline{s}\overline{c}$, $sb\overline{s}\overline{b}$, $cb\overline{c}\overline{b}$, $nc\overline{n}\overline{c}$ and $nb\overline{n}\overline{b}$ shows that $Z_c(4200)$ is a $1^{+-}$ state of tetraquark $nc\overline{n}\overline{c}$ and Z(4020) is a $1^{+-}$ state of tetraquark $nc\overline{n}\overline{c}$ with a mass of 4079 MeV. All of these tetraquarks are above their lowest thresholds of two mesons and unstable against the strong decays.