Eur. Phys. J. Plus (2024) 139: 707
https://doi.org/10.1140/epjp/s13360-024-05480-w

Regular Article

Mass spectrum of fully charmed $[cc][\overline{c}\overline{c}]$ tetraquarks

Department of Physics, Shanghai University, 200444, Shanghai, China

^c zhangal@shu.edu.cn

Received: 20 March 2024
Accepted: 21 July 2024
Published online: 8 August 2024

Abstract

There are three S and seven P fully charmed $[cc][\overline{c}\overline{c}]$ tetraquarks, the mass spectrum from 1S to 2P excitations is calculated in a nonrelativistic quark potential model. In the calculation, the interactions among four internal quarks/antiquark are approximated as a dominant color interaction between a diquark and an antidiquark, and a residual interaction responsible for the diquark/antidiquark cluster effect. The color interaction between the diquark and the antidiquark is characterized by the conventional Cornell potential, while the residual interaction is modeled as the Yukawa-type scalar $\sigma$ and vector $\omega$ boson-exchange potentials. In the numerical results, though the scalar $\sigma$ and vector $\omega$ boson-exchange interactions reduce the masses of S-wave $[cc][\overline{c}\overline{c}]$ tetraquarks 40–50 MeV, they contribute to the masses of other $[cc][\overline{c}\overline{c}]$ tetraquarks small. The mass splittings of $[cc][\overline{c}\overline{c}]$ tetraquarks between different multiplets and within the same multiplet are smaller than those in charmonium, and the splittings are affected by the scalar $\sigma$ or vector $\omega$ boson-exchange interactions small. Our calculations suggest that the observed X(6600), X(6900) and X(7300) should be different radial excitations of $[cc][\overline{c}\overline{c}]$. The measurements of the $J^{\mathit{PC}}$ quantum numbers and the mass splittings will be helpful to identify and understand of the $[cc][\overline{c}\overline{c}]$ candidates.