Higher fully charmed tetraquarks: Radial excitations and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>-wave states

Abstract

We systematically calculate the mass spectrum of the higher excited fully charmed tetraquark $cc\overline{c}\overline{c}$ states including the $S$-wave radial excitations and the $P$-wave states with a nonrelativistic quark model. The quark model is composed of a vector one-gluon-exchange and a scalar linear confinement interaction with the parameters determined by the charmonium spectrum. In the calculation, we consider both the ${3}_{c}\ensuremath{-}{\overline{3}}_{c}$ and the ${6}_{c}\ensuremath{-}{\overline{6}}_{c}$ color representations. For the $cc\overline{c}\overline{c}$ state, the ${6}_{c}\ensuremath{-}{\overline{6}}_{c}$ component is located lower than the ${\overline{3}}_{c}\ensuremath{-}{3}_{c}$ one because of the stronger attractive interactions between the diquark and antidiquark. We focus on two excited modes and their properties for the $P$-wave tetraquarks. The mass splitting for the $\ensuremath{\rho}$-mode excitations with different color configurations is large. The low-lying ${6}_{c}\ensuremath{-}{\overline{6}}_{c}$ $\ensuremath{\rho}$-mode component helps to explain the small mass gap between the ground $S$-wave and the $P$-wave tetraquark states. The recently observed $X(6900)$ state may be the candidate of the first radially excited tetraquarks with ${J}^{PC}={0}^{++}$ or ${2}^{++}$, or the ${1}^{+\ensuremath{-}}$ or ${2}^{\ensuremath{-}+}$ $P$-wave states based on the mass spectrum. Moreover, the lowest ${T}_{c}$ states with the exotic ${J}^{PC}$ quantum numbers ${0}^{\ensuremath{-}\ensuremath{-}}$ and ${1}^{\ensuremath{-}+}$ may decay into the $P$-wave ${\ensuremath{\eta}}_{c}J/\ensuremath{\psi}$ and di-$J/\ensuremath{\psi}$ modes, respectively. The future experimental search of these ${T}_{c}$ states will enrich the hadronic spectrum.

Topics & Concepts