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

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