Mass spectrum of fully charmed [cc][ c c] tetraquarks

There are three S and seven P fully charmed [cc][ c c] tetraquarks, the mass spectrum from $1S$ to $2P$ excitations is calculated in a non-relativistic 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 σ and vector ω boson exchange potentials. In the numerical results, though the scalar σ and vector ω boson exchange interactions reduce the masses of $S-$wave [cc][ c c] tetraquarks $40-50$ MeV, they contribute to the masses of other [cc][ c c] tetraquarks small. The mass splittings of [cc][ c c] tetraquarks between different multiplets and within the same multiplet are smaller than those in charmonium, and the splittings are affected by the scalar σ or vector ω boson exchange interactions small. Our calculations suggest that the observed $X(6600)$, $X(6900)$ and $X(7300)$ should be different radial excitations of [cc][ c c]. The measurements of the JPC quantum numbers and the mass splittings will be helpful to identify and understand of the [cc][ c c] candidates.