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 and vector boson exchange potentials. In the numerical results, though the scalar and vector 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 or vector 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 J^PC quantum numbers and the mass splittings will be helpful to identify and understand of the cc c c candidates.