The $X(6550), X(6900), X(7280)$ resonances as the $nS, cc\bar c\bar c$ states

Abstract

\date{\today} Within the diquark-antidiquark model the masses of the $0^{++}, cc\bar c\bar c$ resonances are calculated, using the expansion of the four-quark wave function in the set of the hyperspherical functions. The interaction is defined via a universal pair-wise potential, which does not contain fitting parameters. The resulting masses $M_4(nS)$ are shown to be very sensitive to the value of $c-$quark mass, chosen in relativistic string Hamiltonian, and $m_c=1.24, 1.30, 1.43$ (in GeV) are considered. The choice of $m_c$, equal to the current mass, $m_c=1.245$ GeV, yields three $nS~(n_r=0,1,2)$ states in a very good agreement with the masses of the $X(6550), X(6900), X(7287)$ resonances, if the gluon-exchange interaction is totally neglected. This fact indicates on a possible screening of the gluon-exchange interaction inhe $cc\bar c\bar c$ system. For $m_c=1.43$~GeV the ground state mass $M_4(1S)=6557$~MeV is obtained in agreement with experiment only if $\alpha_{\rm V}\cong 0.39(1)$ is used, however, in this case the masses of the $2S, 3S$ radial excitations exceed the masses of $X(6900), X(7280)$ by $\sim 100$~MeV.