String-like confinement model for multi-quark systems applied to fully-charmed tetraquarks

Quark confinement mechanism in multi-quark systems is non-trivial because the color configuration in multiquark systems is not unique. It is important to identify the color basis to represent both a compact multi-quark state and two- (or multi-) hadron asymptotic states. We propose a new color basis system and confinement mechanism for the tetra-quark hadrons according to the string confinement picture of QCD. As a concrete example we take the fully-charmed tetraquark "cc c-bar c-bar" system, where a few resonant states were recently observed at the LHC experiments.

First we extend the color Hilbert space to include a “hidden color” (HC) state, which is mixed with the two-meson states such as J/psi-J/psi. The mixing of the HC state leads to attraction sufficient to form a bound state. We apply a realistic Hamiltonian model with the new color scheme for the fully charmed tetraquark sysytem. The full four-body Schroedinger equation is solved with the use of the Gaussian expansion method and the bound and resonant states are obtained as poles of the scattering amplitude in the complex plane by the use of the complex scaling method. We find a bound state and some resonant states in the J(PC)= 1(+-) and 2(++) channels of the cc c-bar c-bar system. The results are compared with recent experimental data and show advantage and validity of our approach.