Tetraquark state X(6900) and the interaction between diquark and antidiquark

Recently LHCb declared a new structure X(6900) in the final state di-J/psi which is popularly regarded as a cc-(c) over bar(c) over bar tetraquark state. Within the Bethe-Salpeter (B-S) framework we study the possible cc-(c) over bar(c) over bar bound states and the interaction between diquark (cc) and antidiquark ((c) over bar(c) over bar). In this work cc ((c) over bar(c) over bar) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of cc-(c) over bar(c) over bar bound state are 0(+), 1(+) and 2(+). Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for the diquark and antidiquark system. Then we deduce the B-S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of X(6900) when we assign appropriate values for parameter kappa introduced in the interaction (kernel). We also briefly calculate the spectra of bb-(b) over bar(b) over bar bound states. Future measurement of bb-(b) over bar(b) over bar state will help us to determine the exact form of effective interaction.

Automated summary

This study investigates the possible cc-(c) over bar(c) over bar bound states and the interaction between diquark (cc) and antidiquark ((c) over bar(c) over bar) within the Bethe-Salpeter framework. Numerical solutions of the B-S equations for different quantum numbers show that some excited states' spectra can be close to the mass of the newly discovered X(6900) with appropriate parameter values. Future measurements of the bb-(b) over bar(b) over bar state may aid in determining the exact form of effective interaction.