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

Abstract

Abstract Recently LHCb declared a new structure X(6900) in the final state di- $$J/\psi $$ J / ψ which is popularly regarded as a cc- $$\bar{c}\bar{c}$$ c ¯ c ¯ tetraquark state. Within the Bethe–Salpeter (B–S) framework we study the possible cc- $$\bar{c}\bar{c}$$ c ¯ c ¯ bound states and the interaction between diquark (cc) and antidiquark ( $$\bar{c}\bar{c}$$ c ¯ c ¯ ). In this work cc ( $$\bar{c}\bar{c}$$ c ¯ c ¯ ) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of cc- $$\bar{c}\bar{c}$$ c ¯ c ¯ bound state are $$0^+$$ 0 + , $$1^+$$ 1 + and $$2^+$$ 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 $$\kappa $$ κ introduced in the interaction (kernel). We also briefly calculate the spectra of bb- $$\bar{b}\bar{b}$$ b ¯ b ¯ bound states. Future measurement of bb- $$\bar{b}\bar{b}$$ b ¯ b ¯ state will help us to determine the exact form of effective interaction.