Coulomb gauge model for hidden charm tetraquarks

Abstract

The spectrum of tetraquark states with hidden charm is studied within an effective QCD Coulomb gauge Hamiltonian approach. Of the four independent color schemes, two are investigated, the $(q\bar{c})_1(c\bar{q})_1$ singlet-singlet (molecule) and the $(qc)_3(\bar{q}\bar{c})_3$ triplet-triplet (diquark), for selected $J^{PC}$ states using a variational method. The predicted masses of triplet-triplet tetraquarks are roughly a GeV heavier than the singlet-singlet states. There is also an interesting flavor dependence with $(q\bar{q})_1(c\bar{c}_1)$ states about half a GeV lighter than $(q\bar{c})_1(\bar{q}c)_1$. The lightest $1^{++}$ and $1^{--}$ predictions are in agreement with the observed X(3872) and Y(4008) masses, respectively, suggesting they both have a $\omega J/ \psi$ rather than $D^*\bar D^*$ molecular type structure. This is consistent with observed $X$, $Y$ decays to $\pi^\pm J/ \psi$ and not $D^*\bar D^*$ .