P-wave fully charm and fully bottom tetraquark states

Abstract

We have studied the mass spectra of the P-wave fully charm and fully bottom tetraquark states in the framework of QCD sum rules. We construct the interpolating currents by inserting the covariant derivative operator ${\overleftrightarrow{\mathcal{D}}}_{\mu }$ between the S-wave diquark and antidiquark fields. The excitation structures show that the pure $\lambda$-mode excited P-wave fully heavy tetraquarks exist for the quantum numbers $J^{PC}=1^{--},1^{-+},2^{--},2^{-+}$ and $3^{--}$, while it is difficult to separate the $\lambda$-mode and $\rho$-mode excitations in the $0^{-+}$ channel. Within three Lorentz indices, there is no pure $\lambda$-mode excited P-wave fully charm/bottom tetraquark operators with $J^{PC}=0^{--}$ and $3^{-+}$. Our results support that the recent observed $X(6900)$ and $X(7200)$ resonances could be interpreted as the P-wave fully charm $cc\bar{c}\bar{c}$ tetraquark states with $J^{PC}=1^{-+}$ and $2^{-+}$, respectively. Some P-wave fully bottom $bb\bar{b}\bar{b}$ tetraquark states are predicted to be lower than the di-${\eta }_b(1S)$ and di-${\rm Y}(1S)$ mass thresholds. Hopefully our calculations will be useful for identifying the nature of new exotic tetraquark states.

Comments: 18 pages, 11 figures. Accepted by Physical Review D