Possible JPC=0-- exotic state

In order to explore the possible existence of the exotic 0(--) state, we have constructed the tetraquark interpolating operators systematically. As a byproduct, we notice the 0(+-) tetraquark operators without derivatives do not exist. The special Lorentz structure of the 0(--) currents forbids the four-quark type of corrections to the spectral density. Now the gluon condensates are the dominant power corrections. None of the seven interpolating currents support a resonant signal. Therefore we conclude that the exotic 0(--) state does not exist below 2 GeV, which is consistent with the current experimental observations.