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We study the exotic $J^{PC}=0^{--}$ four-quark states in Laplace sum rules(LSR) and finite energy sum rules (FESR). We use the vector tetraquark-likecurrents as interpolating currents in the correlator, from which the $1^{+-}$states are also studied. In the mass extraction, we use the standard stabilitycriterion with respect to the Borel parameters and the QCD continuum thresholdsand consider the effect of the violation of factorization in estimating thehigh dimensional condensates as a source of uncertainties. The obtained massprediction $1.66\pm0.14$ GeV is much lower than the previous sum rulepredictions obtained using the scalar currents. Our result favours thefour-quark interpretation of the possible $\rho\pi$ dominance in the $D^0$decay. We also discuss the possible decay patterns of these exotic four-quarkstates.

Investigation of the light four-quark states with exotic $J^{PC}=0^{--}$