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

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-like currents as interpolating currents in the correlator, from which the $1^{+-}$ states are also studied. In the mass extraction, we use the standard stability criterion with respect to the Borel parameters and the QCD continuum thresholds and consider the effect of the violation of factorization in estimating the high dimensional condensates as a source of uncertainties. The obtained mass prediction $1.66\pm0.14$ GeV is much lower than the previous sum rule predictions obtained using the scalar currents. Our result favours the four-quark interpretation of the possible $\rho\pi$ dominance in the $D^0$ decay. We also discuss the possible decay patterns of these exotic four-quark states.