The Possible J^{PC}=0^{--} Exotic State

TL;DR

This paper investigates the existence of the exotic $0^{--}$ tetraquark state using QCD sum rules and finds no evidence for such a state below 2 GeV, aligning with current experimental data.

Contribution

The study systematically constructs tetraquark operators for the $0^{--}$ state and demonstrates its non-existence below 2 GeV using finite energy sum rules.

Findings

No resonant $0^{--}$ signals found below 2 GeV

$0^{+-}$ tetraquark operators without derivatives do not exist

Gluon condensate dominates the spectral density correction

Abstract

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 correction to the spectral density. Now the gluon condensate is the dominant power correction. Within the framework of the finite energy sum rule, none of the seven interpolating currents supports 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.