Test for exotic isoscalar resonance dominating $D^0 \to π^+ π^- π^0$ decays

The decay $D^0 \to π^+ π^- π^0$ appears to be dominated by $ρπ$ states in a configuration of zero total isotopic spin. The spin $J$, parity $P$, and charge-conjugation eigenvalue $C$ of this final state are therefore $J^{PC} = 0^{--}$, which cannot be formed of a quark $q$ and antiquark $\bar q$. If a resonance near $M(D^0)$ dominates the final state, it must be a {\it hybrid} composed of a quark-antiquark pair and a constituent gluon, or a {\it tetraquark} $q q \bar q \bar q$. A test for this resonance in electroproduction is proposed.

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