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

Abstract

The decay $D^0 \to \pi^+ \pi^- \pi^0$ appears to be dominated by $\rho \pi$ 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.