Dalitz Plot Structure in $D^0 \to \pi^+ \pi^- \pi^0$

TL;DR

This paper investigates the Dalitz plot structure in the decay $D^0 o \pi^+ ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{ and its relation to isospin-zero dominance and amplitude cancellations.

Contribution

The paper explains the Dalitz plot depletion in $D^0 o \pi^+ ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{-} ext{ decays as arising from amplitude cancellations without requiring exotic resonances.

Findings

Dalitz plot shows near-complete depletion along diagonals.

Depletion explained by cancellation of isospin amplitudes.

No evidence for exotic resonance with $J^{PC} = 0^{--}$.

Abstract

The BaBar Collaboration has pointed out that $D^0 \to \pi^+ \pi^- \pi^0$ is dominated by an isospin-zero final state, leading to nearly complete depletion of the Dalitz plot along all three diagonals. In flavor-SU(3) approaches to charmed particle decays to a light vector and a light pseudoscalar particle, this behavior is seen, but does not appear to have a fundamental origin. Instead, it arises as a result of approximate cancellation of higher-isospin combinations of several types of amplitudes: color-favored tree, color-suppressed tree, and exchange. Interpretation in terms of a direct-channel effect would require an exotic resonance, with spin, parity, and charge-congjugation eigenvalues $J^{PC} = 0^{--}$.