Therefore, we rule out a spin-0 assignment for the $A^-$.

To determine the $J^P$ we need a more well defined final state. This is provided by analysis of $B\to D\omega\pi^-$ decays.

Observation of $\overline{B}\to D\omega\pi^-$ Decays {#sec:Domegapi}
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$B$ candidate selection
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Here we study the reactions $\overline{B}\to D\omega\pi^-$, with either a $D^o\to K^-\pi^+$ or $D^+\to K^-\pi^+\pi^+$ decay. Other $D^o$ or $D^+$ decays have substantially larger backgrounds.

Although we are restricting our search to $\omega$’s, we define two $\pi^+\pi^-\pi^0$ samples. One within 20 MeV of the known $\omega$ mass (782 MeV) and the other in either low mass or high mass sideband defined as three $\pi$ mass either between 732 and 752 MeV or between 812 and 832 MeV. We also require a cut on the $\omega$ Dalitz plot of $r < 0.7.$

To reduce backgrounds we define $$\label{eq:chisqD} 
\chi_b^2=  
\left({{\Delta M_{D}}\over {\sigma(\Delta M_{D})}}\right)^2 +  
\left({{\Delta M_{\omega}}\over {\sigma(\Delta 
M_{\omega})}}\right)^2 +  
\left({{\Delta M_{\pi^o}}\over {\sigma(\Delta 
M_{\pi^o})}}\right)^2~~~,$$ where $\Delta M_{D}$ is the invariant candidate $D^o$ mass minus the known $D^o$ mass, $\Delta M_{\omega}$ is the invariant candidate $\omega$ mass minus the known $\omega$ mass, and $\Delta M_{\pi^o}$ is the measured $\gamma\gamma$ invariant mass minus the known $\pi^o$ mass. The $\sigma$’s are the measurement 