Dalitz plot as follows. Let $T_0$, $T_+$ and $T_-$ be the kinetic energies of the pions, and $Q$ be the difference between the $\omega$ mass, $M_{\omega}$, and the mass of the 3 pions. We define two orthogonal coordinates $X$ and $Y$, where $$\begin{aligned}
        X &= &3T_0/Q - 1       \\
        Y &= &\sqrt{3}(T_+ - T_-)/Q~~~.\end{aligned}$$ The kinematic limit that defines the Dalitz plot boundary is defined as $$Y_{boundary}^2 = {1\over 3} 
(X_{boundary}+1)(X_{boundary}+1+a) (1+b/(X_{boundary}+1-c))$$ where $a = 6m_0 / Q$, $b = 6m^2 / (M_{\omega}Q)$, $c = 3(M_{\omega}-m_0)^2/(2M_{\omega}Q)$, $m$ is the mass of a charged pion and $m_0$ the mass of the neutral pion.

For any set of three pion kinetic energies, we define a variable $r$, properly scaled to the kinematic limit as $$r=\sqrt{{X^2+Y^2}\over{X_{boundary}^2+Y_{boundary}^2}}~~~,$$ where the boundary values are found by following the radial vector from (0,0) through $(X,Y)$.

For events in the $B$ mass peak we show in Fig. \[m3\_dal\_all\] the $\pi^+\pi^-\pi^o$ invariant mass for three different cuts on $r$. The $\omega$ signal is purified by using a selection on $r$.

For further analysis we select $\omega$ candidates within the the $\pi^+\pi^-\pi^o$ mass window of 782$\pm$20 MeV with $r<0.7$. We also abandon the $\chi^2$ cut as background is less of 