= Tau hadronic polarimetry
{title2=$d\Gamma/d\cos\vartheta\propto1+\alpha_hP_\tau\cos\vartheta$}
The visible <angular distribution> and laboratory <energy> in $\tau^-\to h^-\nu_\tau$ carry information about the parent's <spin>. For fixed hadronic <invariant mass>, $E_h=\gamma(E_h^*+\beta p_h^*\cos\vartheta)$. A spin-zero recoil has analyzing coefficient $\alpha_h=1$. For a spin-one recoil coupled through the <V-A interaction>, longitudinal and transverse partial rates have weights $m_\tau^2:2m_h^2$ and opposite slopes, giving $\alpha_h=(m_\tau^2-2m_h^2)/(m_\tau^2+2m_h^2)$. Thus the harder-helicity ordering can reverse when the recoil <mass> exceeds $m_\tau/\sqrt2$. A mean <invariant mass> without spin-dependent spectral weights cannot fix the sign for a mixed sample.
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