A theorem about two-body decay and its application for a doubly-charged boson $H^{\pm\pm}$ going to $\tau^{\pm}\tau^{\pm}$
In a general decay chain $A\to B_1B_2\to C_1C_2\ldots$, we prove that the angular correlation function $I(\theta_1,\theta_2,\phi_+)$ in the decay of $B_{1,2}$ is irrelevant to the polarization of the mother particle $A$ at production. This guarantees that we can use these angular distributions to determine the spin-parity nature of $A$ without knowing its production details. As an example, we investigate the decay of a potential doubly-charged boson $H^{\pm\pm}$ going to same-sign $\tau$ lepton pair.