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 $A\to B_1{B}_2\to C_1{C}_2\dots$, we prove that the angular correlation function $I({\theta }_1,{\theta }_2,{\varphi }_{+})$ 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.