# A theorem about two-body decay and its application for a doubly-charged boson $H^{\pm\pm}$ going to $\tau^{\pm}\tau^{\pm}$

## TL;DR

This paper proves a general property of decay chains that allows the determination of a particle's spin-parity from angular distributions, exemplified by the decay of a hypothetical doubly-charged boson to tau pairs.

## Contribution

It establishes that angular correlations in certain decay chains are independent of the initial particle's polarization, aiding spin-parity analysis without production details.

## Key findings

- Angular correlation function is independent of the mother particle's polarization.
- Applicable to decay chains involving multiple steps.
- Demonstrates method with doubly-charged boson decay to tau pairs.

## Abstract

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.