Endpoint Symmetries of Helicity Amplitudes

We investigate helicity amplitudes (HAs) of $A \to B C$-type decays for arbitrary spin towards the kinematic endpoint. We show that they are proportional to product of Clebsch-Gordan coefficients (CGC) and the velocity to some positive power. The latter can be zero in which case the HA is non-vanishing at the endpoint. In essence the spatial rotational symmetry, broken by the relative spatial momenta of the particles, is restored at the kinematic endpoint. Therefore SO(3) and SU(2), for bosons and fermion in the decay, act like a global internal symmetry groups. Some of our results can be understood in terms of the Wigner- Eckart theorem. The findings are useful for i) checking theoretical computations and ii) the case where there is a sequence of decays, say $B \to B_1B_2$ with the pair $(B_1B_2)$ not interacting (significantly) with the $C$-particle. An example is $H \to Z Z^* \to 4\ell$ where our findings might be of use for experimentally determining the Higgs quantum numbers. Angular observables, which are essentially ratios of HAs, are given by ratios of CGC at the endpoint. We briefly discuss power corrections in the velocity to the leading order.