Endpoint symmetries of helicity amplitudes

We investigate helicity amplitudes (HAs) of A -> BC-type decays for arbitrary spin towards the kine-matic endpoint. We show that HAs are proportional to product of Clebsch-Gordan coefficients (CGC) and the velocity to a non-negative power. The latter can be zero in which case the HA is non-vanishing at the endpoint. At the kinematic endpoint the explicit breaking of rotational symmetry, through the external momenta, is restored and the findings can be interpreted as a special case of the Wigner-Eckart theorem. Our findings are useful for i) checking theoretical computations and ii) the case where there is a sequence of decays, say B -> B1B2 with the pair (B1B2) not interacting (significantly) with the C-particle. Angular observables, which are ratios of HAs, are given by ratios of CGC at the endpoint. We briefly discuss power corrections in the velocity to the leading order. Crown Copyright (C) 2022 Published by Elsevier B.V.

Automated summary

The study investigates helicity amplitudes (HAs) of A -> BC-type decays for arbitrary spin towards the kinematic endpoint, showing that HAs are proportional to the product of Clebsch-Gordan coefficients (CGC) and the velocity to a non-negative power. At the kinematic endpoint, the explicit breaking of rotational symmetry through external momenta is restored, interpreted as a special case of the Wigner-Eckart theorem. Angular observables are given by ratios of CGC at the endpoint.