Weaving the covariant three-point vertices efficiently

An efficient algorithm is developed for compactly weaving all the Lorentz-covariant three-point vertices in relation to the decay of a massive particle of mass and spin into two particles with equal mass and spin . The closely related equivalence between the helicity formalism and the covariant formulation is utilized so as to identify the basic building blocks for constructing the covariant three-point vertex corresponding to each helicity combination explicitly. The massless case with is worked out straightforwardly and the (anti)symmetrization of the three-point vertex required by the spin statistics of identical particles is made systematically. We show that the off-shell electromagnetic photon coupling to the states and can be accommodated in this framework. The power of the algorithm is demonstrated with a few typical examples with specific and values.