Constructing the covariant three-point vertices systematically

TL;DR

This paper presents an algorithm for systematically constructing Lorentz covariant three-point vertices for particle decays involving arbitrary masses and spins, bridging helicity and covariant formalisms.

Contribution

It introduces a systematic method to construct all covariant three-point vertices, leveraging the helicity formalism for efficient enumeration.

Findings

Provides a one-to-one correspondence between helicity and covariant formalisms.

Enables systematic construction of all covariant three-point vertices.

Facilitates analysis of particle decay processes with arbitrary parameters.

Abstract

An algorithm is developed for efficiently constructing the Lorentz covariant effective three-point vertices of the decay of a particle into two daughter particles in which all the masses and spins of the three particles can be arbitrary. The closely-related one-to-one correspondence between the helicity formalism and the covariant formulation is exploited for counting the number of independent terms and identifying the basic covariant three-point vertices. Assembling the basic operators according to the developed algorithm enables us to construct all the covariant three-point vertices systematically.