Constructing on-shell operator basis for all masses and spins

TL;DR

This paper introduces a systematic method for constructing complete on-shell operator bases involving massive particles of any spin, eliminating redundancies and enabling automated basis generation.

Contribution

The paper presents a novel, general approach to construct on-shell operator bases for massive particles with arbitrary spins, incorporating non-abelian little groups and avoiding redundancies.

Findings

Method systematically constructs complete bases without redundancies.

Bases can be generated automatically using computer programs.

Applicable to identical particles and complex spin cases.

Abstract

We first propose a general method to construct the complete set of on-shell operator bases involving massive particles with any spins. To incorporate the non-abelian little groups of massive particles, the on-shell scattering amplitude basis should be factorized into two parts: one is charged, and the other one is neutral under little groups of massive particles. The complete set of these two parts can be systematically constructed by choosing some specific Young diagrams of Lorentz subgroup and global symmetry $U(N)$ respectively ($N$ is the number of external particles), without the equation of motion and integration by part redundancy. Thus the complete massive amplitude bases without any redundancies can be obtained by combining these two complete sets. Some examples are presented to explicitly demonstrate this method. This method is applicable for constructing amplitude bases involving identical particles, and all the bases can be constructed automatically by computer programs based on it.