Constructing on-shell operator basis for all masses and spins
Zi-Yu Dong, T. Ma, Jing Shu
Abstract
We propose a theory to systematically construct a complete set of on-shell effective operator bases involving massive particles with any spins. The amplitude bases involving massive fields can be factorized into two charged and neutral parts under the little groups of massive particles, respectively. The complete bases of these two parts can be constructed by the Young diagrams of Lorentz subgroup $SU(2{)}_{r}$ and global symmetry $U(N)$ ($N$ is the number of external particles), respectively, without any redundancies. The corresponding effective field theory bases with the lowest dimension can be obtained by eliminating the linear correlation bases from a complete but redundant set of bases with all possible polarization tensors. Based on this theory, the amplitude bases involving identical particles can be constructed by a matrix projection method. A generic massive effective field theory can thus be constructed automatically by computer programs.