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  • Letter
  • Open Access

Constructing on-shell operator basis for all masses and spins

Zi-Yu Dong1,2,3, Teng Ma4, and Jing Shu5,6,7

  • 1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
  • 3Department of Physics, LEPP, Cornell University, Ithaca, New York 14853, USA
  • 4Physics Department, Technion–Israel Institute of Technology, Haifa 3200003, Israel
  • 5School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
  • 6Center for High Energy Physics, Peking University, Beijing 100871, China
  • 7Beijing Laser Acceleration Innovation Center, Huairou, Beijing 101400, China

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Phys. Rev. D 107, L111901 – Published 27 June, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.L111901

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.

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Phys. Rev. D 107, L111901– Published 27 June, 2023
  • Received 17 June 2022
  • Accepted 30 May 2023
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