Operators for generic effective field theory at any dimension: on-shell amplitude basis construction

A bstract We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-c...

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Bibliographic Details
Published in:The journal of high energy physics 2022-04, Vol.2022 (4), p.140-89, Article 140
Main Authors: Li, Hao-Lin, Ren, Zhe, Xiao, Ming-Lei, Yu, Jiang-Hao, Zheng, Yu-Hui
Format: Article
Language:English
Subjects:
Algorithms
Amplitudes
Classical and Quantum Gravitation
Effective Field Theories
Elementary Particles
Field theory
Flavor (particle physics)
Group theory
High energy physics
Linear algebra
Mathematical analysis
Matrix representation
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum numbers
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scattering Amplitudes
SMEFT
String Theory
Tensors
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Summary:A bstract We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-called amplitude operator correspondence, we provide a unified construction of the Lorentz and gauge and flavor structures by Young Tableau tensor. Several bases are constructed to emphasize different aspects: independence (y-basis and m-basis), repeated fields with flavors (p-basis and f-basis), and conserved quantum numbers (j-basis). We also provide new algorithms for finding the m-basis by defining inner products for group factors and the p-basis by constructing the matrix representations of the Young symmetrizers from group generators. The on-shell amplitude basis gives us a systematic way to convert any operator into such basis, so that the conversions between any other operator bases can be easily done by linear algebra. All of these are implemented in a Mathematica package: ABC4EFT ( A mplitude B asis C onstruction for E ffective F ield T heories).
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2022)140