Operators For Generic Effective Field Theory at any Dimension: On-shell Amplitude Basis Construction

TL;DR

This paper introduces a comprehensive method for constructing complete operator bases in effective field theories using on-shell amplitude techniques, applicable to any dimension, gauge symmetry, and field content.

Contribution

It presents a unified on-shell amplitude approach to systematically build operator bases for EFTs, including new algorithms and a Mathematica package for practical implementation.

Findings

Constructed various operator bases emphasizing independence, flavor, and quantum numbers.

Developed algorithms for basis generation using group theory and Young tableaux.

Implemented a Mathematica package for basis conversion and construction.

Abstract

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 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 (Amplitude Basis Construction for Effective Field Theories).