The Bottom-Up EFT: Complete UV Resonances of the SMEFT Operators

TL;DR

This paper develops a systematic method to identify all possible UV resonances that can generate SMEFT operators at tree level, using the j-basis construction based on symmetry principles.

Contribution

It introduces the j-basis/UV correspondence and applies it to classify all tree-level UV origins of SMEFT operators up to dimension 8.

Findings

Complete list of UV origins for dimension 5, 6, 7 operators

Identification of all bosonic operators at dimension 8

Framework for bottom-up EFT analysis

Abstract

The standard model effective field theory (SMEFT) provides systematic parameterization of all possible new physics above the electroweak scale. According to the amplitude-operator correspondence, an effective operator can be decomposed into a linear combination of several j-basis operators, which correspond to local amplitudes carrying certain spin and gauge quantum numbers in a particular scattering channel. Based on the Poincare and gauge symmetries of scattering amplitude, we construct the j-basis using the Casimir method for both the Lorentz and gauge sectors. The quantum numbers of the j-basis operators fix the quantum numbers of any intermediate state in the corresponding amplitudes, such as a UV resonance. This can be re-interpreted as the j-basis/UV correspondence, thus obtaining the j-bases in all partitions of fields for an operator amounts to finding all of its UV origins at tree level, constituting the central part of the bottom-up EFT framework. Applying the j-basis analysis to SMEFT, we obtain a complete list of possible tree-level UV origins of the effective operators at the dimension 5, 6, 7, and all the bosonic operators at the dimension 8.