Complete UV Resonances of the Dimension-8 SMEFT Operators

TL;DR

This paper systematically classifies dimension-8 SMEFT operators and their UV origins, identifying 146 tree-level resonances and clarifying the operator-resonance correspondence using the j-basis method.

Contribution

It introduces the dimension-8 j-basis operators in SMEFT and maps them to UV resonances, providing a comprehensive database and computational tools.

Findings

Identified 146 tree-level UV resonances for dimension-8 operators.

Clarified subtleties in operator generation and field redefinitions.

Provided a Mathematica toolkit and database for researchers.

Abstract

The effective field theory approach parameterizes the low energy behaviors of all possible ultraviolet (UV) theories in a systematic way. One of the most important tasks is thus to find the connection between the effective operators and their UV origins. The redundancy relations among operators make the connection very subtle, hence we proposed the j-basis prescription to illuminate the correspondence between operators and their UV resonances in the bottom-up way. In this work, we work out the dimension-8 j-basis operators in the standard model effective field theory (SMEFT), and find all the 146 (82) tree-level UV resonances along with their couplings up to mass dimension 5 (4). Furthermore, we point out a few subtleties on operator generation via field redefinition and on the UV Lagrangian for generic spin resonances. We also provide a data base storing our results and a \texttt{Mathematica} notebook for extracting those results for the reader's conveinence.