A complete tree-level dictionary between simplified BSM models and SMEFT (d $\leq$ 7) operators

TL;DR

This paper systematically maps all tree-level UV resonances to SMEFT operators up to dimension 7, creating a comprehensive dictionary that aids in understanding possible UV completions of effective operators.

Contribution

It provides the first complete tree-level UV resonance to SMEFT operator dictionary for operators up to dimension 7, using functional matching and operator reduction methods.

Findings

All tree-level UV resonances for dimension-5, -6, and -7 operators identified.

Established the correspondence between UV resonances and Wilson coefficients.

Methods extendable to higher-dimensional operators and other EFTs.

Abstract

Finding all possible UV resonances of effective operators is an important task in the bottom-up approach of effective field theory. We present all the tree-level UV resonances for the dimension-5, -6 and -7 operators in the Standard Model effective field theory (SMEFT), and then obtain the correspondence between the UV resonances and the effective operators from the relations among their Wilson coefficients, through the functional matching and operator reduction procedure. This provides a cross-dimension UV/IR dictionary for the SMEFT at tree-level, and the methods used here, especially the on-shell construction of general UV Lagrangian and the systematic reduction of operators, are extendable for UV resonances of $d \geq 8$ operators in SMEFT and other EFTs.