Low-Energy Effective Field Theory below the Electroweak Scale: Dimension-8 Operators

TL;DR

This paper develops a comprehensive basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak scale, essential for precise matching with the Standard Model Effective Field Theory.

Contribution

It provides the first complete enumeration of dimension-8 operators in LEFT for multiple generations, facilitating advanced theoretical analyses.

Findings

Identifies 35,058 dimension-8 operators for specified fermion generations.

Establishes a necessary operator basis for matching to SMEFT at dimension-8.

Enables more accurate low-energy phenomenological studies.

Abstract

We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level.