Low Energy Effective Field Theory Operator Basis at $d \le 9$

TL;DR

This paper systematically constructs a complete basis of operators up to dimension 9 for the low energy effective field theory, crucial for understanding physics effects between the QCD and electroweak scales.

Contribution

It introduces a novel algorithm ensuring basis independence and provides the first comprehensive list of operators at dimensions 8 and 9, including flavor and violation classifications.

Findings

Complete operator bases at dimensions 5-9 are established.

Lists include over 700,000 operators for three generations.

Algorithm guarantees basis independence despite fermion masses.

Abstract

We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for the low energy effective field theory (LEFT), which parametrize various physics effects between the QCD scale and the electroweak scale. The independence of the operator basis regarding the equation of motion, integration by parts and flavor relations, is guaranteed by our algorithm, whose validity for the LEFT with massive fermions involved is proved by a generalization of the amplitude-operator correspondence. At dimension 8 and 9, we list the 35058 (756) and 704584 (3686) operators for three (one) generations of fermions categorized by their baryon and lepton number violations $(\Delta B, \Delta L)$, as these operators are of most phenomenological relevance.