23, 381, 6242, 103268, 1743183, ...: Hilbert series for CP-violating operators in SMEFT

TL;DR

This paper presents a systematic, efficient method using Hilbert series to classify CP-violating operators in SMEFT across multiple dimensions, providing a complete enumeration up to dimension 14.

Contribution

The authors develop a novel Hilbert series-based approach for classifying CP properties of SMEFT operators, enabling rapid enumeration of CP-violating operators.

Findings

Complete classification of dimension eight CP-violating operators.

Enumeration of CP-odd operators up to dimension 14.

Provision of a FORM code for reproducing results.

Abstract

We introduce a systematic method to classify the Standard Model Effective Field Theory (SMEFT) operators based on their CP properties with the Hilbert series techniques. Our method makes it possible to enumerate operators violating CP symmetry in a few seconds. We present the complete classification of dimension eight operators under CP transformation, and the number of CP-odd or CP-violating operators are listed up to dimension 14. We also provide a companion code in FORM that allows anybody to reproduce our results.