Hilbert series for ALP EFTs

TL;DR

This paper computes Hilbert series for ALP effective field theories, classifying operators and revealing symmetry structures, aiding the systematic study of ALP interactions with the Standard Model.

Contribution

It explicitly calculates Hilbert series for ALP EFTs up to dimension 8 and provides a comprehensive operator basis, including a dataset up to dimension 15.

Findings

Hilbert series isolates shift-symmetry breaking interactions

Enumeration of CP-violation sources in ALP EFTs

Provided an ancillary file with Hilbert series up to dimension 15

Abstract

Axions and axion-like particles (ALPs) are ubiquitous in popular attempts to solve supercalifragilisticexpialidocious puzzles of Nature. A widespread and vivid experimental programme spanning a vast range of mass scales and decades of couplings strives to find evidence for these elusive but theoretically well-motivated particles. In the absence of clear guiding principle, effective field theories (EFTs) prove to be an efficient tool in this experimental quest. Hilbert series technologies are a privileged instrument of the EFT toolbox to enumerate and classify operators. In this work, we compute explicitly the Hilbert series capturing the interactions of a generic ALP to the Standard Model particles above and below the electroweak symmetry scale, which allow us to build bases of operators up to dimension 8. In particular, we revealed a remarkable structure of the Hilbert series that isolates the shift-symmetry breaking and preserving interactions. In addition, with the Hilbert series method, we enumerate the sources of CP violation in terms of CP-even, CP-odd and CP-violating operators. Furthermore, we provide an ancillary file of the Hilbert series up to dimension 15 to supplement our findings, which can be used for further analysis and exploration.