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Hilbert series for ALP EFTs
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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.
Forward citations
Cited by 5 Pith papers
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Finite-temperature operator basis on $\mathbb{R}^3 \times S^1$ for SMEFT
The paper delivers the first complete non-redundant dimension-six operator basis for SMEFT at finite temperature using the Hilbert series on R^3 x S^1.
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Baryon-number-violating nucleon decays into a dark photon particle
A complete XLEFT basis for nucleon decay into a dark photon is matched to ChPT, yielding width formulas and first recast lifetime bounds from Super-K data.
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ALP pair production at the LHC
Non-resonant gg→aa→4γ production could constrain the dimension-6 ALP-gluon coupling down to ~10^-3 TeV^-2 at 300 fb^-1, but the allowed parameter space remains unbounded along multiple flat directions.
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Positivity and partial wave unitarity bounds on ALP theories via amplitude methods
Complete partial-wave unitarity and positivity bounds are derived for ALP effective interactions up to dimension 8, with new SMEFT positivity constraints as a byproduct.
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Axions and Axion-like particles: collider searches
A pedagogical review of the ALP effective field theory, production and decay at colliders, indirect search strategies, and a summary of current bounds on the ALP-photon coupling.
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