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  • Open Access

Hilbert series and the flavor invariants of the 3HDM

Eric Bryan* and Arvind Rajaraman†

  • *Contact author: ebryan2@uci.edu
  • †Contact author: arajaram@uci.edu
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Phys. Rev. D 114, 015047 – Published 30 July, 2026

DOI: https://doi.org/10.1103/xhq1-k7jm

Abstract

We perform a systematic study of invariant operators in the three-Higgs-doublet model (3HDM). We compute the closed-form multigraded Hilbert series associated with the global symmetry group of the theory. In addition, we construct explicit expressions for the corresponding invariant operators up to cubic order in the couplings. As a phenomenological application, we further organize the invariants up to quadratic order in the field content into CP-even and CP-odd combinations. For the special case of invariants involving no 27 representations, our results are complete to all orders.

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Information

Phys. Rev. D 114, 015047– Published 30 July, 2026
  • Received 13 May 2026
  • Accepted 13 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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