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Machine Learning insights on the Z3 3HDM with Dark Matter

Fernando Abreu de Souza, Rafael Boto, Miguel Crispim Romão, Pedro N. de Figueiredo, Jorge C. Romão

Abstract

We study a 3-Higgs Doublet Model (3HDM) with an imposed Z3 symmetry, allowing for two Inert scalar doublets and one active Higgs doublet. The WIMP dark matter candidates correspond to two mass-degenerate states, H1 and A1, which possess opposite CP quantum numbers and can reproduce the correct relic density simultaneously with all theoretical and experimental constraints. We use state-of-the-art machine learning algorithms to probe the parameter space of the model by employing an Evolutionary Strategy augmented with Novelty Reward. We consider two situations: a limit for the dark matter mixing angle θ that closes a gauge annihilation channel that would deplete the DM relic density, and the general case without imposing this limit. For both scenarios, we find viable dark matter candidates within two separate mass regimes, ranging from 50 GeV < mDM < mW and 380 < mDM < 1000 GeV. Moreover, we find it is possible to fulfill all the existing constraints while still obtaining values for the dark matter-higgs coupling of order O(0.1). Exploring the model outside the θ = π/4 limit proved to be an extremely challenging task, as there are regions which seem easy to explore when projected on a 2D plane, yet may be completely disconnected on the hypersurface supporting the valid points, given its non-convex and multi-dimensional nature. We consider new methods of prototype selection to seed new exploration runs, which allow for efficient global scans over the parameter space.

Machine Learning insights on the Z3 3HDM with Dark Matter

Abstract

We study a 3-Higgs Doublet Model (3HDM) with an imposed Z3 symmetry, allowing for two Inert scalar doublets and one active Higgs doublet. The WIMP dark matter candidates correspond to two mass-degenerate states, H1 and A1, which possess opposite CP quantum numbers and can reproduce the correct relic density simultaneously with all theoretical and experimental constraints. We use state-of-the-art machine learning algorithms to probe the parameter space of the model by employing an Evolutionary Strategy augmented with Novelty Reward. We consider two situations: a limit for the dark matter mixing angle θ that closes a gauge annihilation channel that would deplete the DM relic density, and the general case without imposing this limit. For both scenarios, we find viable dark matter candidates within two separate mass regimes, ranging from 50 GeV < mDM < mW and 380 < mDM < 1000 GeV. Moreover, we find it is possible to fulfill all the existing constraints while still obtaining values for the dark matter-higgs coupling of order O(0.1). Exploring the model outside the θ = π/4 limit proved to be an extremely challenging task, as there are regions which seem easy to explore when projected on a 2D plane, yet may be completely disconnected on the hypersurface supporting the valid points, given its non-convex and multi-dimensional nature. We consider new methods of prototype selection to seed new exploration runs, which allow for efficient global scans over the parameter space.
Paper Structure (24 sections, 38 equations, 12 figures)

This paper contains 24 sections, 38 equations, 12 figures.

Table of Contents

  1. Introduction
  2. The Z3 3HDM
  3. The Model
  4. Bounded from below conditions
  5. Global Minimum
  6. Machine Learning scan strategy
  7. Evolutionary Strategy and Novelty Detection for Parameter Space Exploration
  8. Prototype Selection for Seed Acquisition
  9. Constraints
  10. Collider constraints
  11. Dark Matter Constraints
  12. Relic Density
  13. Direct Detection
  14. Indirect Detection
  15. Results
  16. ...and 9 more sections

Figures (12)

  • Figure 1: In solid lines, the most recent direct detection limits from XENONnT XENON:2025vwd, PandaX-4T PandaX:2024qfu and LZ LZ:2024zvo for the mass region of interest. In dashed lines, the pojections for the upcoming DarkSide-20k DarkSide-20k:2017zyg and XLZD XLZD:2024nsu experiments, which is expected to breach the neutrino fog in the region of interest for the WIMP mass OHare:2021utq, shown as the grey shaded region.
  • Figure 2: Indirect detection constraints for $WW$ and $bb$ channels in the region of interest for the WIMP mass. The experimental lines originate from Fermi-LAT Fermi-LAT:2015att, H.E.S.S. HESS:2022ygk and AMS-02 AMS:2016oquAMS:2016brs, following the approach in Ref. Reinert:2017aga.
  • Figure 3: Benchmarks B and G from Ref. Aranda:2019vda, for the low and high mass regions, respectively, with colour code for $g_1$. All the theoretical constraints are applied, except the CB and $\mathbb{Z}_{3}$-specific BFB conditions described in Eq. \ref{['eq:bfbfull']}. HiggsTools, direct and indirect detection limits are also not enforced. The horizontal dashed lines are the bounds from relic density.
  • Figure 4: Plane of the direct detection cross-section $\sigma_{H_1}^{SI}$ and $m_{\textrm{DM}}$. The points in blue pass relic bounds exactly, all theoretical and experimental constraints. The lines shown are the experimental upper bounds from XENONnT XENON:2025vwd, PandaX-4T PandaX:2024qfu and LZ LZ:2024zvo. In dashed lines, the pojections for the next generation experiments DarkSide-20k DarkSide-20k:2017zyg and XLZD XLZD:2024nsu experiments. The neutrino fog OHare:2021utq is shown as the grey shaded region.
  • Figure 5: Results obtained for the limit $\theta = \frac{\pi}{4}$ without fixing any of the variables in Eq. \ref{['eq:massvariables']}, with colour code for $|g_1|$. All necessary theoretical constraints are applied, along with the relevant updated bounds from HiggsTools and direct detection. These points are sampled using seeds and focus on the parameters and observables of interest shown.
  • ...and 7 more figures