Machine Learning in the 2HDM2S model for Dark Matter

TL;DR

This work analyzes a $2$HDM extended by two inert real singlets $S$ and $P$ under a $\mathbb{Z}_2'$ symmetry to provide Dark Matter candidates within a Type-II Higgs sector. It develops the scalar potential, establishes bounded-from-below and global-minimum conditions using a copositivity-based approach and a bilinear formalism, and enforces perturbative unitarity and precision constraints including oblique parameters $S,T,U$. The parameter space is explored with three strategies—random scans, near-alignment scans, and CMA-ES optimization with novelty rewards—demonstrating that ML-guided exploration can efficiently locate viable regions that satisfy Planck relic density and LZ direct-detection bounds, as well as indirect limits. The results show a broad viable Dark Matter mass range, with many points near the neutrino floor, highlighting the practical impact of combining ML optimization with stringent theoretical and experimental constraints in complex BSM scalar sectors.

Abstract

We introduce a two real scalar singlet extension of the two Higgs doublet model. We study the vacuum structure, the bounded from below conditions, the restrictions from the oblique parameters S,T and U, as well as the unitarity constraints. We submit the model to collider and Dark Matter experimental constraints and explore its allowed parameter space. We compare randomly populated simulations, simulations starting near the alignment limit, and a Machine Learning based exploration. Using Evolutionary Strategies, we efficiently search for regions with two Dark Matter candidates.

Figures (6)

• Figure 1: Combined relevant limits from indirect searches on the total $\langle\sigma v\rangle$ as a function of the mass of the DM candidate $m_{DM}$. The lines coming from Fermi-LAT Fermi-LAT:2015att and H.E.S.S. HESS:2022ygk assume a Navarro-Frenk-White (NFW) DM density profile and the AMS-02 AMS:2016oqu lines correspond to the conservative approach derived in Ref. Reinert:2017aga.
• Figure 2: Points obtained with a random sampling using the ranges of parameters in eq. \ref{['eq:scanparameters']}, shown in the $\alpha_1-\beta$ plane. The points in red consider the expressions of Sections \ref{['vacuum']}-\ref{['sec:exp']}, in order to satisfy BFB, unitarity, global minimum, flavour bounds, coupling modifiers and signal strengths. The points in green combine points originally in red that are found to also satisfy HiggsTools-1.1.3. The blue point is a green point that, in addition, meets the condition $\Omega h^2 \in [0.09,0.15]$.
• Figure 3: Results in the mass - relic density plane for the scan near the alignment limit, considering eq. \ref{['eq:scanparameters']}, except for $\alpha$ obtained as a random number within $\pm 10\%$ of $-\beta$. The color code coincides with Fig. \ref{['random_sample']}.
• Figure 4: Direct detection results for the scan near the alignment limit $\alpha_1=-[0.9,1.1]\beta$, with the relevant quantity for nucleon scattering $\sigma_{SI}^{Xe}$ obtained from eq. \ref{['sigmascat']}. The color code is the same as Fig. \ref{['random_sample']}, with the addition of the LZ exclusion line from 2024 LZ:2024zvo drawn in blue.
• Figure 5: Results from a run using the optimization algorithm CMA-ES, without the novelty reward or seeded runs methods described in the text. In the Left panel we show the rapid convergence towards the imposed interval on the total relic density, $\Omega_T h^2 \in [0.1164,0.1236]$, and in the Right panel the obtained value for the direct detection quantity $\sigma_{\text{SI}}^{\text{Xe}} \xi$, with the most recent constraint from LZ LZ:2024zvo, shown as the blue line. The points in red fail one of the constraints not related to DM and the points in green meet all constraints except DM. The points with a blue color are points in green that also satisfy the correct relic density and direct detection scattering bounds.