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Topological Landscapes of the BSM Higgs Sector

Jyotiranjan Beuria

TL;DR

The paper tackles the problem of characterizing high-dimensional BSM Higgs-sector parameter spaces under current collider constraints. It combines Topological Data Analysis with persistent Betti numbers, supervised UMAP, and Linear Discriminant Analysis to map the global geometry and topology of SSDM and N2HDM parameter landscapes, anchored to the observed SM-like Higgs at $125 \pm 3$ GeV. The results show finely tuned islands of collider viability for SSDM and N2HDM Type I, while the N2HDM Type II space is excluded by Higgs measurements, with topology evolving with $\tan\beta$. A multi-head neural network enables fast, accurate classification of allowed versus excluded regions and provides $\chi^2$ predictions to guide further scans. The approach yields quantitative topological descriptors and a scalable framework for exploring complex multi-parameter BSM Higgs sectors.

Abstract

We explore the structure of the parameter space in the Singlet Scalar Dark Matter (SSDM) model and the Next-to-Two Higgs Doublet Model (N2HDM) with $\tanβ= 5$ and $\tanβ= 45$. Parameter points are classified as allowed or excluded based on compatibility with the Higgs observation constraints. Using a combined framework of Topological Data Analysis (TDA), Uniform Manifold Approximation and Projection (UMAP), and Linear Discriminant Analysis (LDA), we characterize the global geometry and topology of these high-dimensional landscapes. Our findings reveal that the SSDM and the N2HDM Type~I model exhibit finely tuned islands of collider viability. In the case of N2HDM Type~I, we also find that increasing $\tanβ$ leads to greater topological fragmentation and higher Betti number persistence, indicating enhanced structural complexity. In contrast, the given choice of parameters excludes the entire N2HDM Type II parameter space based on current Higgs measurements. The topological properties serve as important quantitative descriptors for the phenomenological viability of the BSM frameworks. We leverage the above mentioned topological features to train machine learning models for faster characterization of the BSM Higgs sector into allowed and excluded parameter regions.

Topological Landscapes of the BSM Higgs Sector

TL;DR

The paper tackles the problem of characterizing high-dimensional BSM Higgs-sector parameter spaces under current collider constraints. It combines Topological Data Analysis with persistent Betti numbers, supervised UMAP, and Linear Discriminant Analysis to map the global geometry and topology of SSDM and N2HDM parameter landscapes, anchored to the observed SM-like Higgs at GeV. The results show finely tuned islands of collider viability for SSDM and N2HDM Type I, while the N2HDM Type II space is excluded by Higgs measurements, with topology evolving with . A multi-head neural network enables fast, accurate classification of allowed versus excluded regions and provides predictions to guide further scans. The approach yields quantitative topological descriptors and a scalable framework for exploring complex multi-parameter BSM Higgs sectors.

Abstract

We explore the structure of the parameter space in the Singlet Scalar Dark Matter (SSDM) model and the Next-to-Two Higgs Doublet Model (N2HDM) with and . Parameter points are classified as allowed or excluded based on compatibility with the Higgs observation constraints. Using a combined framework of Topological Data Analysis (TDA), Uniform Manifold Approximation and Projection (UMAP), and Linear Discriminant Analysis (LDA), we characterize the global geometry and topology of these high-dimensional landscapes. Our findings reveal that the SSDM and the N2HDM Type~I model exhibit finely tuned islands of collider viability. In the case of N2HDM Type~I, we also find that increasing leads to greater topological fragmentation and higher Betti number persistence, indicating enhanced structural complexity. In contrast, the given choice of parameters excludes the entire N2HDM Type II parameter space based on current Higgs measurements. The topological properties serve as important quantitative descriptors for the phenomenological viability of the BSM frameworks. We leverage the above mentioned topological features to train machine learning models for faster characterization of the BSM Higgs sector into allowed and excluded parameter regions.

Paper Structure

This paper contains 17 sections, 12 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Models and Parameters
  3. Singlet Scalar Dark Matter (SSDM)
  4. Next-to-2HDM (N2HDM)
  5. Yukawa sector and Type I vs Type II
  6. Type I.
  7. Type II.
  8. Scan over Parameter space
  9. Clustering Framework for Parameter Space Landscapes
  10. Topological Data Analysis and Betti number Profiles
  11. Manifold Learning with UMAP
  12. Linear Discriminant Analysis
  13. ML Classification and Regression in BSM Parameter space
  14. Results and Discussion
  15. SSDM parameter space
  16. ...and 2 more sections

Figures (8)

  • Figure 1: Sampled SSDM parameter space showing allowed (blue) and excluded (red) points in the $(\lambda_S,\, \lambda_{SH})$ plane. Exclusion concentrates at small $\lambda_{SH}$ values.
  • Figure 2: Betti curves for the SSDM parameter space.
  • Figure 3: Supervised UMAP projection for the SSDM parameter space. Left: true labels and Right: predicted probability for allowed label.
  • Figure 4: Supervised LDA projection for the SSDM parameter space.
  • Figure 5: Sampled N2HDM parameter space showing allowed (blue) and excluded (red) points in the $(\lambda_6,\, \lambda_8)$ plane.
  • ...and 3 more figures