Probing dark matter through charged Higgs pair production at future multi-TeV muon colliders: A machine-learning analysis

Technical Summary: Probing Dark Matter through Charged Higgs Pair Production at Future Multi-TeV Muon Colliders

Problem Statement
The Standard Model (SM) of particle physics, while successful, fails to account for Dark Matter (DM), neutrino masses, and baryon asymmetry. The Inert Doublet Model (IDM) offers a minimal extension to the SM by introducing an additional $SU(2)_L$ scalar doublet ($\Phi_2$) that is odd under a discrete $Z_2$ symmetry, while the SM fields and the first doublet ($\Phi_1$) are even. This symmetry ensures the stability of the lightest $Z_2$-odd scalar, identified here as the neutral scalar $H$, serving as a viable Weakly Interacting Massive Particle (WIMP) DM candidate.

Despite extensive studies at the Large Hadron Collider (LHC) and proposed future lepton colliders (ILC, CLIC), the IDM parameter space remains largely unconstrained in specific regions. This paper investigates the potential of future multi-TeV muon colliders to probe the IDM via the production of charged Higgs pairs ($H^\pm H^\mp$) in association with neutrinos, followed by decays into SM particles and the stable DM candidate $H$. The study specifically addresses the challenge of distinguishing these signals from substantial SM backgrounds using advanced analysis techniques.

Methodology
The analysis proceeds in three main stages:

1. Parameter Space Constraint:
   The viable parameter space of the IDM was first updated by imposing theoretical constraints (vacuum stability, perturbative unitarity, and the inert vacuum condition) and current experimental bounds. These bounds include:

   • Electroweak Precision Observables (EWPOs) ($S, T, U$ parameters).
   • LEP-II and LHC direct search limits on scalar masses and decays.
   • Higgs precision measurements (including the trilinear Higgs coupling $\kappa_{hhh}$ and invisible branching ratios).
   • Cosmological constraints on DM relic density ($\Omega_H h^2$) from the Planck Collaboration.
   • Direct detection limits from the LUX-ZEPLIN (LZ) experiment.

   Using the public packages 2HDMC, HiggsBounds, HiggsSignals, anyH3, and micrOMEGAs, 23 benchmark points (BP1–BP23) were identified that satisfy all constraints. Particular emphasis was placed on points BP3 through BP8, which feature specific mass hierarchies and coupling strengths conducive to charged Higgs pair production.

2. Signal and Background Simulation:
   The study focuses on three signal channels at future muon colliders ($\mu^- \mu^+$) with center-of-mass energies ($\sqrt{s}$) of 3, 10, and 14 TeV:

   • $\mu^- \mu^+ \to \nu_\mu \bar{\nu}_\mu H^\pm H^\mp \to 4 \text{ jets} + \text{missing energy}$
   • $\mu^- \mu^+ \to \nu_\mu \bar{\nu}_\mu H^\pm H^\mp \to \ell^\pm + 2 \text{ jets} + \text{missing energy}$
   • $\mu^- \mu^+ \to \nu_\mu \bar{\nu}_\mu H^\pm H^\mp \to \ell^+ \ell^- + \text{missing energy}$

   Signal and SM background events were generated using MadGraph5_aMC@NLO. Backgrounds included QCD-induced dijet production, pure electroweak processes (e.g., $W^+W^-$, $ZZ$, $Zh$), and multi-boson final states.

3. Analysis Techniques:
   Two distinct analysis strategies were employed to evaluate signal significance ($Z$):

   • Cut-based Analysis: Standard kinematic cuts on transverse momentum ($p_T$), pseudorapidity ($\eta$), and angular separation ($\Delta R$) were applied.
   • Machine Learning (ML) Analysis: Differential kinematic distributions were used as input features for an XGBoost classifier. The model was trained to discriminate signal from background. The interpretability of the ML model was verified using SHAP (SHapley Additive exPlanations) values to identify the most influential kinematic observables.

Key Contributions and Results

• Benchmark Selection: The study successfully isolated a subset of viable IDM benchmark points (BP3–BP8) that are consistent with all current theoretical, experimental, and cosmological constraints, specifically tailored for charged Higgs pair production studies.
• Enhanced Sensitivity via ML: The application of the ML framework yielded a substantial improvement in signal sensitivity compared to conventional cut-based methods. For instance, at $\sqrt{s} = 10$ TeV with an integrated luminosity of $10,000 \text{ fb}^{-1}$, the cut-based analysis often failed to reach discovery thresholds, whereas the ML-enhanced analysis achieved statistical significances ($Z$) exceeding $5\sigma$ for multiple benchmark points.
• Discovery Potential:
  • 4-jet Channel: At $\sqrt{s} = 10$ TeV, BP3, BP6, BP7, and BP8 achieved $Z > 5\sigma$ with ML. BP3 reached $Z \approx 40.5$.
  • Semileptonic Channel: At $\sqrt{s} = 10$ TeV, BP3, BP6, BP7, and BP8 exceeded the $5\sigma$ threshold, with BP7 reaching $Z \approx 37.6$.
  • Dilepton Channel: At $\sqrt{s} = 10$ TeV, BP6, BP7, and BP8 achieved $Z > 5\sigma$, with BP7 reaching $Z \approx 29.8$.
  • High Energy Performance: At $\sqrt{s} = 14$ TeV, the significance further increased for most viable points, demonstrating the scalability of the discovery potential with collider energy and luminosity.
• ML Interpretability: SHAP analysis revealed that the classifier relies on physically meaningful observables. The sum of jet transverse momenta ($H_T^j$), dijet invariant masses, and the missing invariant mass ($M_{miss}$) were identified as the most discriminative features, consistent with the expected signal topology of heavy scalar decays and invisible DM particles.

Significance and Claims
The paper claims that future multi-TeV muon colliders possess strong potential for indirectly probing the IDM parameter space through charged Higgs pair production. The authors assert that:

1. Indirect Probing: DM signatures can be effectively probed even without direct detection of the DM particle, by observing the kinematic imbalances and specific decay chains of the associated charged Higgs bosons.
2. Necessity of ML: The study demonstrates that for complex final states with significant SM backgrounds (such as multi-jet and missing energy signatures), machine learning techniques are not merely beneficial but essential for achieving discovery-level significance ($Z > 5\sigma$) across a wide range of viable benchmark points.
3. Feasibility: Several benchmark points consistent with all current constraints can be discovered with statistical significances well exceeding the $5\sigma$ threshold at proposed muon collider facilities (e.g., 10 TeV and 14 TeV), highlighting the unique capability of these machines to explore BSM physics in the Higgs sector.

The authors conclude that their results underscore the importance of future lepton colliders in addressing fundamental questions regarding the nature of Dark Matter and the structure of the Higgs scalar sector.