Relic Density Topology as a Discriminatory Tool: A Comparative Analysis of IDM, MSSM, and NMSSM Dark Matter

TL;DR

The paper introduces a relic-density topology framework to differentiate scalar doublet DM (IDM) from supersymmetric DM (MSSM and NMSSM) by performing a unified, heavy-mass regime scan with micrOMEGAs and enforcing the Planck relic-density bound via $\Omega h^2 = 0.1199 \pm 0.0027$. It shows IDM produces a broad, natural viability plateau with low fine-tuning, while MSSM/NMSSM require narrow resonances and exhibit higher fine-tuning; a distinctive MSSM slepton-mediated dip near $m_{\rm DM} \approx 500$ GeV contrasts with NMSSM’s damped signature due to singlino admixture, providing practical discriminants. The analysis also tracks freeze-out parameters $X_f$, $T_f$, and $z_f$ and checks CMB constraints through $p_{\mathrm{ann}}$, confirming cosmological consistency across models. Collectively, the framework offers a concrete diagnostic to guide future dark matter searches and model interpretation, with potential extensions to global fits and collider observables.

Abstract

This study proposes a diagnostic mechanism based on the relic density topology to discriminate between the Inert Doublet Model (IDM), the Minimal Supersymmetric Standard Model (MSSM), and the Next-to-Minimal Supersymmetric Standard Model (NMSSM). Using a unified numerical scan with micrOMEGAs over the heavy-mass regime ($m_{x} > 300$ GeV), we contrast the phenomenological profiles of these frameworks. We demonstrate that the IDM admits a broad, stable viability plateau driven by efficient gauge couplings, while the MSSM and NMSSM typically overproduce dark matter, reaching the Planck relic density only through narrow, fine-tuned resonance channels. A quantitative fine-tuning measure reveals the IDM's viable parameter space is an order of magnitude more natural than its SUSY counterparts. Furthermore, by examining the thermal decoupling epoch ($z_{f}$) and the CMB energy-injection parameter ($p_{ann}$), we confirm that all identified viable regions are consistent with cosmological observations, and that the models exhibit different thermal history scenarios for the Universe. Our findings establish a multi-faceted discriminative framework: the IDM is characterized by a robust plateau and low fine-tuning, the MSSM by a sharp slepton-mediated annihilation dip, and the NMSSM by a diluted signature due to singlino admixture. The discovery of a heavy WIMP without sharp resonance features would therefore phenomenologically favor scalar doublet extensions over minimal supersymmetric frameworks.

Figures (14)

• Figure 1: Dark matter relic density in the IDM as a function of the DM-Higgs coupling $\lambda_L$ for varying mass-splitting parameter $\delta$.
• Figure 2: Relic density in the IDM as a function of DM mass for different $\lambda_L$, with $\delta=0.1$. The horizontal band indicates the Planck observational bounds.
• Figure 3: Relic density in the MSSM as a function of $\mu$ and $\tan\beta$, illustrating resonance peaks and the dependence on LSP composition.
• Figure 4: The topological profiles of Wino and Higgsino-like DM in the MSSM.
• Figure 5: Cross-model comparison of relic densities in the light dark matter mass regime (50–200 GeV) for the IDM, MSSM, and NMSSM. The horizontal band indicates the Planck bounds.