⚛️ phenomenology

Exploring the Singlino-dominated Thermal Neutralino Dark Matter in the $Z_3$ invariant NMSSM

This paper investigates the parameter space of the $Z_3$ -invariant NMSSM where a Singlino-dominated neutralino serves as dark matter, identifying viable regions consistent with experimental constraints, analyzing dominant annihilation mechanisms, and evaluating the discovery potential of triple-boson final states at the High-Luminosity LHC.

Original authors: Amandip De, Rahool Kumar Barman, Amit Adhikary, Biplob Bhattacherjee, Rohini M. Godbole

Published 2026-09-23

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CC BY 4.0

Original authors: Amandip De, Rahool Kumar Barman, Amit Adhikary, Biplob Bhattacherjee, Rohini M. Godbole

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is filled with invisible matter that holds galaxies together, yet we cannot see it, touch it, or directly detect it. Scientists call this dark matter, and while they know it exists because of its gravitational pull, they have never identified what particles make it up. One leading theory suggests that dark matter consists of weakly interacting massive particles, or WIMPs, which were created in the early universe and have been drifting through space ever since. These particles are thought to be their own antiparticles, meaning that if two of them collide, they can annihilate each other and disappear, leaving behind only energy. The challenge for physicists is that these particles are so elusive that they rarely interact with normal matter, making them incredibly difficult to find in underground laboratories or to spot in the debris of high-energy collisions.

To solve this mystery, researchers often look to theories that extend our current understanding of physics, such as a framework called the Next-to-Minimal Supersymmetric Standard Model. This model proposes that for every known particle in nature, there is a heavier, invisible partner. In this extended family of particles, the lightest and most stable partner is a prime candidate for dark matter. Specifically, this paper focuses on a version of the model where this lightest particle is dominated by a component called a "singlino," a type of particle that arises from a unique field not present in the standard model. The researchers wanted to know if such a particle could exist without contradicting what we already know about the universe, and if so, how we might finally catch a glimpse of it.

The team began by mapping out the vast landscape of possible properties for this singlino-dominated particle. They had to ensure that any particle they imagined would not have been seen by previous experiments at the Large Electron-Positron collider or the Large Hadron Collider, nor would it have been detected by sensitive underground experiments looking for dark matter hitting atomic nuclei. They also had to make sure the particle's abundance in the universe matched the precise amount of dark matter astronomers observe today. By running millions of computer simulations, they filtered out the impossible scenarios and found a specific region of possibilities where a singlino-dominated particle could exist. They discovered that for lighter particles, the key to their survival was a special resonance, where the particle's mass was perfectly tuned to allow it to annihilate efficiently through a light, invisible Higgs-like particle. For heavier particles, the survival mechanism shifted to a process where the dark matter particle would team up with a slightly heavier partner to annihilate together, a scenario that requires the two to be very close in mass.

Having confirmed that this type of dark matter could theoretically exist, the researchers turned their attention to how we might find it in the future. They focused on the High-Luminosity Large Hadron Collider, a future upgrade to the world's most powerful particle accelerator that will smash protons together with unprecedented intensity. The team proposed a specific search strategy that looks for a very rare and complex signature: the simultaneous production of three force-carrying particles, including a light Higgs boson, along with missing energy that would indicate the escape of the invisible dark matter. This specific combination of particles is a hallmark of the singlino scenario and is much harder to produce in simpler models of physics. They simulated the collisions and the subsequent decay of heavy particles into this triple-boson final state, which would appear in the detector as three charged leptons, two bottom quarks, and a significant amount of missing energy.

The analysis revealed that this signal is distinct enough to be separated from the background noise of ordinary particle interactions. The researchers developed a sophisticated method to identify the light Higgs boson, which in their scenario is so light that its decay products are squeezed together into a single, large "fat jet" rather than two separate streams. By using advanced techniques to look inside these jets and identify the specific pattern of the bottom quarks, they could isolate the signal from the overwhelming background. Their calculations showed that with the data expected from the High-Luminosity Large Hadron Collider, this specific scenario could be confirmed with a high degree of statistical certainty. The study concludes that while direct detection experiments might struggle to find these light particles due to their weak interactions, the collider route offers a promising path to discovery, provided the search is tailored to look for these specific, multi-particle signatures. This work provides a clear roadmap for experimentalists, showing exactly what to look for if nature has chosen this particular path for the dark matter that shapes our cosmos.

Technical Summary: Exploring the Singlino-dominated Thermal Neutralino Dark Matter in the Z3 invariant NMSSM

Problem Statement
The nature of Dark Matter (DM) remains a central mystery in particle physics. While Weakly Interacting Massive Particles (WIMPs) are a favored candidate, the Minimal Supersymmetric Standard Model (MSSM) faces significant challenges in accommodating a viable DM candidate that satisfies both the observed relic density and stringent experimental constraints. Specifically, a pure Bino-like Lightest Supersymmetric Particle (LSP) in the MSSM typically results in an over-abundant relic density unless specific co-annihilation or resonance conditions are met, while Higgsino-like LSPs require masses $\gtrsim 1$ TeV to avoid over-annihilation, introducing a "little fine-tuning problem." Furthermore, direct detection experiments (e.g., LZ) have placed severe limits on spin-independent (SI) scattering cross-sections, pushing many MSSM scenarios into unobservable regions or requiring specific "blind spots."

The Next-to-Minimal Supersymmetric Standard Model (NMSSM), particularly with a $Z_3$ symmetry, offers a solution by introducing a singlet superfield. This generates the $\mu$ -term dynamically and extends the neutralino sector to five states, allowing for a Singlino-dominated LSP. The paper investigates whether a Singlino-dominated LSP can serve as a thermal DM candidate with an under-abundant relic density (consistent with $\Omega h^2 \leq 0.122$ ) while evading current collider and direct detection constraints, and explores the potential for discovering such scenarios at the High-Luminosity LHC (HL-LHC) via non-conventional channels.

Methodology
The authors perform a comprehensive phenomenological study using the following approach:

Parameter Space Scan: A random scan of the $Z_3$ -invariant NMSSM parameter space was conducted using NMSSMTools-v6.0.0 and MicrOmegas. The scan focused on regions where the LSP ( $\tilde{\chi}^0_1$ ) is Singlino-dominated ( $N_{15}^2 > 0.8$ ). Key input parameters included:
- Couplings: $0.0001 < \lambda < 0.4$ , $|\kappa/\lambda| \leq 0.5$ .
- Mass parameters: $M_1 \in (70, 2000)$ GeV, $M_2 \in (200, 3000)$ GeV, $\mu \in (100, 900)$ GeV.
- Trilinear couplings and $\tan\beta$ were varied within broad ranges.
- Third-generation squark masses were varied up to 10 TeV, while other sfermions were fixed at 3 TeV.
Constraints: The scanned points were subjected to a rigorous set of constraints:
- LEP: Chargino mass limits ( $m_{\tilde{\chi}^\pm_1} > 103.5$ GeV) and limits on $e^+e^- \to \tilde{\chi}^0_2 \tilde{\chi}^0_1$ .
- Flavor Physics: Rare $B$ -meson decays ( $b \to s\gamma$ , $B_s \to \mu^+\mu^-$ , etc.) and $\Upsilon$ decays.
- Higgs Sector: The SM-like Higgs mass ($122-128$ GeV) and signal strengths (via HiggsSignals), and exclusion limits on BSM Higgs bosons (via HiggsBounds).
- LHC Searches: Limits on electroweakinos, gluinos, and squarks (via SModels).
- Dark Matter: Relic density ( $\Omega h^2 < 0.122$ ) and direct detection limits (Spin-Independent and Spin-Dependent) from LZ, SuperCDMS, and PICO-60.
Annihilation Analysis: The dominant DM annihilation mechanisms were identified across the LSP mass range ( $\sim 4$ GeV to 1 TeV), distinguishing between resonant s-channel annihilation (via light Higgs $A_1/H_1$ or $Z/H_{SM}$ ) and co-annihilation with Next-to-Lightest Supersymmetric Particles (NLSPs).
Collider Phenomenology (Benchmark Study): A specific benchmark point (BP) was selected from the low-mass LSP regime ( $m_{\tilde{\chi}^0_1} \approx 20.5$ GeV) where resonant annihilation is dominant. The study focused on direct electroweakino pair production ( $pp \to \tilde{\chi}^\pm_1 \tilde{\chi}^0_3 + \tilde{\chi}^\pm_1 \tilde{\chi}^0_4$ ) leading to triple-boson final states ( $ZWH_1$ ).
- Simulation: Events were generated using MG5aMC@NLO with NNPDF23LO PDFs, showered with Pythia-8, and simulated through a fast detector simulation (Delphes-3.5.0) configured for the HL-LHC.
- Signal Channel: $pp \to \tilde{\chi}^\pm_1 \tilde{\chi}^0_{3,4} \to Z W^\pm H_1 + E_T^{\text{miss}}$ , with $H_1 \to b\bar{b}$ , $Z \to \ell\ell$ , and $W \to \ell\nu$ .
- Analysis Strategy: Due to the light mass of $H_1$ ( $m_{H_1} \approx 14.2$ GeV) and its boosted nature, the $b\bar{b}$ pair was reconstructed as a single "fatjet" using jet substructure techniques (Cambridge-Aachen algorithm, SoftDrop grooming, and Mass-drop tagging). A cut-based analysis optimized kinematic variables ( $E_T^{\text{miss}}$ , transverse mass $M_T$ , and fatjet mass) to maximize signal significance.

Key Contributions and Results

Parameter Space Viability: The study identifies a viable region of the NMSSM parameter space where a Singlino-dominated LSP yields an under-abundant thermal relic density. Approximately 24% of points satisfying LEP and theoretical constraints are Singlino-dominated.
Annihilation Mechanisms:
- Low Mass ( $m_{\tilde{\chi}^0_1} \lesssim m_Z/2$ ): Dominated by resonant s-channel annihilation via light singlet-like pseudoscalar ( $A_1$ ) or scalar ( $H_1$ ) Higgs bosons, where $m_{A_1/H_1} \approx 2m_{\tilde{\chi}^0_1}$ .
- High Mass ( $m_{\tilde{\chi}^0_1} \gtrsim 100$ GeV): Resonant annihilation via singlet Higgs is kinematically forbidden due to mass relations. Consistency with relic density is achieved primarily through co-annihilation with nearly degenerate Higgsino-like NLSPs ( $\tilde{\chi}^0_2, \tilde{\chi}^\pm_1$ ).
Direct Detection Constraints:
- Roughly 70% of the allowed parameter points are excluded by current LZ Spin-Independent (SI) limits.
- However, a significant fraction of the remaining points lies below the "neutrino floor," making them inaccessible to future SI-based direct detection experiments.
- Spin-Dependent (SD) limits are less constraining, with only a few points excluded.
HL-LHC Discovery Potential:
- The paper highlights the $ZWH_1$ channel as a unique signature of the NMSSM, distinct from typical MSSM decay topologies.
- For the benchmark point (BP), the production cross-section for $\tilde{\chi}^\pm_1 \tilde{\chi}^0_{3,4}$ is $\sim 358$ fb, leading to a $ZWH_1$ final state rate of $\sim 43$ fb.
- By employing fatjet reconstruction for the light $H_1 \to b\bar{b}$ and optimizing cuts on $E_T^{\text{miss}}$ and transverse mass, the analysis achieves a signal significance of $\sim 7\sigma$ (assuming 5% systematic uncertainty) with an integrated luminosity of $3000 \text{ fb}^{-1}$ .
- The signal-to-background ratio improves from $\sim 10^{-4}$ at baseline cuts to $\sim 1$ after applying the full selection criteria.

Significance and Claims
The paper claims that the NMSSM framework offers a robust solution to the DM problem that remains viable despite stringent direct detection limits, particularly in the low-mass Singlino regime. The primary significance of this work lies in:

Mapping Viable Scenarios: It delineates the specific annihilation mechanisms (resonant vs. co-annihilation) required to satisfy relic density constraints across the LSP mass spectrum in the Singlino-dominated limit.
Novel Search Channels: It demonstrates that standard MSSM search strategies may miss these scenarios. Instead, the paper proposes triple-boson final states (specifically $ZWH_1$ ) involving a light singlet-like Higgs as a promising discovery channel.
Feasibility at HL-LHC: The detailed collider analysis suggests that the HL-LHC has the potential to discover such Singlino-dominated scenarios through dedicated searches for light Higgs bosons in boosted fatjet topologies, achieving a discovery-level significance for the benchmark point studied.

The authors conclude that targeted searches for these specific triple-boson signatures are essential to probe the allowed parameter space of the NMSSM that is otherwise inaccessible to conventional direct detection or standard LHC searches.

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