⚛️ phenomenology

Scalar Resonances near 650 and 95 GeV in the GNMSSM with Correct Dark Matter Relic Abundance

This paper proposes a General Next-to-Minimal Supersymmetric Standard Model (GNMSSM) scenario featuring a 650 GeV heavy scalar and a 95 GeV light singlet-like scalar to simultaneously explain recent CMS and ATLAS diphoton and $b\bar{b}$ excesses while satisfying constraints from dark matter relic abundance, Higgs properties, and LHC searches.

Original authors: Jingwei Lian, Yao-Bei Liu

Published 2026-03-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jingwei Lian, Yao-Bei Liu

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

Imagine the universe as a giant, incredibly complex puzzle. For decades, physicists have been trying to fit the pieces together to understand how everything works. The biggest piece they found in 2012 was the Higgs boson, a particle that gives other particles their mass. It was a huge victory, but the puzzle wasn't finished. There were still some loose pieces and some strange "glitches" in the data that didn't quite fit the picture.

This paper is like a team of detectives (the authors) proposing a new theory to explain those glitches using a specific type of puzzle box called the GNMSSM (a fancy name for an extended version of the "Supersymmetry" theory).

Here is the story of their investigation, broken down into simple concepts:

1. The Mystery: Two Strange Glitches

The scientists at the world's biggest particle collider (the LHC) noticed two weird things happening:

Glitch A (The "95 GeV" Whisper): They saw a faint signal suggesting a light, new particle exists with a mass of about 95 GeV. It's like hearing a faint whisper in a noisy room. This particle seems to decay into pairs of photons (light) and pairs of bottom quarks (heavy particles).
Glitch B (The "650 GeV" Roar): They also saw a heavier, louder signal around 650 GeV. This looks like a heavy particle decaying into two things: a standard Higgs boson (the one we know) and that mysterious light particle from Glitch A.

It's as if they found a heavy box (650 GeV) that, when opened, releases a standard toy (125 GeV Higgs) and a strange, new gadget (95 GeV particle).

2. The Suspect: The "GNMSSM"

The authors suggest that these glitches aren't errors; they are real particles predicted by a theory called the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM).

Think of the Standard Model (our current best theory) as a house with two rooms. The GNMSSM is like adding a third room (a "singlet" field) to that house.

In this new room, there are extra particles.
One of these extra particles is light (the 95 GeV one).
Another is heavy (the 650 GeV one).
The theory explains how the heavy one can break apart into the light one and the standard Higgs, perfectly matching the "glitches" the scientists saw.

3. The Hidden Hero: Dark Matter

The universe is mostly made of Dark Matter, an invisible substance that holds galaxies together. We can't see it, but we know it's there.

The paper argues that this new theory doesn't just explain the glitches; it also provides the perfect candidate for Dark Matter.
They propose that the lightest particle in this new "third room" (a Bino-dominated neutralino) is the Dark Matter.
The Analogy: Imagine the universe is a crowded dance floor. The Dark Matter particles are shy dancers who usually just stand in the corner. But in this specific theory, they occasionally bump into each other and disappear (annihilate) in a very specific way, leaving just the right amount of them to fill the universe today. The authors calculated that this "dance move" works perfectly to match the amount of Dark Matter we observe.

4. The Investigation: Running the Numbers

The authors didn't just guess; they ran a massive computer simulation.

They tested millions of different versions of this theory, tweaking the "knobs" (parameters) to see if any version could explain both glitches and the Dark Matter and not break any other known laws of physics.
The Result: They found two main "scenarios" (solutions) that work.
- Scenario 1: The most popular solution. It fits the data very well and explains the Dark Matter perfectly.
- Scenario 2: A slightly different version that also works but is a bit more constrained.

5. The Verdict: A Viable Theory

The paper concludes that this theory is a strong contender.

It explains the 95 GeV and 650 GeV signals.
It provides a Dark Matter candidate that survives all current tests (like the "LZ" experiment, which tries to catch Dark Matter).
It predicts that the "new room" (the extra particles) is heavy enough that we haven't seen them directly yet, but light enough that the High-Luminosity LHC (a supercharged version of the current collider) might catch them soon.

The Big Picture Analogy

Imagine you are trying to solve a crime.

The Evidence: You found a muddy footprint (the 95 GeV signal) and a broken window (the 650 GeV signal).
The Old Theory: Said the culprit was a ghost, which didn't make sense.
The New Theory (GNMSSM): Says, "Wait, there's a hidden basement in the house we didn't know about."
The Suspect: A person who lives in that basement (the Dark Matter candidate).
The Proof: If you look at the basement, the footprints and the broken window make perfect sense. The person in the basement explains the mess, and they also explain why the house feels heavier than it looks (Dark Matter).

In short: This paper says, "We have a new theory that fits all the weird data we found, explains the invisible stuff holding the universe together, and gives us a clear target for what to look for in the next few years of experiments." It's a promising lead in the hunt for new physics.

1. Problem Statement

The paper addresses the simultaneous interpretation of several persistent anomalies observed in collider experiments, which suggest the existence of new scalar particles beyond the Standard Model (SM):

The 95 GeV Anomaly: A combined excess in the diphoton ( $\gamma\gamma$ ) channel observed by CMS and ATLAS, and a $b\bar{b}$ excess observed at LEP. These point to a light scalar resonance ( $\phi$ or $h_s$ ) with a mass around 95.4 GeV.
The 650 GeV Anomaly: A recent CMS search in the diphoton plus $b\bar{b}$ channel ( $\gamma\gamma b\bar{b}$ ) revealed a local excess at an invariant mass of $\sim 650$ GeV. This is interpreted as a heavy resonance ( $X$ or $H$ ) decaying into a SM-like Higgs ( $h$ ) and the light 95 GeV scalar ( $h_s$ ).

The challenge is to construct a theoretical framework that explains both excesses simultaneously while satisfying stringent constraints from:

The properties of the 125 GeV Higgs boson.
Dark Matter (DM) relic density (Planck data) and direct detection limits (LZ experiment).
B-physics observables and electroweak precision tests.
LHC searches for Supersymmetric (SUSY) particles (electroweakinos).

2. Methodology

The authors utilize the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM) as the theoretical framework. Unlike the $Z_3$ -invariant NMSSM, the GNMSSM includes $Z_3$ -violating terms ( $\mu, \mu', \xi$ ) in the superpotential and soft-breaking Lagrangian, which resolve the tadpole and domain-wall problems.

Key Theoretical Features:

Higgs Sector: The model predicts a light singlet-dominated CP-even scalar ( $h_s \approx 95$ GeV) and a heavy doublet-dominated CP-even scalar ( $H \approx 650$ GeV). The heavy scalar decays via $H \to h h_s$ , where $h$ is the 125 GeV SM-like Higgs.
Dark Matter Sector: The Lightest Supersymmetric Particle (LSP) is the lightest neutralino ( $\tilde{\chi}^0_1$ ). The study investigates whether a Singlino-dominated or Bino-dominated LSP can satisfy relic density constraints without violating direct detection limits.

Computational Strategy:

Parameter Scan: A comprehensive 12-dimensional parameter scan was performed using the MultiNest algorithm (nested sampling) to explore the Bayesian posterior probability distribution and profile likelihood.
Tools:
- SARAH/SPheno: For generating analytical model files and computing the SUSY mass spectrum and low-energy flavor observables.
- MicrOMEGAs: For calculating DM relic density, annihilation channels, and direct detection cross-sections.
- HiggsBounds/HiggsSignals: To enforce constraints from Higgs searches and precision measurements.
- CheckMATE/MadGraph/Pythia/Delphes: To simulate LHC electroweakino searches and calculate exclusion limits ( $R$ -values).
Likelihood Function: Constructed as $L = L_{650+95} \times L_{Res}$ , where $L_{650+95}$ quantifies the fit to the observed excesses ( $\sigma_{\gamma\gamma b\bar{b}}$ , $\mu_{\gamma\gamma}$ , $\mu_{b\bar{b}}$ ) and $L_{Res}$ enforces hard constraints (masses, DM density, LZ limits, etc.).

3. Key Contributions and Results

A. Unified Explanation of Excesses

The study demonstrates that the GNMSSM can simultaneously explain the 95 GeV and 650 GeV excesses at the 2 $\sigma$ confidence level.

Mechanism: The 95 GeV excess is driven by the light singlet-like scalar $h_s$ . The 650 GeV excess arises from the resonant production of the heavy scalar $H$ decaying into $h h_s$ , followed by $h \to \gamma\gamma$ and $h_s \to b\bar{b}$ .
Two Distinct Scenarios: The viable parameter space clusters into two scenarios based on the DM annihilation mechanism:
1. Scenario I (Dominant, ~92% of viable points): Features a Bino-dominated LSP ( $\tilde{\chi}^0_1$ ) with mass $\sim 300\text{--}500$ GeV. Relic density is achieved via $A_s$ -funnel annihilation ( $\tilde{\chi}^0_1 \tilde{\chi}^0_1 \to h_s A_s$ ) or co-annihilation with a Singlino-like $\tilde{\chi}^0_2$ . This scenario provides the best simultaneous fit to all three excesses ( $\sigma_{\gamma\gamma b\bar{b}}$ , $\mu_{\gamma\gamma}$ , $\mu_{b\bar{b}}$ ).
2. Scenario II (~8% of viable points): Features a Bino-dominated LSP with heavier masses ( $\gtrsim 500$ GeV). Relic density is achieved via co-annihilation with Higgsino-like $\tilde{\chi}^0_2$ or $\tilde{\chi}^\pm_1$ (channels like $\tilde{\chi}^0_2 \tilde{\chi}^0_2 \to h_s A_s$ ). This scenario fits the $\sigma_{\gamma\gamma b\bar{b}}$ and $\mu_{\gamma\gamma}$ excesses well but predicts a lower $\mu_{b\bar{b}}$ .

B. Dark Matter Viability

Bino Dominance: The study finds that a Bino-dominated LSP is strongly favored over a Singlino-dominated one. A Singlino LSP requires a large $\lambda$ coupling to explain the excesses, which leads to a Higgs-mediated scattering cross-section that violates current LZ direct detection limits.
Suppression Mechanisms: The Bino LSP avoids direct detection bounds through "blind-spot" conditions or cancellations in the Higgs coupling, keeping spin-independent (SI) and spin-dependent (SD) cross-sections well below current experimental limits.
Relic Density: The correct relic abundance is naturally achieved through specific resonant annihilation or co-annihilation channels involving the new scalars ( $h_s, A_s$ ) and electroweakinos.

C. Constraints and Predictions

LHC Constraints: Constraints from LHC searches for electroweakinos are found to be negligible for the viable parameter space. The electroweakino masses are generally heavy ( $> 500$ GeV), and in some cases, the mass spectra are compressed, leading to soft final states that evade current detection thresholds (low $R$ -values $< 0.35$ ).
Electroweak Precision: Scenario I is largely consistent with oblique parameters ( $S, T, U$ ). Scenario II faces tighter constraints from these parameters, excluding roughly half of its sampled points.
Benchmark Points: Four benchmark points (P1–P4) are identified:
- P1, P2, P3 (Scenario I): Successfully explain the excesses with Bino LSPs annihilating via the $A_s$ -funnel.
- P4 (Scenario II): Explains the combined $\sigma_{\gamma\gamma b\bar{b}}$ and $\mu_{\gamma\gamma}$ excesses but fails electroweak precision tests.

D. Future Prospects

The paper provides clear predictions for future tests:

High-Luminosity LHC (HL-LHC): The channel $pp \to H \to h_s h_s \to b\bar{b}b\bar{b}$ is predicted to have a significant cross-section (up to 120 fb in Scenario II), offering a promising discovery channel.
Direct Detection: While current SI limits are satisfied, future LZ runs and neutrino floor sensitivity could probe the parameter space, particularly for Scenario II.
Distinctive Signature: The presence of non-zero bilinear parameters $\mu$ and $\mu'$ serves as a direct signature distinguishing the GNMSSM from the minimal $Z_3$ -NMSSM and MSSM.

4. Significance

This work provides a unified and consistent theoretical framework for multiple independent collider anomalies that have been difficult to explain simultaneously.

Model Validation: It demonstrates that the GNMSSM, with its extended Higgs sector and $Z_3$ -breaking terms, is a viable BSM candidate that can accommodate light scalars and heavy resonances without conflicting with the 125 GeV Higgs data or DM constraints.
DM Connection: It establishes a robust link between the observed scalar excesses and the nature of Dark Matter, specifically favoring a Bino-dominated LSP with specific annihilation mechanisms.
Experimental Guidance: By identifying specific benchmark points and predicting cross-sections for future channels (e.g., $H \to h_s h_s$ ), the paper offers concrete targets for the High-Luminosity LHC and future colliders to confirm or rule out this scenario.

In conclusion, the paper argues that the GNMSSM offers a compelling solution to the 95 GeV and 650 GeV anomalies while maintaining a viable Dark Matter candidate, making it a priority target for upcoming experimental investigations.