Current status of the light neutralino thermal dark matter in the phenomenological MSSM

This paper reaffirms the robustness of strong experimental constraints on light neutralino thermal dark matter within the phenomenological MSSM, explores the impact of light staus and non-standard cosmology, and proposes machine learning-optimized benchmarks for future LHC Run-3 searches.

The Gist

Here is an explanation of the paper "Current status of the light neutralino thermal dark matter in the phenomenological MSSM," translated into simple, everyday language with creative analogies.

The Big Picture: The Cosmic Hide-and-Seek Game

Imagine the universe is a giant, dark room filled with invisible ghosts. We know these ghosts exist because they have mass (they pull on stars), but we can't see them. These are Dark Matter.

For decades, physicists have had a favorite suspect for what these ghosts might be: a particle called the Neutralino. Think of the Neutralino as a "ghostly cousin" of the particles we know (like electrons). It's part of a theory called the MSSM (Minimal Supersymmetric Standard Model), which is like an "expanded instruction manual" for the universe that predicts these extra cousins exist.

This paper is a detective report. The authors are asking: "Can our favorite suspect, the 'Light Neutralino,' still be hiding in the shadows, or have the police (experiments) finally caught it?"

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1. The Suspect: The "Light" Neutralino

Usually, we expect these ghost particles to be heavy. But this paper focuses on a specific type: a Light Neutralino.

• The Analogy: Imagine a thief who is so light they can slip through a crack in a door that heavier thieves can't.
• The Catch: If this thief is too light, they should be able to hide inside a "safe" called the Higgs Boson (the particle that gives other things mass). If the Higgs Boson decays into these light ghosts, it would disappear invisibly.

2. The Police Raid: The New Evidence

The authors looked at the latest "police reports" from two main sources:

1. The LHC (Large Hadron Collider): This is the world's biggest particle accelerator (a giant racetrack for atoms). It's been smashing particles together to see if it can catch these ghosts.
2. LZ (LUX-ZEPLIN): This is a super-sensitive underground detector filled with liquid xenon. It's waiting for a ghost to bump into an atom and make a tiny splash.

The Verdict: The new evidence is very bad news for the "Light Neutralino" in most scenarios.

• The "Positive" Scenario (µ > 0): It's like the suspect was wearing a bright red shirt. The LZ detector saw the "red shirt" (a specific interaction) and said, "You're not allowed to be this light!" The police have effectively ruled out almost all the places where this suspect could hide, unless the suspect is very heavy (over 850 GeV).
• The "Negative" Scenario (µ < 0): Here, the suspect is wearing a camouflage suit. The physics works differently (destructive interference), making the ghost harder to see. The police haven't caught them yet, but they have cornered them into a very small, dark alley. The suspect can only survive if they are either very heavy OR very light (between 125 and 160 GeV).

3. The "Funnel" Analogy

The paper talks about "Z-funnel" and "H-funnel" regions.

• The Analogy: Imagine trying to get a ball (Dark Matter) to stop moving. Usually, it rolls forever. But if there is a specific hole in the floor (a resonance) at exactly the right size, the ball drops in and disappears.
• The Z-funnel: The hole is the size of the Z-boson.
• The H-funnel: The hole is the size of the Higgs boson.
• The Result: The new detectors (LZ) have poured concrete over the "Z-funnel" for the positive scenario. It's completely blocked. The "H-funnel" is still open, but only for very heavy ghosts.

4. The "Getaway Car": Light Staus

What if the suspect has a getaway car?

• The Analogy: The authors realized that if there is another light particle called a Stau (a heavy cousin of the tau particle), the Neutralino can jump into the Stau's car and escape.
• The Impact: If this "Stau car" exists, the police (LZ) can't catch the Neutralino as easily. It opens up new hiding spots, even in the previously blocked "Z-funnel." This means the suspect is still at large if this specific car exists.

5. The "Alien Cosmology" Twist

Finally, the authors ask: "What if the rules of the universe are different?"

• The Analogy: Imagine the universe is a bathtub. Usually, we think the water level (Dark Matter density) is fixed. But what if someone poured a giant bucket of water in after the ghosts were made? The water level would rise, diluting the concentration of ghosts.
• The Result: If the universe had a "non-standard" history (like a late burst of energy), the ghosts could be much heavier and more abundant than we thought, and they would still fit the data. It's like saying, "The suspect isn't hiding; the crime scene was just cleaned up differently than we expected."

6. The Hunt Continues: Machine Learning

Since the suspect is hiding in a very small, tricky area (the "light" region), the authors used XGBoost (a super-smart computer algorithm) to analyze the data from the LHC.

• The Analogy: Instead of looking for a needle in a haystack with your eyes, they built a robot that can smell the needle.
• The Finding: The robot says, "Hey! If you look really closely at the next run of the LHC (Run-3), you might just catch these light ghosts, especially if they are wearing the 'Stau getaway car' or if the universe is 'camouflaged' (negative µ)."

Summary: What does this mean for us?

1. The "Easy" Suspects are Gone: The light, "positive" Neutralinos are almost certainly ruled out by new experiments.
2. The "Hard" Suspects are Cornered: The "negative" ones are still possible, but they are squeezed into a tiny, specific range of masses.
3. New Hiding Spots: If there are light "Stau" particles, the suspect can still hide.
4. The Future: The next run of the LHC (Run-3) and future upgrades of the LZ detector are the final showdown. If the suspect is still out there, these machines are the only ones that can catch them.

In short: The universe is playing a very tough game of hide-and-seek. The "easy" hiding spots are gone, but the game isn't over yet. The detectives are now focusing on the most complex, tricky hiding spots, using super-computers to find the last remaining clues.

Technical Summary

Here is a detailed technical summary of the paper "Current status of the light neutralino thermal dark matter in the phenomenological MSSM" (BONN-TH-2024-03).

1. Problem Statement

The paper investigates the viability of a light neutralino ($\tilde{\chi}^0_1$) as a thermal dark matter (DM) candidate within the Phenomenological Minimal Supersymmetric Standard Model (pMSSM). Specifically, it focuses on the scenario where the neutralino mass is light ($M_{\tilde{\chi}^0_1} \leq M_h/2$), allowing the Standard Model-like Higgs boson to decay invisibly ($h \to \tilde{\chi}^0_1 \tilde{\chi}^0_1$).

The core problem is that recent experimental results from the LHC (Run-2 and early Run-3) and Dark Matter Direct Detection (DD) experiments, particularly the LUX-ZEPLIN (LZ) collaboration, have placed severe constraints on this scenario. Previous studies suggested that light neutralinos are largely excluded, but this work aims to rigorously test the robustness of that conclusion across the high-dimensional pMSSM parameter space, considering:

• The sign of the Higgsino mass parameter ($\mu > 0$ vs. $\mu < 0$).
• The impact of light staus (sleptons) as Next-to-Lightest Supersymmetric Particles (NLSPs).
• Non-standard cosmological scenarios (entropy dilution).

2. Methodology

The authors employed a comprehensive computational framework involving random scans and dedicated analyses:

• Parameter Space: A 10-parameter pMSSM scan was performed. Key parameters included Gaugino masses ($M_1, M_2$), Higgsino mass ($\mu$), $\tan\beta$, pseudoscalar mass ($M_A$), third-generation squark masses, trilinear coupling ($A_t$), and gluino mass ($M_3$).
  • Scan Strategy: Random scans were conducted for both $\mu > 0$ and $\mu < 0$. Dedicated scans were performed to populate the "funnel regions" (Z-funnel: $M_{\tilde{\chi}^0_1} \approx M_Z/2$; h-funnel: $M_{\tilde{\chi}^0_1} \approx M_h/2$) by dynamically tuning $M_1$.
  • Light Staus: A second scan introduced light right-handed (RH) staus ($M_{\tilde{e}_{3R}} \in [85, 500]$ GeV) while keeping other sfermions heavy.
• Tools:
  • FeynHiggs 2.18.1: Calculated the SUSY particle spectrum, Higgs masses, and branching ratios.
  • MicrOMEGAS 5.2.13: Computed relic density ($\Omega h^2$), direct detection (DD) cross-sections (Spin-Independent and Spin-Dependent), and LEP/Flavor observables.
  • SModelS 2.2.1/2.3.0 & CheckMATE 2: Applied constraints from LHC electroweakino searches (charginos/neutralinos).
  • HiggsBounds/HiggsSignals: Applied constraints on heavy Higgs searches and Higgs signal strengths.
  • XGBOOST: A machine learning framework used to analyze specific benchmark points in the $3\ell + \not{E}_T$ channel to estimate LHC sensitivity.
• Constraints Applied:
  • Higgs mass ($122-128$ GeV) and signal strength.
  • Invisible Higgs decay branching ratio ($<11\%$).
  • LEP limits on charginos/neutralinos and Z-width.
  • Flavor observables ($b \to s\gamma$, $B_s \to \mu^+\mu^-$, $B \to \tau\nu$).
  • Relic Density: $\Omega h^2 \leq 0.122$ (allowing for multi-component DM).
  • Direct Detection: Limits from LZ (SI), PandaX-4T (SDn), and PICO-60 (SDp).

3. Key Contributions and Results

A. Impact of LZ on the $\mu > 0$ Scenario

• Z-Funnel: Completely excluded. The constructive interference between light ($h$) and heavy ($H$) Higgs boson contributions to the Spin-Independent (SI) cross-section, combined with the tight LZ bounds, rules out this region.
• h-Funnel: Only heavy Higgsinos ($M_{\tilde{\chi}^0_1} \gtrsim 350$ GeV, typically $>850$ GeV to satisfy electroweakino searches) survive. These require very low $\tan\beta$ to suppress the coupling to the Higgs.
• Conclusion: The $\mu > 0$ scenario for light neutralinos is under "severe tension" or effectively ruled out for thermal DM in standard cosmology.

B. Impact of $\mu < 0$ Scenario

• Survival Mechanism: For $\mu < 0$, there is destructive interference between the $h$ and $H$ contributions to the SI cross-section (specifically for down-type quarks at large $\tan\beta$). This significantly reduces the DD cross-section, allowing light neutralinos to survive LZ constraints.
• Allowed Regions:
  • Z-Funnel: Light Higgsinos ($125-145$ GeV) survive.
  • h-Funnel: Light Higgsinos ($145-160$ GeV) survive.
  • Heavy Higgsinos: Regions with $M_{\tilde{\chi}^0_1} \gtrsim 850$ GeV also survive.
• Significance: The $\mu < 0$ scenario remains viable, with specific "light Higgsino" benchmarks that are currently allowed by all constraints but are prime targets for LHC Run-3.

C. Collider Analysis and Machine Learning

• The authors identified benchmark points (e.g., BP2, BP3) in the light Higgsino region ($M_{\tilde{\chi}^0_1} \sim 45-60$ GeV, $M_{\tilde{\chi}^\pm_1} \sim 125-155$ GeV) that evade current SModelS/CheckMATE limits due to compressed spectra (small mass differences).
• XGBOOST Analysis: Using the $3\ell + \not{E}_T$channel at$\sqrt{s}=14$TeV with$137$fb$^{-1}$ (Run-2) and projected Run-3 luminosities:
  • BP2 (Z-funnel): Achieved $\sim 3.1\sigma$ significance with 20% systematic uncertainty.
  • BP3 (h-funnel): Achieved $\sim 4.5\sigma$ significance with 20% systematic uncertainty.
• Result: These light Higgsinos are within the reach of LHC Run-3, provided systematic uncertainties can be controlled.

D. Impact of Light Staus

• Introducing light RH staus ($M_{\tilde{\tau}_1} \sim 90-150$ GeV) opens new annihilation channels ($\tilde{\chi}^0_1 \tilde{\chi}^0_1 \to \tilde{\tau} \tilde{\tau}^*$), reducing the relic density.
• Effect on $\mu > 0$: This relaxation allows a small region in the Z-funnel to survive, which was previously excluded. It also lowers the mass limit for Higgsinos in the h-funnel (allowing $\sim 500$ GeV Higgsinos).
• Collider Impact: If Higgsinos decay to staus, the branching ratios change, potentially weakening current electroweakino exclusion limits (which assume 100% decay to $W/Z/h$).

E. Non-Standard Cosmology

• In scenarios with late-time entropy injection (diluting the DM relic density), the constraint on the annihilation cross-section is relaxed.
• Result: This allows for very heavy Higgsinos (up to 2 TeV) and non-resonant masses to be viable thermal DM candidates. These scenarios would produce very small DD cross-sections, making them invisible to current DD experiments but potentially detectable via heavy Higgsino signals at the LHC.

4. Significance and Conclusion

• Robustness of Exclusion: The paper confirms that for standard cosmology, the $\mu > 0$ light neutralino scenario is effectively ruled out by the combination of LZ and LHC data.
• Viable Pathways: The $\mu < 0$ scenario with light Higgsinos remains the most promising thermal DM candidate. The paper provides specific benchmark points (BP2, BP3) that are testable in the near future.
• Role of Run-3: The LHC Run-3 is crucial. The authors demonstrate that with machine learning techniques (XGBOOST) and improved systematic control, the surviving light Higgsino regions can be probed with high significance.
• Interplay of Physics: The study highlights the critical role of the sign of $\mu$ (determining interference patterns in DD) and the presence of light staus (altering relic density and collider decay chains) in defining the viable parameter space.
• Future Outlook: Future DD experiments (e.g., 1000 days of LZ) and high-luminosity LHC (HL-LHC) will be decisive in either discovering these light Higgsinos or pushing the thermal neutralino DM hypothesis into non-standard cosmological regimes.

In summary, this work refines the "light neutralino" landscape, ruling out the positive $\mu$ case while identifying specific, testable signatures for the negative $\mu$ case, emphasizing the synergy between direct detection, collider searches, and machine learning analysis.