The ABC of RPV II: Classification of R-parity Violating Signatures from UDD Couplings and their Coverage at the LHC

This paper utilizes the CheckMATE 2 framework to analyze R-parity violating signatures from UDD couplings in the MSSM, revealing that while colored LSPs are well-constrained by current LHC data, electroweakino and slepton LSPs remain significantly under-covered due to a lack of targeted experimental searches.

The Gist

Imagine the universe as a giant, incredibly complex Lego set. For decades, physicists have been trying to figure out the rules of how these Lego bricks snap together. The standard rules (the Standard Model) work well, but they leave some big gaps, like why gravity is so weak or where the "dark matter" that holds galaxies together is hiding.

To fill these gaps, scientists proposed a "Supersymmetric" (SUSY) version of the Lego set. In this new version, every known particle has a heavier, invisible "shadow twin." For a long time, the leading theory was that these shadow twins always come in pairs and that the lightest one is stable, invisible, and never decays. This invisible twin was the perfect candidate for Dark Matter.

The Plot Twist: R-Parity Violation
However, this paper explores a "what if" scenario. What if the rules are slightly different? What if these shadow twins aren't stable? What if the lightest one (the LSP) is actually unstable and decays into ordinary particles, like a Lego brick that suddenly turns into a handful of smaller, colorful pieces?

This is called R-parity violation (RPV). Instead of disappearing into the darkness (missing energy), the shadow twin explodes into a shower of jets (streams of particles) and maybe some leptons (electrons or muons).

The Mission: The "ABC" of the Explosion
The authors of this paper, led by Herbi Dreiner, are like a team of forensic investigators. Their goal is to map out every possible way these unstable shadow twins could explode. They call this the "ABC of RPV."

Specifically, they are focusing on a specific type of explosion caused by a rule called the UDD coupling. Think of the UDD coupling as a specific chemical reaction that turns a heavy shadow twin into three ordinary quarks (which look like jets of energy in a detector).

The Detective Work: Checking the Evidence
The Large Hadron Collider (LHC) is the giant machine smashing particles together to create these shadow twins. The ATLAS and CMS experiments are the cameras recording the crashes.

The problem? The cameras are set up to look for specific things.

• If the shadow twin is invisible (the old theory), the cameras look for a "missing piece" in the puzzle.
• If the shadow twin explodes into jets (the new theory), the cameras need to look for a pile of debris.

The authors asked: "Have we looked at the right piles of debris?"

They took a massive list of possible explosion scenarios (different types of shadow twins exploding in different ways) and ran them through a digital simulation tool called CheckMATE. This tool acts like a "recaster"—it takes the raw data from the LHC and asks, "If we had looked for this specific explosion pattern, would we have seen it?"

The Findings: The Good, The Bad, and The Missing

1. The Heavyweights are Caught (The Gluinos):
   The "gluino" is the heavy, colored shadow twin of the gluon (the particle that holds quarks together). The study found that the LHC has done a great job catching these. If a gluino shadow twin exists and explodes via the UDD rule, it would have to be incredibly heavy (over 1.8 TeV) to have escaped detection so far. The "multijet" searches (looking for piles of 6, 7, or 8 jets) are very effective here.

2. The Middleweights are Getting Trapped (The Squarks):
   Squarks are the shadow twins of quarks. The coverage here is decent, but there are some "loopholes." Some specific types of squark explosions (involving top or bottom quarks) are harder to spot because the background noise is high. The authors suggest that if experimentalists tweak their search strategies to look for specific combinations of jets and heavy quarks, they could push the limits even higher.

3. The Lightweights are Hiding in Plain Sight (The Electroweakinos and Sleptons):
   This is the big gap. The "electroweakinos" (shadow twins of the W/Z bosons and Higgs) and "sleptons" (shadow twins of electrons and muons) are much harder to catch in this scenario.

   • Why? Because their explosions often involve leptons (electrons/muons) mixed with jets. The current searches either aren't looking for this specific mix, or the tools to "recast" the data (re-analyze old data for new theories) aren't set up for it yet.
   • The Metaphor: Imagine the LHC cameras are looking for a pile of red bricks. But the slepton shadow twin explodes into a pile of red bricks and a blue balloon. The cameras are ignoring the blue balloons, so the slepton is hiding in plain sight.

The Conclusion: What's Next?
The paper concludes that while the "heavy" colored particles are well-covered, the "light" electroweak particles are largely unexplored territory in this specific "exploding twin" scenario.

The Takeaway for Everyone:
Science is a game of hide-and-seek. For a long time, we were looking for the "invisible" twins. Now we are looking for the "exploding" twins. This paper is a map that says, "We found the heavy ones, but we need to build better flashlights to find the light ones before we give up on the game."

They are calling on experimentalists (the people building the cameras) and theorists (the people drawing the maps) to work together to update the search strategies. If they do, they might finally catch the elusive shadow twins that could explain the mysteries of our universe.

Technical Summary

Here is a detailed technical summary of the paper "The ABC of RPV II: Classification of R-parity Violating Signatures from UDD Couplings and their Coverage at the LHC."

1. Problem Statement

The paper addresses the phenomenological status of R-parity violating (RPV) Supersymmetry (SUSY) within the Minimal Supersymmetric Standard Model (MSSM), specifically focusing on baryon-number violating (BNV) operators known as UDD couplings ($\lambda''_{ijk}\bar{U}_i\bar{D}_j\bar{D}_k$).

• Context: While R-parity conserving (RPC) SUSY is heavily constrained by Large Hadron Collider (LHC) searches (pushing colored sparticle masses to 1–2 TeV), RPV SUSY offers a viable alternative where the Lightest Supersymmetric Particle (LSP) is unstable and decays into Standard Model (SM) particles. This eliminates the Missing Transverse Energy ($E_T^{miss}$) signature typical of RPC SUSY, often resulting in complex multi-jet or multi-lepton final states.
• The Gap: Previous studies (specifically Ref. [92] by the same authors) analyzed LLE operators (lepton-number violating) and found comprehensive experimental coverage. However, the coverage for UDD operators was suspected to be less complete. There is a risk that specific LSP decay channels via UDD couplings have "loopholes" where current LHC searches are either not implemented in recasting frameworks or lack sensitivity to specific final states.
• Objective: To perform a systematic, detailed numerical study of all possible LSP decays via the four unique benchmark UDD coupling sets, identifying gaps in experimental coverage and determining mass exclusion limits for various LSP candidates (gluinos, squarks, electroweakinos, and sleptons).

2. Methodology

The authors extend the framework established in their previous work (Ref. [92]) to the UDD sector.

• Benchmark Scenarios:

  • LSP Candidates: The study considers a wide range of possible LSPs: Gluinos ($\tilde{g}$), Squarks ($\tilde{q}_L, \tilde{q}_R, \tilde{t}, \tilde{b}$), Electroweakinos (Bino $\tilde{B}$, Wino $\tilde{W}$, Higgsino $\tilde{H}$), and Sleptons ($\tilde{l}, \tilde{\nu}$).
  • Couplings: The 9 antisymmetric UDD couplings are grouped into 4 sets based on unique collider signatures. One benchmark coupling is selected from each set for numerical analysis:
    1. $\lambda''_{112}$ (Light quarks)
    2. $\lambda''_{113}$ (Light + Bottom)
    3. $\lambda''_{312}$ (Top + Light)
    4. $\lambda''_{313}$ (Top + Bottom)
  • Production Modes: Two scenarios are analyzed:
    1. Direct Production: Pair production of the LSP itself.
    2. Cascade Production: Pair production of a heavier Next-to-Lightest SUSY Particle (NLSP) which decays via gauge interactions to the LSP, which then decays via the RPV UDD coupling.
  • Assumptions: The UDD couplings are assumed to be in an intermediate range ($10^{-7} \lesssim \lambda'' \ll g$), ensuring prompt decays (decay length$< 1$ cm) but not affecting production cross-sections. Only one coupling is non-zero at a time.

• Computational Framework:

  • Event Generation: Processes are generated using MadGraph5_aMC@NLO with the RPV-MSSM UFO model.
  • Cross Sections: State-of-the-art NNLL-fast (for colored sparticles) and Resummino (for electroweak sparticles) cross-sections are used, rescaled for non-degenerate spectra.
  • Recasting: Events are processed through CheckMATE 2, a framework for recasting LHC searches.
  • New Implementations: To address coverage gaps, the authors manually implemented three critical searches into CheckMATE 2 (creating a modified version, CM2-mod):
    1. ATLAS Multijet Search (13 TeV): ATLAS-2024-01-16333 (sensitive to 6–8 jets).
    2. CMS OSSF Lepton + Jets Search (8 TeV): CMS-1602-04334 (sensitive to 2 opposite-sign same-flavor leptons + jets).
    3. CMS Leptoquark Search (13 TeV): CMS-1811-00806 (sensitive to $\tau\tau jj$).

3. Key Contributions

1. Systematic Classification: A complete mapping of final states for all possible LSPs decaying via the four benchmark UDD couplings, distinguishing between direct and cascade decays.
2. Framework Enhancement: The implementation of the ATLAS multijet search and the CMS 8 TeV OSSF lepton search into the CheckMATE 2 framework, significantly improving the theoretical capability to test UDD scenarios.
3. Gap Identification: A quantitative assessment revealing that while the colored sector is well-covered, significant gaps exist for electroweakino and slepton LSPs.

4. Key Results

A. Colored Sector (Gluinos and Squarks)

• Gluino LSPs: The colored sector is well-covered. The ATLAS multijet search (implemented in CM2-mod) provides the strongest constraints.
  • Gluino masses are excluded up to $\sim 1.85$ TeV (depending on the coupling).
  • The presence of $b$-jets or top quarks in the final state (e.g., $\lambda''_{113}, \lambda''_{313}$) generally leads to stricter limits due to better background rejection.
• Squark LSPs:
  • Direct Production: Limits vary significantly based on the final state. 4-jet topologies (e.g., $\tilde{u}_R \to ud$ via $\lambda''_{112}$) have weaker bounds ($\sim 800$ GeV) compared to multijet topologies with $b$-tags.
  • Cascade Production: When produced via gluino decays ($I_{\tilde{g} \to \tilde{q}}$), exclusion limits improve significantly.
    • For $\tilde{b}_L$ and $\tilde{t}_L$ LSPs, gluino masses up to 1.8–2.3 TeV are excluded.
    • For $\tilde{b}_R$ and $\tilde{t}_R$, limits reach 1.7–2.0 TeV.
  • Gap: Some right-handed squark scenarios (specifically 4-jet final states without heavy flavor) still have mass bounds below 500 GeV, indicating a need for targeted searches.

B. Electroweak Sector (Electroweakinos and Sleptons)

• Electroweakinos (Bino, Wino, Higgsino):
  • Coverage is Limited. Due to small production cross-sections and the presence of vector bosons ($W/Z/H$) in the decay chains, current searches lack sensitivity.
  • Bino LSPs: No significant exclusion limits were found for direct production. In cascade scenarios (from gluinos/squarks), limits are weak (e.g., gluinos excluded up to $\sim 1.6$ TeV for a 100 GeV bino, but the bino mass itself is unconstrained).
  • Wino/Higgsino: Exclusion limits are negligible (e.g., Higgsino limit $\sim 150$ GeV). The presence of $E_T^{miss}$ or leptons in intermediate steps often vetoes these events in multijet searches.
• Slepton LSPs:
  • Coverage is Limited. Slepton pair production leads to $2\ell + \text{jets}$or$2\ell + E_T^{miss}$ final states.
  • The CMS 8 TeV OSSF search (implemented in CM2-mod) provides the best sensitivity but fails to exclude any region of the parameter space.
  • The 13 TeV leptoquark search showed no improvement.
  • Conclusion: There is a clear experimental gap for slepton LSPs decaying via UDD couplings.

5. Significance and Conclusion

• Naturalness Implications: The results challenge the "Natural SUSY" scenario within the RPV framework. While RPC limits are severe, RPV limits on gluinos and stops are also pushing into the 1.5–2 TeV range, making it difficult to accommodate naturalness (which requires light stops/gluinos) without fine-tuning.
• Experimental Gaps: The study highlights a critical disparity: LLE operators are comprehensively covered, but UDD operators are not. Specifically, the electroweak sector (sleptons, winos, higgsinos) and specific right-handed squark channels are under-explored.
• Future Directions:
  • Recasting: Theoretical community needs more tools to recast searches with complex final states (e.g., neural network-based discriminators).
  • Targeted Searches: Experimentalists are urged to design specific searches for:
    • $2\ell + \text{jets}$ (for sleptons).
    • $2V + \text{jets}$ (for electroweakinos).
    • Specific 4-jet topologies for right-handed squarks.
  • Run 3 & HL-LHC: The authors suggest that Run 3 data and the High-Luminosity LHC (HL-LHC) are essential to close these gaps, particularly for the electroweak sector.

In summary, this paper provides a rigorous "ABC" (classification) of UDD signatures, demonstrating that while the colored sector is under strong pressure from LHC data, the electroweak sector remains a potential "hiding place" for low-mass SUSY particles due to a lack of targeted experimental coverage.