R-parity violation and 8 TeV four-jet events at the LHC

This paper proposes a supersymmetry model with R-parity violation to explain two rare 8 TeV four-jet events observed by the CMS Collaboration as a heavy down-squark decaying into two lighter first-generation right-handed squarks, while outlining the constraints and predictions for future LHC verification.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smashing machine. Scientists at the LHC's CMS detector recently spotted something very strange: two rare events where four distinct "jets" of particles flew out, carrying a total energy equivalent to 8 TeV (tera-electronvolts). To put that in perspective, that's roughly the energy of a flying mosquito, but packed into a space smaller than an atom.

Even stranger, these four jets weren't just random debris. They looked like two pairs of jets, where each pair had an energy of about 2 TeV. It's as if a giant, invisible boulder (8 TeV) smashed into two smaller boulders (2 TeV each), which then shattered into pieces.

This paper, written by Pedro Bittar, Subhojit Roy, and Carlos E.M. Wagner, tries to explain this mystery using a theory called Supersymmetry (SUSY), but with a twist.

The Mystery: A Heavy Rock Breaking into Lighter Rocks

In the standard rules of physics, creating such heavy particles is incredibly difficult, like trying to hit a bullseye on a dartboard that is moving at the speed of light. The fact that the CMS team saw two of these events suggests something specific is happening, not just random noise.

The authors propose a scenario where a heavy particle (a "squark," which is a super-heavy cousin of the down-quark) is created. This heavy particle weighs about 8 TeV. Instead of disappearing into nothingness, it splits into two lighter particles (other squarks), each weighing about 2 TeV. These lighter particles then immediately decay into the four jets of energy we see.

The Twist: Breaking the Rules (R-Parity Violation)

Usually, physicists believe in a rule called "R-Parity," which acts like a cosmic safety net. It ensures that the lightest supersymmetric particle is stable (a candidate for Dark Matter) and prevents protons from decaying too quickly.

However, this paper suggests that for this specific event, R-Parity is broken. Imagine a safety net with a small hole in it. Through this hole, the heavy 8 TeV particle can decay into the lighter 2 TeV particles, which then turn into the jets we see. This "hole" is caused by a specific interaction called a baryon-number violating coupling (a fancy way of saying a rule that usually keeps matter stable is temporarily ignored).

The Recipe for Success

To make this work, the authors had to cook up a very specific recipe:

1. The Heavy Ingredient: A "down-squark" from the third generation (related to bottom quarks) weighing 8 TeV.
2. The Light Ingredients: Two "up" or "down" squarks from the first generation (related to regular protons and neutrons) weighing 2 TeV each.
3. The Glue: A specific mathematical "coupling" (a strength of interaction) that connects them. The authors found that if this coupling is about 0.33, the math works out to produce exactly the number of events the CMS team saw (about 2 events).

The Safety Checks: Why We Haven't Seen Protons Exploding

If you break the rules of physics to explain a new particle, you have to make sure you don't break the universe. The authors had to check two major safety concerns:

1. Neutron Oscillations: If the rules are broken too easily, neutrons (particles inside atoms) might turn into anti-neutrons and vanish. The paper shows that for their recipe to work, the "mixing" between the heavy third-generation particles and the lighter first-generation particles must be incredibly tiny—like finding a specific grain of sand in a desert. They propose a "flavor symmetry" (a hidden order in nature) that keeps these generations separate, preventing the neutrons from vanishing.
2. Dinucleon Decay: This is the fear that two protons or neutrons might decay into pions or kaons (lighter particles). The authors show that their specific recipe avoids this disaster, provided the mixing between the second and third generations is also kept very small.

The Verdict

The paper concludes that this specific "broken rule" scenario is a plausible explanation for the two rare 8 TeV events seen by CMS. It fits the data without contradicting other known laws of physics, provided that:

• The heavy particle is about 8 TeV.
• The lighter particles are about 2 TeV.
• The "mixing" between different types of particles is kept extremely low to prevent protons from decaying.

What's Next?
The authors say this isn't a proven fact yet, but a strong hypothesis. To confirm it, the LHC needs to run longer and collect more data. If this theory is right, future collisions should reveal:

• More of these 8 TeV four-jet events.
• Specifically, two of the four jets in these events should be identifiable as bottom quarks (a signature of the heavy particle they proposed).

If future data shows these bottom quarks, the "hole in the safety net" theory gains credibility. If not, the mystery of the 8 TeV events remains unsolved.

Technical Summary

Technical Summary: R-parity violation and 8 TeV four-jet events at the LHC

Problem Statement
The CMS Collaboration at the Large Hadron Collider (LHC) has reported the observation of two rare four-jet events with a total invariant mass of approximately 8 TeV. Within these events, the jets can be paired into two dijets, each with an invariant mass of roughly 2 TeV. These events are statistically significant due to the extremely low Standard Model (QCD) background expected at such high invariant masses and the specific dijet substructure suggesting a heavy resonance decaying into two lighter resonances. The paper investigates whether these anomalies can be interpreted within the framework of Supersymmetry (SUSY) with R-Parity Violation (RPV), specifically utilizing a single baryon-number violating coupling.

Methodology and Model Setup
The authors propose a minimal RPV SUSY scenario characterized by the following components:

• Superpotential: The model relies on a single non-zero RPV coupling, $\lambda''_{11k}$ (where $k=2,3$), in the superpotential term $W_{RP} = \frac{\lambda''_{ijk}}{2} \epsilon_{\alpha\beta\gamma} U^{\alpha}_i D^{\beta}_j D^{\gamma}_k$. This coupling allows for the resonant production of a heavy right-handed down-type squark ($\tilde{d}^*_k$) via valence quark collisions ($ud \to \tilde{d}^*_k$).
• Mass Spectrum: The heavy parent squark ($\tilde{d}^*_k$) is assigned a mass of approximately 8 TeV. It decays into two lighter first-generation squarks ($\tilde{u}_i, \tilde{d}_j$) with masses of approximately 2 TeV.
• Decay Mechanism: The decay chain $\tilde{d}^*_k \to \tilde{u}_i \tilde{d}_j$ is mediated by an antisymmetric soft trilinear coupling $A_{ijk}$. The lighter squarks subsequently decay into quark pairs ($\tilde{u}_i \to ud$, $\tilde{d}_j \to ud$) via the same $\lambda''_{11k}$ coupling, resulting in a fully hadronic four-jet final state.
• Simulation and Constraints: The authors utilize MadGraph5 aMC@NLO to calculate production cross-sections and branching ratios, applying a K-factor of 1.3 to emulate NLO QCD effects. They confront these predictions with:
  • CMS and ATLAS dijet resonance searches (specifically looking for resonant production of the 2 TeV squarks).
  • Non-resonant four-jet production limits.
  • Low-energy constraints from neutron-antineutron ($n-\bar{n}$) oscillations and dinucleon decays.

Key Contributions and Results

1. Benchmark Scenario: The authors identify a benchmark point where $m_{\tilde{d}^*_k} \approx 8$ TeV, $m_{\tilde{q}} \approx 2$ TeV, $\lambda''_{11k} \approx 0.33$, and $A_{11k} \approx 5$ TeV.

   • This configuration yields a branching ratio of $\approx 0.75$ for the decay into lighter squarks.
   • The total width is narrow ($\Gamma \approx 1.8\%$), consistent with resonance treatments.
   • The predicted cross-section for the four-jet signal is $\sigma \approx 7.0 \times 10^{-2}$ fb. With an acceptance of $\approx 20\%$ and an integrated luminosity of 139 fb$^{-1}$, this predicts approximately 2.5 events, consistent with the two observed CMS candidates (plus potential off-shell contributions).

2. Flavor Constraints ($k=2$ vs. $k=3$):

   • Case $k=2$ (Strange squark): The coupling $\lambda''_{112}$ is tightly constrained by dijet searches and dinucleon decay limits. The analysis shows that satisfying the 2 TeV dijet bounds requires $\lambda''_{112} \lesssim 0.26$, which is insufficient to generate the observed 8 TeV four-jet rate. Furthermore, dinucleon decay bounds force $\lambda''_{112} \lesssim 3 \times 10^{-5}$, effectively ruling out this specific flavor configuration for the observed excess.
   • Case $k=3$ (Bottom squark): The coupling $\lambda''_{113}$ remains consistent with current dijet limits ($\lambda''_{113} \lesssim 0.38$) and can accommodate the required production rate. In this scenario, two of the four final-state jets originate from bottom quarks, offering a potential "b-tagging" handle for future verification.

3. Low-Energy Bounds and Flavor Structure:

   • The model must satisfy stringent bounds from $n-\bar{n}$ oscillations and dinucleon decays. These processes depend on the mixing between the first/second generation squarks and the third generation ($\delta^d_{RR}$).
   • To survive these bounds with $\lambda''_{113} \sim 0.33$, the mixing parameters $(\delta^d_{RR})_{13}$ and $(\delta^d_{RR})_{23}$ must be strongly suppressed (e.g., $< 10^{-5}$).
   • The authors suggest that a $U(2) \times U(2)$ flavor symmetry in the right-handed sector, where the third generation is neutral and the first two are charged, could naturally enforce this suppression and prevent dangerous flavor mixing.

4. Mass Distribution: The simulated signal distribution in the four-jet invariant mass ($m_{4j}$) and the kinematic ratio $\alpha = m_{2j}/m_{4j}$ aligns with the CMS data, showing a peak near $m_{4j} \approx 8$ TeV and $\alpha \approx 0.25$. The authors note that while ATLAS has not observed a significant excess, their observation of one event is not statistically sufficient to exclude the CMS anomaly.

Significance and Claims
The paper claims to provide a well-defined, minimal theoretical framework that interprets the rare 8 TeV four-jet events as the resonant production and decay of a heavy third-generation squark into lighter first-generation squarks via R-parity violation.

• Falsifiability: The scenario makes specific, testable predictions:
  1. An increase in 8 TeV four-jet events with higher luminosity.
  2. The presence of b-tagged jets in two of the four final-state jets (in the $k=3$ benchmark).
  3. A resonant dijet feature near 2 TeV at higher luminosities.
• Constraints: The authors emphasize that the viability of this explanation relies heavily on the suppression of flavor mixing between the third generation and the first two generations to satisfy low-energy baryon-number violation bounds. They do not claim to have definitively proven the existence of these particles but rather outline a consistent scenario that fits the current data and offers clear paths for experimental verification or exclusion.