Searching for apparent baryon number violation in $\Lambda_c^+$ decays at the Super Tau-Charm Facility

This paper proposes and evaluates a dedicated search for apparent baryon number violation in $\Lambda_c^+$ decays at the Super Tau-Charm Facility, demonstrating that with 1 ab$^{-1}$ of integrated luminosity, the facility can probe new-physics scales of several TeV and constrain R-parity-violating supersymmetry parameters through model-independent sensitivity studies and theoretical interpretations.

The Gist

Imagine the universe as a giant, perfectly balanced ledger. For decades, physicists have believed that one specific entry in this ledger—Baryon Number (a count of the "stuff" that makes up matter, like protons and neutrons)—can never be erased or created out of thin air. It's a rule as strict as "you can't create money out of nothing."

However, we know the universe has a problem: there is way more matter than antimatter. If the ledger was perfectly balanced from the start, they should have canceled each other out, leaving nothing but empty space. To explain why we exist, there must have been a time when this rule was broken.

This paper is a proposal to go hunting for that broken rule, but instead of looking at the biggest, loudest explosions (like at the Large Hadron Collider), the authors suggest looking at a very specific, quiet corner of the physics world: the decay of a "charmed" particle called the $\Lambda_c^+$.

Here is the story of their proposal, broken down with some everyday analogies.

1. The Setting: A Perfectly Organized Ballroom

The authors are proposing to use a new machine called the Super Tau-Charm Facility (STCF), which is being built in China.

• The Analogy: Imagine a ballroom where couples (particles) are dancing. Usually, in other ballrooms (like the LHC), it's a chaotic mosh pit. But the STCF is a special ballroom where the music is tuned to a specific beat (energy level) that forces the dancers to pair up perfectly as $\Lambda_c^+$ and $\Lambda_c^-$ (a particle and its anti-particle).
• Why this matters: Because they are created in pairs and are almost at rest, if one partner does something weird, we can easily spot it by looking at the other partner. It's like having a perfect "twin" to compare against.

2. The Crime Scene: The "Vanishing Act"

The scientists are looking for a specific type of "magic trick." They want to see a $\Lambda_c^+$ particle decay (break apart) into two things:

1. A visible particle (a charged pion or a kaon, which are like heavy versions of pions).
2. Missing Energy.

• The Analogy: Imagine you see a magician on stage. He holds a heavy gold coin (the $\Lambda_c^+$). He snaps his fingers, and suddenly, you see a silver coin (the pion/kaon) on the table. But the gold coin is gone, and there is no second silver coin to balance the equation.
• The Twist: In normal physics, the gold coin should have turned into two silver coins. If only one is there, it means something invisible escaped.
• The Culprit: The "missing" part is likely a Sterile Neutrino or a Light Bino (particles from "Beyond the Standard Model"). These are ghosts that don't interact with our detectors, so they just vanish, taking the "baryon number" with them.

3. The Investigation: The "Double-Tag" Method

How do they know the gold coin didn't just fall off the table? They use a technique called Double-Tagging.

• The Analogy: Since the particles are created in pairs, the scientists catch the other partner (the $\Lambda_c^-$) and identify exactly what it is. If they know the starting weight and the weight of the visible silver coin, they can calculate exactly how much "ghost" weight is missing.
• The Tool: They use a super-computer simulation called OSCAR (like a digital twin of the detector) to predict how often they would catch this trick if it were happening. They found that with a lot of data (1 "ab" of luminosity, which is a huge amount of collisions), they could spot this trick even if it happens only 1 time in 10 million.

4. The Theory: Two Suspects

The paper tests two main theories about who the "ghost" might be:

• Suspect A: The Sterile Neutrino. A particle that is a cousin to the neutrino but doesn't talk to anything else. It's the ultimate ghost.
• Suspect B: The Light Bino. A particle from a theory called Supersymmetry (SUSY). Think of this as a "shadow particle" that is the lightest of its kind and also escapes detection.

The authors calculated that if these particles exist, the STCF could detect them and measure how heavy they are. If they find nothing, they can rule out these particles existing up to very high energy scales (about 3 to 6 times heavier than the heaviest particles we currently know).

5. Why This Matters

If they find this "missing energy," it would be the smoking gun for New Physics.

• It would prove that the "Baryon Number" rule can be broken.
• It would help explain why the universe is made of matter and not empty space.
• It would be a discovery of a completely new type of particle that has never been seen before.

The Bottom Line

This paper is a blueprint for a "ghost hunt." The authors are saying: "We have built a perfect, quiet ballroom (STCF) where we can watch these particles dance. If we watch closely enough, we might catch one of them sneaking a ghost particle out of the room. If we do, we solve one of the biggest mysteries in the universe: why we are here at all."

Even if they don't find the ghost, the fact that they can look so deeply into the "darkness" of the particle world is a massive step forward for physics.

Technical Summary

1. Problem Statement

• Physics Context: Baryon number (B) is conserved in the Standard Model (SM) at all perturbative orders. Its violation (BNV) is a necessary condition for baryogenesis (explaining the matter-antimatter asymmetry) but has never been observed experimentally. Current limits on proton lifetime ($O(10^{34})$ years) are extremely stringent, yet BNV could manifest in rare decays of heavy hadrons involving long-lived new particles.
• The Gap: While BNV searches have been proposed in meson decays (e.g., $B$-mesogenesis), searches in charm-baryon decays remain largely unexplored. Specifically, the decay $\Lambda_c^+ \to M^+ + \text{missing energy}$ (where $M = \pi, K$) offers a unique signature where a visible meson is produced alongside a long-lived, invisible fermion (sterile neutrino or light neutralino) that escapes detection, creating an "apparent" BNV signal.
• The Opportunity: The Super Tau-Charm Facility (STCF), proposed for Hefei, China, will operate at center-of-mass energies ($\sqrt{s}$) between 2–7 GeV. Operating near the $\Lambda_c^+ \Lambda_c^-$ production threshold ($\sqrt{s} \approx 4.682$ GeV) provides a uniquely clean environment with high luminosity ($0.5 \times 10^{35} \text{ cm}^{-2}\text{s}^{-1}$) and copious production of charm baryon pairs, enabling precise kinematic reconstruction via double-tagging.

2. Methodology

The authors employ a multi-step approach combining theoretical effective field theories (EFT) and advanced detector simulations.

A. Theoretical Frameworks

The study focuses on two specific Beyond-the-Standard-Model (BSM) scenarios where a long-lived particle ($X$) is produced:

1. Sterile Neutrino Extended Low-Energy EFT ($\nu$LEFT):
   • Introduces a sterile neutrino ($\nu_s$) and dimension-6 BNV operators involving charm, down, and strange quarks (e.g., $O_{cdd}^{S,RR}$).
   • Matching: The authors match $\nu$LEFT operators to Baryon Chiral Perturbation Theory (BChPT). Since BChPT is formally valid only for light baryons, they extrapolate nucleon matrix elements to the $\Lambda_c^+$ baryon.
   • Uncertainty Handling: To account for the extrapolation uncertainty (SU(3) and heavy-quark symmetry breaking), they vary the hadronic form factor $\beta_{\Lambda_c}$ by factors of 2 and 1/2.
   • Mechanisms: The decay $\Lambda_c^+ \to M^+ \nu_s$ proceeds via "pole" (intermediate baryon exchange) and "non-pole" (direct) diagrams.
2. R-Parity Violating Supersymmetry (RPV-SUSY):
   • Assumes a light bino neutralino ($\tilde{\chi}_1^0$) as the Lightest Supersymmetric Particle (LSP).
   • Focuses on a single non-zero RPV coupling $\lambda''_{212}$, which allows the decay $\Lambda_c^+ \to K^+ \tilde{\chi}_1^0$.
   • The squark masses are assumed to be heavy ($\sim$ TeV), allowing integration out to form a dimension-6 effective operator matching the $\nu$LEFT structure.

B. Experimental Simulation & Analysis

• Facility: STCF at $\sqrt{s} = 4.682$ GeV with an integrated luminosity of $1 \text{ ab}^{-1}$.
• Event Generation:
  • Simulated $e^+e^- \to \Lambda_c^+ \Lambda_c^-$ pairs using the OSCAR detector simulation framework (based on GEANT4 and SNiPER architecture).
  • Used KKMC for initial state radiation, EvtGen for decay modeling, and PHOTOS for final state radiation.
• Tagging Strategy (Double-Tag Method):
  • Tag Side: Reconstruct the $\Lambda_c^-$ baryon using the dominant decay mode $\Lambda_c^- \to p K^+ \pi^-$ (BR $\approx 6.35\%$).
  • Signal Side: Search for $\Lambda_c^+ \to M^+ + \text{missing}$ ($M = \pi^+, K^+$).
  • Kinematic Cuts: Applied strict cuts on beam-constrained mass ($m_{BC}$) and energy difference ($\Delta E$) for the tag side. The signal side requires a positive missing mass squared ($m_{\text{missing}}^2 > 0$).
• Signal Efficiency: Calculated reconstruction efficiencies ($\epsilon$) as a function of the missing particle mass ($m_{\text{missing}}$).
• Sensitivity Calculation: Assuming negligible background, the exclusion limit at 95% Confidence Level (C.L.) corresponds to 3 signal events ($N_S = 3$).

3. Key Contributions

1. First Dedicated Proposal: This is the first study proposing a dedicated search for apparent BNV in $\Lambda_c^+$ decays at a threshold charm factory.
2. Realistic Simulation: Unlike previous theoretical studies, this work utilizes full detector simulations (OSCAR) specific to the proposed STCF design, providing realistic efficiency estimates.
3. Theoretical Extrapolation: The authors provide a rigorous framework for applying BChPT to charmed baryons by introducing a controlled uncertainty band for the hadronic form factors.
4. Dual Interpretation: The results are interpreted in two distinct theoretical contexts: $\nu$LEFT (sterile neutrinos) and RPV-SUSY (light bino), bridging the gap between low-energy effective operators and specific UV-complete models.

4. Results

• Reconstruction Efficiency:
  • For low missing masses, signal reconstruction efficiencies are approximately 40%.
  • Efficiencies drop rapidly as the missing mass approaches the kinematic threshold ($m_{\Lambda_c} - m_M$).
• Branching Ratio Sensitivity:
  • With $1 \text{ ab}^{-1}$, STCF can probe branching ratios down to $\mathcal{O}(10^{-7})$ for $\Lambda_c^+ \to \pi^+/K^+ + \text{missing}$.
• New Physics (NP) Scale Limits ($\nu$LEFT):
  • For Wilson coefficients $c \sim 1$, STCF can probe NP scales ($\Lambda$) up to 3–6 TeV.
  • This sensitivity exceeds current LHC constraints (MET+jets) for the specific mass range of the sterile neutrino considered ($m_{\nu_s} \in [m_p, m_{\Lambda_c}-m_M]$).
  • If strong coupling ($c \sim 4\pi$) is assumed, the reach extends to $\sim 8$ TeV.
• RPV-SUSY Constraints:
  • STCF can constrain the RPV parameter combination $\lambda''_{212}/m_{\tilde{q}}^2$ down to $\sim 0.1 \text{ TeV}^{-2}$ for a light bino mass between 1 GeV and the kinematic limit.
  • This complements LHC searches, which are less sensitive to the specific kinematic configurations of charm baryon decays.

5. Significance

• Unique Discovery Potential: The threshold production of $\Lambda_c^+ \Lambda_c^-$ pairs at STCF offers a "clean" environment where the baryons are nearly at rest and produced in correlated pairs. This allows for double-tagging, a technique that drastically suppresses background and enables precise kinematic closure for missing energy signatures, which is difficult to achieve at $B$-factories (like Belle II) or high-energy colliders (LHC).
• Complementarity: The proposed search probes BNV operators in a mass range and kinematic regime inaccessible to current proton decay experiments and LHC searches. It specifically targets long-lived fermions that escape the detector, a signature often missed in standard MET searches.
• Feasibility: The study demonstrates that with realistic detector performance and standard analysis techniques, STCF can significantly improve upon current bounds on BNV in the charm sector, potentially providing the first evidence of baryon number violation in a laboratory setting.
• Future Outlook: The authors note that including additional tag channels (currently only the dominant $pK\pi$ mode is used) could further enhance sensitivity, potentially pushing the NP scale reach to $\sim 8$ TeV.

In conclusion, the paper establishes STCF as a premier facility for probing rare, semi-invisible charm-baryon decays, offering a competitive and unique pathway to discovering physics beyond the Standard Model related to baryon number violation.