Probing baryon number with missing energy

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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

The Big Picture: The Great Cosmic Balance Sheet

Imagine the universe is a giant bank. In this bank, there is a strict rule called Baryon Number. Think of "Baryons" as the heavy, stable coins (like protons and neutrons) that make up all the matter we see—stars, planets, and you.

For a long time, physicists thought this bank had an impenetrable vault. The rule was: You can never create or destroy matter coins out of thin air. If you have 10 coins, you must always have 10 coins. This is why your body doesn't just spontaneously vanish, and why the sun doesn't just explode into nothingness.

However, the paper suggests that maybe the vault has a tiny, secret backdoor.

The New Character: "N" (The Invisible Ghost)

The authors propose a new particle, which they call N.

What is it? It's a "singlet fermion." In plain English, it's a ghostly particle that doesn't talk to light, electricity, or the strong force. It only interacts with the "heavy coins" (quarks) in a very specific, rare way.
The Trick: This ghost particle carries a "baryon number" of its own.
The Heist: Imagine a proton (a heavy coin) decays. Usually, this is forbidden. But if the proton breaks apart into a regular particle and the ghost N, the total "baryon number" is actually conserved! The ghost just took the "coin" with it into the shadows.

To us, looking at the experiment, it looks like the coin vanished (Baryon Number Violation). But really, it just went invisible.

The Detective Work: Hunting for "Missing Energy"

How do we find a ghost? You can't see it, but you can see what it leaves behind.

The authors looked at data from the Large Hadron Collider (LHC), the world's biggest particle smasher. They imagined a scenario where protons smash together, and a ghost N is created.

The Scene: Two protons collide. A jet of regular particles flies out one way. A ghost N flies out the other way.
The Clue: The detectors see the jet. They don't see the ghost. So, the energy and momentum seem unbalanced. The detector screams, "Hey! Something is missing!"
The Metaphor: Imagine you are at a pool party. You see a guest (a jet of particles) run across the room. You look at the empty space where they started, and you realize, "Wait, the air pressure changed! Someone invisible must have pushed them!" That "invisible pusher" is the missing energy.

The Results: How Strong is the Vault?

The team crunched the numbers from the LHC to see how heavy the "backdoor" (the scale of new physics) could be.

The Findings: They found that if this ghost particle exists, the "door" to the new physics must be incredibly high up—around 10 to 11 TeV (Tera-electronvolts).
The Analogy: Think of the energy scale as the height of a wall. The LHC can jump about 13 TeV high. The authors are saying, "If there is a secret tunnel, it's buried under a wall that is 10 stories high." It's a very high wall, meaning this ghost is hard to catch, but the LHC is getting close to the top.

They also looked at different "flavors" of the ghost:

Ghost + Jet: Caught up to 10 TeV.
Ghost + Top Quark: Caught up to 8 TeV.
Ghost + Bottom Quark: Caught up to 11 TeV (The strongest limit!).

The "Disappearing Act" (Displaced Vertices)

Sometimes, the ghost N isn't too light or too heavy. It might live for a tiny fraction of a second before it decays.

The Metaphor: Imagine a firefly that flies into a dark room, glows for a split second, and then vanishes.
The Search: If the ghost travels a few millimeters or meters inside the detector before disappearing, it leaves a "displaced vertex"—a tiny, secondary explosion of particles away from the main crash site. The authors suggest that future searches should look specifically for these "fireflies" that travel a short distance before vanishing.

The Low-Energy Hunt: The Charm Baryon

The paper also looks at the "slow motion" version of this crime. Instead of smashing protons at high speed, they looked at Charm Baryons (a specific type of heavy particle made of quarks).

The Crime: A charm baryon decays into a pion (a light particle) and the ghost N.
The Challenge: This is like trying to hear a whisper in a hurricane. The "background noise" of normal physics is huge, and the signal is tiny.
The Future: To catch this, we need a "Tera-Z factory" (a future super-collider like FCC-ee). These machines will produce billions of charm particles, giving us enough data to finally hear that whisper.

The Top Quark Connection

Finally, they looked at the Top Quark, the heaviest particle in the Standard Model.

The Possibility: A top quark could decay into a bottom quark and the ghost N.
The Potential: The authors calculate that this could happen in about 1 out of every 100,000 to 1 million top quark decays. While rare, the LHC produces so many top quarks that we might actually see this happening if we look closely enough.

The Conclusion: Why This Matters

This paper is a roadmap for finding a "ghost" that could explain why the universe is made of matter and not just energy.

It's a General Search: They didn't just look for one specific theory; they looked for any interaction that creates this ghost.
It Connects the Dots: They showed how high-energy crashes (LHC) and low-energy decays (charm baryons) are two sides of the same coin.
The Verdict: The "vault" is still very secure (no ghost found yet), but the walls are being tested more thoroughly than ever before. If the ghost exists, the next generation of colliders (like the High-Luminosity LHC or FCC-ee) might finally catch it in the act.

In short: The universe might have a secret exit for matter, but it's a very well-hidden one. This paper is the map showing us exactly where to look for the door handle.

1. Problem Statement

Baryon number ( $B$ ) is an accidental symmetry in the Standard Model (SM) but is violated in many Beyond-the-Standard-Model (BSM) scenarios (e.g., GUTs, Leptoquarks). While proton decay searches place stringent limits on $B$ -violating operators, these limits assume that the decay products include standard particles.
The authors address a specific loophole: Apparent Baryon Number Violation (BNV) where the decay products include a light, stable (or long-lived) SM-singlet fermion $N$ that carries baryon number. In this scenario, $B$ is conserved globally ( $B_{SM} + B_N = \text{const}$ ), but the SM sector appears to violate $B$ because $N$ escapes detection as Missing Transverse Energy (MET).
The paper aims to:

Quantify the constraints on such interactions using current LHC data.
Explore the phenomenology of $N$ as a long-lived particle (displaced vertices).
Investigate low-energy probes in charm and top decays.
Constrain specific UV-complete models, particularly those related to "mesogenesis" (baryogenesis via meson decays).

2. Methodology

Model Framework

The authors introduce a minimal extension of the SM with a vector-like, SM-singlet fermion $N$ with mass $M_N > m_p$ (to avoid proton decay). The interaction is described by Dimension-6 Effective Field Theory (EFT) operators at a scale $\Lambda$ :

$O_{qqdN}$ : $\epsilon_{ab}\epsilon_{\alpha\beta\gamma}(\bar{q}^C_{L,a,\alpha,i} q_{L,b,\beta,j}) (\bar{d}^C_{R,\gamma,k} N_R)$
$O_{uddN}$ : $\epsilon_{\alpha\beta\gamma}(\bar{u}^C_{R,\alpha,i} d_{R,\beta,j}) (\bar{d}^C_{R,\gamma,k} N_R)$

These operators connect three quarks to the singlet $N$ . The paper considers two UV completions involving heavy color-triplet mediators (scalar or vector leptoquarks) that generate these operators at tree level.

High- $p_T$ Collider Analysis (LHC)

The authors perform a comprehensive recast of LHC Run 2 data ( $\sqrt{s}=13$ TeV) to constrain the scale $\Lambda$ . They analyze three distinct signatures based on the lifetime of $N$ :

MET + Jets: $N$ is stable on detector scales. The signal is $pp \to N + \text{jets}$ . They analyze inclusive MET + jets, MET + $b$ -jet, and MET + top channels.
Displaced Vertices (DV): For intermediate lifetimes, $N$ decays inside the detector ( $N \to \text{jets}$ ). They estimate sensitivity using a zero-background approach based on ATLAS DV searches.
Prompt Decays (Multijets): For short lifetimes, $N$ decays at the primary vertex, appearing as multijet events.

They calculate production cross-sections and decay widths using MadGraph5_aMC@NLO, Pythia8, and FastJet, implementing the EFT operators as a UFO model. They account for parton distribution functions (NNPDF40) and interference effects between different flavor combinations.

Low-Energy Probes

Charm Decays: They calculate the branching ratios for $\Lambda_c \to \pi(K) + \bar{N}$ using QCD Factorization (QCDF) and heavy quark expansion. They estimate hadronic form factors and uncertainties.
Top Decays: They calculate $t \to \bar{N} \bar{d} \bar{d}'$ branching ratios.
Neutron Decay: They analyze the kinematic window $m_p < M_N < m_n$ where neutron decay to $N$ is allowed, providing constraints from radiative neutron decay.

3. Key Contributions

Comprehensive LHC Constraints: The first systematic recast of LHC MET searches specifically for $qqqN$ operators. They derive limits on the EFT scale $\Lambda/\sqrt{C}$ for all flavor combinations ( $i,j,k$ ).
Lifetime-Dependent Signatures: A unified framework connecting MET, Displaced Vertices, and Prompt decays, showing how the experimental signature evolves with $M_N$ and coupling strength.
Charm Baryon Phenomenology: A detailed calculation of $\Lambda_c \to \text{meson} + \bar{N}$ amplitudes within QCDF, identifying these as clean null tests for BNV.
Mesogenesis Constraints: A rigorous test of "mesogenesis" models (where $N$ is produced in $B$ -meson decays to explain the baryon asymmetry). They show that current LHC data severely constrains or rules out specific parameter spaces of these models.
Top Quark Reach: Identification of top quark decays as a promising channel for BNV, with branching ratios potentially reaching $\sim 10^{-6}$ .

4. Key Results

Collider Limits (High- $p_T$ )

Scales: Current LHC data constrains the new physics scale $\Lambda$ $Λ$ up to:
- $\sim 10$ TeV for MET + jets (inclusive).
- $\sim 8$ TeV for MET + top.
- $\sim 11$ TeV for MET + $b$ -jet (the strongest bound, due to reduced background and PDF enhancement).
Flavor Dependence: Bounds are strongest for first-generation quarks (due to PDFs) and specific flavor combinations involving $b$ -quarks.
Displaced Vertices: For $M_N \gtrsim 1$ GeV and specific couplings, $N$ can have decay lengths in the mm–m range. Dedicated DV searches could probe regions inaccessible to MET searches.
UV Models:
- Model 1 (Scalar $\Psi$ ): The constraints from single $N$ production completely exclude the parameter space required for successful mesogenesis with heavy scalar triplets.
- Model 2 (Scalar $\Phi$ ): A small viable window remains for flavor combinations $cbs$, $cbd$, and $ubs$. These correspond to specific $B$ -meson decays (e.g., $B^0 \to \Lambda N$ , $B^+ \to \Lambda_c N$ ).

Low-Energy Results

Charm Decays: The branching ratio for $\Lambda_c \to \pi(K) + \bar{N}$ $Λ_{c} \to π (K) + \overset{ˉ}{N}$ can be as large as $10^{-9}$ $1 0^{- 9}$ (for $CqqdN$) or $10^{-8}$ $1 0^{- 8}$ (for $CuddN$) given current LHC limits.
- Future Reach: A Tera- $Z$ factory (FCC-ee) or Super $\tau$ -charm factory could probe scales up to 3–3.5 TeV, complementary to LHC.
- Uncertainties: Hadronic uncertainties in QCDF form factors are significant (up to order 1 for right-handed operators), necessitating further theoretical work.
Top Decays: Branching ratios for $t \to \bar{N} \bar{b} \bar{b}$ can reach few $\times 10^{-6}$ . This is significant because existing searches for $t \to \ell \bar{q} \bar{q}$ are already constrained by proton stability, whereas the $N$ -mediated operators are not.

5. Significance

New Window for BNV: The paper demonstrates that baryon number violation can be probed at the TeV scale via missing energy, bypassing the extreme suppression ( $\Lambda \sim 10^{16}$ GeV) usually associated with proton decay.
Complementarity: It highlights the synergy between high-energy colliders (LHC) and high-luminosity flavor factories (FCC-ee, CEPC). While LHC sets strong limits on the production scale, flavor factories can probe specific flavor structures and lower masses with high precision.
Mesogenesis Viability: The results provide a critical "reality check" for mesogenesis models. The paper shows that simple UV completions of mesogenesis are largely ruled out by current LHC data, narrowing the viable parameter space to specific flavor structures that can be tested by future HL-LHC runs or dedicated resonance searches.
Experimental Guidance: The study provides concrete targets for experimentalists:
- Search for MET + $b$ -jet and MET + top.
- Perform dedicated searches for displaced vertices in the $N$ decay channel.
- Investigate rare charm baryon decays ( $\Lambda_c \to \pi/K + \text{inv}$ ) and top decays ( $t \to \text{inv} + b\text{-jets}$ ).

In conclusion, the paper establishes that the search for baryon number violation via missing energy is a highly motivated and experimentally accessible frontier, capable of probing new physics scales up to 11 TeV and testing cosmological baryogenesis mechanisms.