Search for new physics with baryons at BESIII

Using $10^{10}$ $J/\psi$ events, the BESIII experiment set the world's most stringent limits on invisible baryon decays and $\bar{\Lambda}-\Lambda$ oscillations, finding no evidence for baryon-number violation or connections to the dark sector.

The Gist

Imagine the universe as a giant, bustling city. For decades, physicists have been the city planners, drawing up a map called the Standard Model. This map explains how the "citizens" of the city (particles like protons, electrons, and neutrons) interact, move, and build things. It's a brilliant map, but it has a few glaring holes.

For one, the map doesn't explain Dark Matter. We know this invisible stuff exists because it holds the city together with gravity, but we can't see it. In fact, there's about five times more Dark Matter than regular matter, which is a strange coincidence. It's like finding out your city has five times more invisible ghosts than living people. Are they related? Do they share a family name?

Then there's the mystery of why the city is full of matter and almost empty of "anti-matter" (the evil twin of matter). If they were created equally, they should have destroyed each other long ago.

To solve these mysteries, scientists need to look for "cracks" in the Standard Model map. This is where the BESIII experiment comes in. Located in China, it's like a high-speed, ultra-clean factory that smashes electrons and positrons together to create billions of J/ψ particles. Think of these J/ψ particles as a magical factory that instantly produces pairs of "baryons" (heavy particles like protons and neutrons, but with a twist: they contain "strange" quarks).

The BESIII team, led by researchers like Amit Pathak, used this factory to look for three specific "ghostly" behaviors that shouldn't happen according to the old map.

1. The Vanishing Act (Invisible Decays)

The Experiment: They watched a particle called a Sigma-plus ($\Sigma^+$) turn into a proton.
The Expectation: In the Standard Model, this transformation is like trying to turn a lead ball into gold; it's so incredibly rare and difficult that it's practically impossible.
The Search: The team asked, "What if the Sigma-plus doesn't just turn into a proton, but also sneaks out a piece of invisible Dark Matter?"
The Analogy: Imagine you see a magician pull a rabbit out of a hat. But instead of just a rabbit, the hat is empty, and the rabbit vanished into thin air. If you see a proton appear but the energy balance is off (like the hat is lighter than it should be), it means something invisible escaped.
The Result: They watched billions of these events. No invisible rabbits were found. They set a strict rule: "If this happens, it's less than 1 in 30,000 times." This is the tightest rule we've ever made for this kind of magic trick.

2. The Secret Family Reunion (Dark Baryons)

The Experiment: They looked at a particle called a Xi-minus ($\Xi^-$) turning into a pion (a lighter particle).
The Theory: Some scientists think Dark Matter isn't just a ghost; maybe it has a "family" of its own, called Dark Baryons. Maybe our regular baryons can decay into a visible particle and a secret Dark Baryon, keeping the total "baryon number" (the family count) the same.
The Analogy: Imagine a father (the Xi-minus) giving a toy (the pion) to his child. But instead of the child being visible, the child is a "shadow child" that only exists in a parallel dimension. The father disappears, the toy appears, and the shadow child is gone.
The Result: They scanned for these shadow children across a wide range of possible weights. Nothing was found. They proved that if these shadow children exist, they are incredibly hard to make in this specific way.

3. The Shape-Shifter (Oscillations)

The Experiment: They watched an Anti-Lambda ($\bar{\Lambda}$) particle.
The Theory: In the world of physics, matter and anti-matter are usually enemies. But what if an Anti-Lambda could spontaneously turn into a regular Lambda particle? This would be a violation of a fundamental rule called "Baryon Number Conservation."
The Analogy: Imagine a red ball (Anti-Lambda) sitting on a table. Suddenly, without anyone touching it, it turns into a blue ball (Lambda). If this happens, it breaks the laws of physics as we know them and could explain why the universe is made of matter instead of anti-matter.
The Result: They watched billions of these particles. No red balls turned blue. They set a limit: "If this shape-shifting happens, it takes longer than 300 nanoseconds to occur." While this is still a long time for a particle, it's a massive improvement over previous guesses.

The Big Picture

The BESIII experiment is like a super-precise microscope looking for the tiniest cracks in the universe's foundation. By using billions of clean, controlled collisions, they looked for:

1. Particles disappearing into the dark.
2. Regular particles turning into dark cousins.
3. Particles flipping from matter to anti-matter.

The Verdict: So far, the universe is behaving exactly as the old map predicts. No cracks were found.

Why does this matter?
Even though they found "nothing," this is a huge victory. It's like a detective clearing a suspect. By proving these specific "ghostly" events don't happen (or happen extremely rarely), they are narrowing down the list of possible new physics theories. They are telling the universe's theorists: "Don't look for new physics in this direction; try looking somewhere else."

The BESIII team has set the most stringent (strictest) rules in the world for these specific phenomena. As they collect more data in the future, they will keep pushing the boundaries, ensuring that if new physics is hiding in the baryon sector, they will be the first to catch it.

Technical Summary

1. Problem Statement and Motivation

The Standard Model (SM) of particle physics, while successful, fails to explain several fundamental cosmological and physical phenomena, including:

• Dark Matter (DM): The observed density of dark matter ($\rho_{DM}$) is approximately 5.4 times that of baryonic matter ($\rho_{baryon}$), suggesting a potential common origin or shared quantum numbers.
• Baryon Asymmetry: The SM cannot explain the matter-antimatter asymmetry of the Universe.
• Neutrino Masses: The origin of neutrino masses and mixing remains unexplained.

These gaps motivate the search for New Physics (NP), specifically in the baryon sector. The paper focuses on three specific avenues where the SM is either forbidden or highly suppressed:

1. Invisible Baryon Decays: Decays into final states containing dark sector particles (e.g., axion-like particles, dark photons, or dark baryons).
2. Baryon-Number Violation (BNV): Processes violating baryon number ($\Delta B = 2$), such as oscillations between a baryon and its antibaryon, which are crucial for explaining baryogenesis.

2. Methodology and Experimental Setup

The study utilizes data from the BESIII experiment at the BEPCII electron-positron collider in Beijing.

• Data Sample: The analysis is based on unprecedented samples of $J/\psi$ decays, totaling approximately $10^{10}$ events (specifically $(1.0087 \pm 0.0044) \times 10^{10}$ events).
• Production Mechanism: $J/\psi$ mesons decay into baryon-antibaryon pairs (e.g., $J/\psi \to \Sigma^+\Sigma^-$, $J/\psi \to \Xi^-\Xi^+$, $J/\psi \to \Lambda\bar{\Lambda}$), providing a clean environment with low background.
• Key Techniques:
  • Double-Tagging: One baryon in the pair is fully reconstructed in a known decay mode to constrain the kinematics of the event.
  • Recoil Mass Technique: The properties of the signal baryon are inferred by analyzing the recoil system against the fully reconstructed partner. This allows for the identification of "invisible" particles (missing energy) without direct detection.
  • Kinematic Constraints: Searches are performed for specific mass ranges and energy distributions to distinguish signal from background.

3. Key Contributions and Specific Searches

The paper presents results from three distinct searches for physics beyond the SM:

A. Search for Invisible Decays: $\Sigma^+ \to p + \text{invisible}$

• Physics Goal: To detect Flavor-Changing Neutral Current (FCNC) processes where a $\Sigma^+$ decays into a proton and a massless or light invisible particle (e.g., axion-like particles). In the SM, $\Sigma^+ \to p\nu\bar{\nu}$ is loop-suppressed with a branching fraction $< 10^{-11}$.
• Method: Reconstruct $J/\psi \to \Sigma^+\Sigma^-$ events. The $\Sigma^-$ is fully reconstructed via $\Sigma^- \to \bar{p}\pi^0$. The signal $\Sigma^+$ is identified by a single proton and zero extra energy in the electromagnetic calorimeter (EMC).
• Result: No significant excess over background was found. The measured branching fraction was $(0.6 \pm 1.5) \times 10^{-5}$.
• Limit: Set an upper limit of $B(\Sigma^+ \to p + \text{invisible}) < 3.2 \times 10^{-5}$ (90% C.L.). This is the first FCNC search with missing energy in the baryon sector.

B. Search for Dark Baryons: $\Xi^- \to \pi^- + \text{invisible}$

• Physics Goal: To test models where dark matter carries a conserved baryon number, allowing SM baryons to decay into visible mesons and invisible dark baryons ($\chi$).
• Method: Analyze $J/\psi \to \Xi^-\Xi^+$ events. The $\Xi^+$ is fully reconstructed via $\Xi^+ \to \pi^+\Lambda \to \pi^+p\pi^-$. The signal $\Xi^-$ is searched for in the mode $\Xi^- \to \pi^- + \chi$ using the recoil mass technique.
• Scope: Scanned dark baryon masses in the range 1.07–1.16 GeV/c².
• Result: No statistically significant signal was observed for any mass hypothesis.
• Limit: Set upper limits on the branching fraction $B(\Xi^- \to \pi^- + \chi)$ at the level of $(4–7) \times 10^{-5}$ across the mass range. These are the most stringent constraints to date on dark baryon production in hyperon decays.

C. Search for $\bar{\Lambda}-\Lambda$ Oscillations

• Physics Goal: To probe $\Delta B = 2$ transitions (baryon-antibaryon oscillations) involving strange quarks, which are complementary to neutron-antineutron oscillation searches.
• Method: Utilize coherent production of $\bar{\Lambda}\Lambda$ pairs in $J/\psi \to pK^-\bar{\Lambda} + c.c.$ (Right-Sign, RS) and search for "Wrong-Sign" (WS) events like $J/\psi \to pK^-\Lambda$ which would only occur if $\bar{\Lambda}$ oscillated to $\Lambda$ before decaying.
• Data Evolution:
  • Initial search with $1.31 \times 10^9$ events yielded $P(\Lambda) < 4.4 \times 10^{-6}$.
  • Updated analysis with the full dataset ($\approx 10^{10}$ events) significantly improved sensitivity.
• Result: No WS signal observed.
• Limit: The updated upper limit is $P(\Lambda) < 1.4 \times 10^{-6}$ (90% C.L.), corresponding to a transition mass $\delta m_{\Lambda\bar{\Lambda}} < 2.1 \times 10^{-18}$ GeV and an oscillation time $\tau_{osc} > 3.1 \times 10^{-7}$ s. This represents a factor of ~3 improvement over previous measurements.

4. Significance and Impact

• Stringent Constraints: The results provide the most stringent limits to date on invisible baryon decays and $\Delta B = 2$ transitions in strange baryons.
• Model Exclusion: These limits strongly constrain theoretical models involving:
  • Light dark sector particles (axion-like particles, dark photons).
  • Baryonic dark matter scenarios.
  • Neutrino-portal interactions.
  • $\Delta B = 2$ effective operators.
• Complementarity: While neutron-antineutron oscillation limits are currently stronger ($\tau > 10^8$ s), this work provides the first direct experimental bounds on baryon-number violation specifically in the hyperon sector, offering unique sensitivity to strange-quark physics.
• Future Prospects: The study validates the use of high-intensity $e^+e^-$ colliders and hyperon decays as a powerful "intensity frontier" probe for new physics. With larger datasets already collected, BESIII is poised to further push the sensitivity of these searches.

In conclusion, the paper demonstrates that while no evidence for new physics was found in the current dataset, the BESIII experiment has successfully established a new benchmark for precision tests of baryon stability and dark sector connections.