Observation of the charmless purely baryonic decay $\Lambda_b^{0} \to \Lambda p \bar{p}$ at LHCb

Using the full Run 2 LHCb dataset, the first observation of the charmless purely baryonic decay $\Lambda_b^{0} \to \Lambda p \bar{p}$ is reported with a statistical significance of $5.1\sigma$, yielding a measured relative branching fraction of $(5.13 \pm 1.28_{\rm stat} \pm 0.27_{\rm syst})\times 10^{-2}$.

The Gist

Imagine the universe as a giant, chaotic construction site where tiny building blocks called quarks are constantly being smashed together and rearranged. For decades, physicists have been watching these blocks to see how they stick together to form larger structures called baryons (like protons and neutrons).

This paper is like a detective report from the LHCb collaboration (a team of scientists working at the Large Hadron Collider in Switzerland). They have just spotted something very rare and special: a specific type of "explosion" where a heavy particle breaks apart into three other particles, none of which are the usual suspects (charm quarks).

Here is the story of their discovery, broken down into simple terms:

1. The Main Character: The Heavy "Grandpa" Particle

The star of the show is a particle called $\Lambda_b^0$ (Lambda-b-zero). Think of it as a heavy, unstable "Grandpa" particle made of three quarks. It doesn't last long; it wants to break apart immediately.

Usually, when this Grandpa breaks up, it leaves behind a mix of particles, often including "charm" quarks (a specific type of heavy building block). But the scientists were looking for a very specific, rare breakup where no charm quarks are involved at all. They wanted to see if the Grandpa could split into a Lambda ($\Lambda$), a proton ($p$), and an antiproton ($\bar{p}$).

2. The Challenge: Finding a Needle in a Haystack

Imagine you are at a massive music festival (the particle collider). Millions of people are dancing, and you are looking for one specific person wearing a red hat (the $\Lambda_b^0 \to \Lambda p \bar{p}$ decay).

• The Haystack: The billions of other particle collisions happening every second.
• The Needle: The specific decay the scientists wanted to find.
• The Problem: This specific decay is incredibly rare. It's like finding a specific grain of sand on a beach.

To make this easier, the scientists didn't just look for the needle; they looked for a "twin" event that happens much more often. They compared the rare event to a common event called $\Lambda_b^0 \to \Lambda K^+ K^-$ (where the Grandpa breaks into a Lambda and two Kaons). Since these two events look very similar in how they happen, comparing them cancels out a lot of the "noise" and measurement errors. It's like weighing a rare coin against a stack of common coins to figure out its exact value without needing a super-precise scale.

3. The Investigation: Sorting the Tracks

The LHCb detector is like a giant, high-speed camera that takes pictures of these collisions.

• The Filter: The scientists used a computer program (an "XGBoost classifier," which is basically a super-smart AI) to sort through the millions of photos. It learned to spot the specific "footprints" left by the particles they were interested in.
• The Two Groups: They split the data into two groups based on where the particles were caught:
  • Long (LL): Particles caught right where they were born.
  • Downstream (DD): Particles that traveled a bit further before being caught.
  • Analogy: Imagine catching fish in a river. Some you catch right at the dam (Long), and some you catch further downstream (Downstream). They kept both groups to get the best possible count.

4. The Big Reveal: The "5-Sigma" Moment

After analyzing 6 years of data (Run 2), the scientists finally saw the signal.

• The Count: They found about 39 of the rare events they were looking for, compared to 640 of the common "twin" events.
• The Confidence: In science, you can't just say "I think I saw it." You need to be sure it's not just a random glitch. They calculated a "significance" score.
  • They got a score of 5.1 sigma.
  • Analogy: Imagine flipping a coin. If you flip it 10 times and get heads every time, that's suspicious. If you get 5.1 sigma, it's like flipping a coin and getting heads 25 times in a row by pure chance. The odds of that happening randomly are about 1 in 3.5 million. In the world of particle physics, this is the gold standard for saying, "We have officially discovered this!"

5. Why Does This Matter?

This isn't just about counting particles. It's about understanding the rules of the universe.

• New Physics: This is the first time anyone has seen a "purely baryonic" decay (breaking into only baryons) that doesn't involve charm quarks. It's like discovering a new way to build a house that no architect has ever used before.
• Testing Theories: Scientists had made predictions about how often this should happen. Their measurement was a bit higher than the prediction, but close enough to be exciting. It helps them refine their theories about how matter is built.
• Future Mysteries: This discovery opens the door to studying CP violation (a phenomenon where matter and antimatter behave slightly differently), which might help explain why the universe is made of matter and not just empty space.

The Bottom Line

The LHCb team successfully found a very rare, previously unseen way for a heavy particle to break apart. They used smart computer filters, compared it to a common event to reduce errors, and proved with 99.9999% certainty that this specific breakup happens. It's a small step for a particle, but a giant leap for our understanding of how the universe is constructed.

Technical Summary

1. Problem and Motivation

• Scientific Gap: While several baryonic $B$-meson decays have been observed, purely baryonic decays of beauty baryons remain largely unexplored. These decays offer a unique laboratory for studying multibody baryonic final-state dynamics and searching for CP-violating effects in systems with rich spin structures.
• Current Status: Prior to this work, the only experimentally established purely baryonic modes were $\Lambda_b^0 \to \Sigma_c^+ \bar{p} p$ and $\Lambda_b^0 \to \Sigma_c^{*+} \bar{p} p$, observed indirectly in $\Lambda_b^0 \to \Lambda_c^+ \bar{p} \pi^-$ studies.
• Objective: The paper reports the first dedicated search and first observation of a charmless purely baryonic decay of a baryon: $\Lambda_b^0 \to \Lambda p \bar{p}$.
• Theoretical Context: Theoretical calculations predict a branching fraction of $\mathcal{B}(\Lambda_b^0 \to \Lambda p \bar{p}) \approx (3.2^{+0.8}_{-0.3} \pm 0.4 \pm 0.7) \times 10^{-6}$. The framework also predicts sizeable direct CP asymmetries in this channel.

2. Methodology

Dataset and Detector

• Data Source: The analysis utilizes the full LHCb Run 2 dataset (collected 2015–2018), corresponding to an integrated luminosity of 6.0 fb$^{-1}$.
• Detector: The LHCb single-arm forward spectrometer ($2 < \eta < 5$) is used, specifically leveraging its tracking system, Ring Imaging Cherenkov (RICH) detectors for particle identification (PID), calorimeters, and muon system.
• Reconstruction Categories: The $\Lambda$ baryon is reconstructed via $\Lambda \to p \pi^-$. Candidates are split into two categories based on the $\Lambda$ decay vertex location:
  • Long (LL): Both decay tracks reconstructed in the vertex detector.
  • Downstream (DD): The $\Lambda$ decays outside the vertex detector acceptance.
  • Note: Approximately half of the signal candidates fall into the DD category, so both are retained to maximize statistics.

Analysis Strategy

• Normalization Mode: To minimize systematic uncertainties, the branching fraction is measured relative to the topologically similar decay $\Lambda_b^0 \to \Lambda K^+ K^-$.
• Selection Criteria:
  • A common strategy is applied to signal and normalization modes, including trigger requirements, offline reconstruction, preselection, and a dedicated XGBoost classifier.
  • PID Requirements: Applied to companion hadrons (protons/kaons).
  • Vetoes: Charm-hadron vetoes are applied to suppress intermediate resonances.
  • Mass Window: A requirement of $m(h^+h^-) < 2.85$ GeV is imposed to exclude the charmonium region (resonances decaying to $p\bar{p}$ or $K^+K^-$).
• Blinding: To avoid experimenter bias, the signal region ($\Lambda p \bar{p}$ invariant mass within $\pm 50$ MeV of the $\Lambda_b^0$ mass) was blinded until the selection, fit model, and systematic studies were finalized.

Efficiency and Fit Model

• Efficiency Correction: Relative efficiencies are corrected for data-simulation differences in tracking, trigger, and PID. Crucially, efficiency maps are constructed from simulation and folded with background-subtracted Dalitz distributions (obtained via the sPlot technique) to account for non-uniform phase-space populations. This correction was found to shift efficiency ratios by ~14% compared to uniform phase-space assumptions.
• Statistical Fit: An extended unbinned maximum-likelihood fit is performed simultaneously on four invariant-mass spectra:
  1. $\Lambda_b^0 \to \Lambda K^+ K^-$ (LL)
  2. $\Lambda_b^0 \to \Lambda K^+ K^-$ (DD)
  3. $\Lambda_b^0 \to \Lambda p \bar{p}$ (LL)
  4. $\Lambda_b^0 \to \Lambda p \bar{p}$ (DD)
• Signal Modeling:
  • Signal shapes: Double-sided Crystal Ball functions.
  • Background: Exponential functions for combinatorial background.
  • Additional components: Partially reconstructed $\Lambda_b^0 \to \Sigma^0 K^+ K^-$ in the normalization mode; potential $\Xi_b^0 \to \Lambda p \bar{p}$ contribution in the signal mode (expected ~175 MeV above the $\Lambda_b^0$ peak).

3. Key Contributions

1. First Observation: This is the first observation of the charmless purely baryonic decay $\Lambda_b^0 \to \Lambda p \bar{p}$.
2. First Baryon Decay: It marks the first observation of a charmless purely baryonic decay originating from a baryon (as opposed to a meson).
3. Methodological Rigor: The use of a simultaneous fit across LL/DD categories and the application of phase-space-dependent efficiency corrections significantly reduce systematic uncertainties.
4. Blind Analysis: The strict blinding procedure ensures the robustness of the result against bias.

4. Results

Signal Significance

• Statistical Significance: The likelihood-ratio test yields a significance of 5.2$\sigma$.
• Total Significance: After including systematic uncertainties, the significance is 5.1$\sigma$, satisfying the standard criterion for an observation in particle physics.

Yields and Branching Fraction

• Fitted Yields:
  • $N(\Lambda_b^0 \to \Lambda p \bar{p}) = 39.3 \pm 9.7$
  • $N(\Lambda_b^0 \to \Lambda K^+ K^-) = 640 \pm 31$
• Branching Fraction Ratio:
  The relative branching fraction is measured in the region $m(h^+h^-) < 2.85$ GeV:
  $$R_{\Lambda_b^0} = \frac{\mathcal{B}(\Lambda_b^0 \to \Lambda p \bar{p})}{\mathcal{B}(\Lambda_b^0 \to \Lambda K^+ K^-)} = (5.13 \pm 1.28_{\text{stat}} \pm 0.27_{\text{syst}}) \times 10^{-2}$$
  • Note: No absolute branching fraction is quoted because the normalization mode was measured without the $m(h^+h^-) < 2.85$ GeV restriction.

Systematic Uncertainties

The total systematic uncertainty is 5.3%. Dominant sources include:

• Tracking efficiency (4.3%)
• Fit modeling (2.8%)
• Limited size of simulated samples (1.0%)
• PID efficiency (0.8%)

Secondary Observation ($\Xi_b^0$)

• A small excess is observed for the $\Xi_b^0 \to \Lambda p \bar{p}$ decay with a significance of 2.3$\sigma$.
• No branching fraction or upper limit is provided for this mode due to the lack of dedicated efficiency determination and knowledge of the relative hadronization fraction between $\Xi_b^0$ and $\Lambda_b^0$.

5. Significance and Future Outlook

• Physics Impact: This result opens a new window for studying the dynamics of multibody baryonic final states and provides a baseline for future CP violation studies in charmless baryonic decays.
• Future Prospects: The authors note that larger datasets from LHCb Run 3 will enable more detailed studies of:
  • Two-body invariant-mass spectra (to probe intermediate resonances).
  • Direct CP violation asymmetries.
  • Searches for the related $\Xi_b^0 \to \Lambda p \bar{p}$ mode.

In summary, the paper successfully establishes the existence of the $\Lambda_b^0 \to \Lambda p \bar{p}$ decay channel with high statistical significance, providing a crucial measurement for testing theoretical models of heavy baryon decays.