Observation of the charmless purely baryonic decay $\mathinner{\mathit{\Lambda}^0_b\!\to \mathit{\Lambda} p \overline{p}}$

Using proton-proton collision data from the LHCb experiment, researchers have observed the charmless purely baryonic decay $\mathinner{\mathit{\Lambda}^0_b\!\to \mathit{\Lambda} p \overline{p}}$ with a significance of 5.1 standard deviations and measured its branching fraction relative to $\mathinner{\mathit{\Lambda}^0_b\!\to \mathit{\Lambda} K^+ K^-}$ for the first time.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as a massive, high-speed particle racetrack. Scientists smash protons together at nearly the speed of light to create a chaotic explosion of new, short-lived particles. Most of these particles are like fleeting bubbles that pop instantly, but some are rare, exotic creatures that scientists spend years trying to catch a glimpse of.

This paper is about the LHCb collaboration (a specific team of scientists at CERN) successfully spotting one of these rare creatures: a specific type of decay called $\Lambda_b^0 \to \Lambda p p$.

Here is the story of how they found it, explained simply:

1. The Rare Event: A "Purely Baryonic" Breakup

In the world of particle physics, particles are often grouped into families. One family is called baryons (which includes protons and neutrons). Usually, when a heavy particle breaks apart, it might turn into a mix of different types of particles.

The scientists were looking for a very specific, "pure" breakup. They wanted to see a heavy particle called a $\Lambda_b^0$ (Lambda-b-zero) split apart and turn only into other baryons: a $\Lambda$ (Lambda) particle and two protons ($p$).

• The Analogy: Imagine a heavy, complex toy car crashing. Usually, it explodes into wheels, glass, and plastic. But this team was looking for a crash where the car somehow turned only into three other toy cars, with no glass or plastic left over. This is what they call a "purely baryonic" decay. It's a very strict, rare rule for the universe to follow.

2. The Challenge: Finding a Needle in a Haystack

The problem is that this specific crash is incredibly rare. For every time this happens, there are millions of other, more common crashes happening that look very similar.

• The Analogy: Imagine trying to find a specific, unique coin in a giant pile of sand. To make it harder, the unique coin looks almost exactly like the millions of other coins in the pile.

To solve this, the scientists used a clever trick: The Normalization Mode.
Instead of trying to count exactly how many unique coins they found (which is hard because they don't know the total size of the sand pile), they looked for a slightly different, but very similar, coin that they already knew how to find.

• They compared the rare "all-proton" crash ($\Lambda_b^0 \to \Lambda p p$) against a more common "proton-and-kaon" crash ($\Lambda_b^0 \to \Lambda K^+ K^-$).
• By comparing the two, many of the messy variables (like how big the sand pile was or how good their coin-sifting machine was) canceled out. It's like saying, "We found 1 rare coin for every 20 common coins," which is much easier to measure than counting the total number of coins in the universe.

3. The Filter: Cleaning Up the Mess

The data they collected was full of "noise"—fake signals caused by particles misbehaving or other types of decays that looked similar.

• The "Charm" Veto: The scientists had to be very careful to ignore particles that came from "charm" quarks (a different type of particle family). They set up digital filters to say, "If this looks like it came from a charm particle, throw it out."
• The "Resonance" Filter: They also had to ignore cases where the particles briefly formed a temporary, heavy "resonance" (like a short-lived intermediate step). They set a rule: "If the combined weight of the particles is too heavy (above 2.85 GeV), ignore it." This ensured they were only looking at the direct, pure breakup they wanted.

4. The Result: A "5-Sigma" Discovery

After running their data through complex computer models and statistical tests, the results were clear:

• The Signal: They found a clear "bump" in the data where the rare decay was happening.
• The Significance: In science, a "5-sigma" result is the gold standard. It means there is less than a 1 in 3.5 million chance that this result is just a random fluke.
• The Metaphor: It's like flipping a coin 100 times and getting heads every single time. You are now 100% sure the coin is rigged. The scientists are now 100% sure this decay exists.

5. What They Measured

They didn't just say "it exists." They measured how often it happens compared to the common decay.

• They found that for every 100 times the common decay happens, the rare "all-proton" decay happens about 5 times.
• They calculated this ratio with a high degree of precision, accounting for all the possible errors in their equipment and math.

6. A Small Mystery

While looking at the data, they also saw a tiny, faint "bump" that might be another rare particle called the $\Xi_b^0$ decaying in a similar way. However, it wasn't strong enough to be a discovery (only about 2.3 sigma). They noted it as a "maybe," but they didn't claim to have found it yet.

Summary

In short, the LHCb team successfully caught a glimpse of a very rare, "pure" particle breakup that had never been seen before. They used a clever comparison method to filter out the noise, confirmed the discovery with high statistical certainty, and measured exactly how often it happens relative to a similar, more common event. This helps physicists understand the rules of the universe and how matter transforms at the most fundamental level.

Technical Summary

Technical Summary: Observation of the Charmless Purely Baryonic Decay $\Lambda_b^0 \to \Lambda p p$

Problem and Motivation
The study of $b$-hadron decays into baryonic final states remains a significant but largely unexplored frontier in hadronic flavour physics. While several new decay modes have been observed recently, including charmless four-body baryonic $B$ decays and the first purely baryonic $B$ meson decays, purely baryonic decays of $b$-baryons (processes involving only baryons in the final state) are scarce. Currently, only two such modes, $\Lambda_b^0 \to \Sigma_c^0 p p$ and $\Lambda_b^0 \to \Sigma_c^{*0} p p$, have been measured. Theoretical predictions suggest that purely baryonic decays, such as $\Lambda_b^0 \to \Lambda p p$, offer unique opportunities to study CP asymmetries and time-reversal (T) symmetry violations due to their rich spin structures. Furthermore, enhancements at the mass threshold of final-state di-baryon pairs are expected. This paper addresses the lack of experimental data by presenting the first search for the charmless, purely baryonic decay $\Lambda_b^0 \to \Lambda p p$.

Methodology
The analysis utilizes proton-proton collision data recorded by the LHCb experiment at a centre-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of $6.0 \text{ fb}^{-1}$ collected during Run 2 (2015–2018).

• Signal and Normalisation: The search targets the $\Lambda_b^0 \to \Lambda p p$ decay. To measure the branching fraction, the analysis employs a topologically similar decay, $\Lambda_b^0 \to \Lambda K^+ K^-$, as a normalisation mode. This approach cancels uncertainties related to the $\Lambda_b^0$ production cross-section and integrated luminosity.
• Reconstruction: $\Lambda$ baryons are reconstructed via $\Lambda \to p \pi^-$. Candidates are categorized into two topologies based on the $\Lambda$ decay vertex location: "long-long" (LL), where both daughter tracks are reconstructed in the vertex detector, and "downstream-downstream" (DD), where the $\Lambda$ decays outside the vertex detector.
• Selection Strategy:
  • Pre-selection: Requires high-quality tracks, significant impact parameters relative to the primary vertex, and particle identification (PID) to distinguish protons from kaons.
  • Multivariate Analysis: An XGBoost classifier is trained on simulated $\Lambda_b^0 \to \Lambda K^+ K^-$ decays to separate signal from combinatorial background, using kinematic and topological variables.
  • Charm Vetoes: To exclude contributions from intermediate charmonium resonances and charm hadrons, invariant mass vetoes are applied. Specifically, the invariant mass of the companion hadron system ($pp$ or $K^+K^-$) is required to be $m(h\bar{h}) < 2.85$ GeV, explicitly excluding the charmonium region. Additional vetoes reject intermediate $D^0$, $\Lambda_c^+$, and $\Xi_c^+$ states.
• Efficiency Determination: Relative efficiencies are calculated using simulation, corrected for data-simulation differences in tracking, trigger, and PID. To account for non-uniform phase-space distributions, efficiency maps are constructed in square Dalitz variables and weighted using sPlot techniques on data.
• Yield Extraction: A simultaneous unbinned maximum-likelihood fit is performed on the invariant-mass distributions of the signal and normalisation candidates across LL and DD categories and four data-taking years. The fit model includes signal components (modeled by double-sided Crystal Ball functions), a partially reconstructed $\Lambda_b^0 \to \Sigma^0 K^+ K^-$ contribution for the normalisation mode, and combinatorial background.

Key Contributions and Results

• First Observation: The analysis reports the first observation of the $\Lambda_b^0 \to \Lambda p p$ decay. The signal significance, calculated using a likelihood-ratio test statistic and accounting for systematic uncertainties, is $5.1\sigma$.
• Branching Fraction Measurement: The branching fraction of $\Lambda_b^0 \to \Lambda p p$ is measured relative to $\Lambda_b^0 \to \Lambda K^+ K^-$. The result is:
  $$\frac{\mathcal{B}(\Lambda_b^0 \to \Lambda p p)}{\mathcal{B}(\Lambda_b^0 \to \Lambda K^+ K^-)} = (5.1 \pm 1.3(\text{stat}) \pm 0.3(\text{syst})) \times 10^{-2}$$
  The total systematic uncertainty is approximately 5.3%, dominated by tracking efficiency and fit modelling uncertainties.
• Signal Yields: The fitted signal yields are $39 \pm 10$ for the signal mode and $640 \pm 31$ for the normalisation mode.
• Secondary Observation: A small excess consistent with the $\Xi_b^0 \to \Lambda p p$ decay is observed with a significance of $2.3\sigma$. However, no branching fraction or upper limit is reported for this mode, as a dedicated efficiency determination and knowledge of relative hadronisation fractions are required.

Significance
The paper establishes the existence of the $\Lambda_b^0 \to \Lambda p p$ decay, a rare charmless purely baryonic process. The measurement provides the first experimental input for this mode, which can be used to test theoretical predictions regarding non-factorisable effects, CKM matrix elements, and hadronic form factors. The authors note that the observed branching fraction is suppressed relative to $\Lambda_b^0 \to \Lambda K^+ K^-$, consistent with predictions in Ref. [7]. The result complements existing measurements of mesonic final states and opens a new avenue for studying CP and T symmetry violations in purely baryonic systems. The authors conclude that future analyses with larger datasets from the upgraded LHCb detector will allow for more detailed studies of the $\Lambda p p$ spectrum, including potential threshold enhancements.