Observation of the rare baryonic decay $B^{+}\rightarrow p \bar{\itΛ}$ and measurement of its weak decay parameter

Using LHCb proton-proton collision data, this paper presents the first observation of the rare baryonic decay $B^{+}\rightarrow p \bar{\Lambda}$ with a significance exceeding seven standard deviations, while measuring its branching fraction to be $(1.24\pm 0.17\pm 0.05\pm 0.03)\times 10^{-7}$ and its weak decay parameter $\alpha_B$ to be $0.87_{-0.29}^{+0.26} \pm 0.09$, which indicates comparable S-wave and P-wave decay amplitudes.

The Gist

Imagine the universe as a giant, high-speed cosmic racetrack. At the center of this track sits the LHCb experiment at CERN, a massive machine designed to smash protons together at nearly the speed of light. When these protons collide, they create a chaotic shower of new particles, some of which are heavy, unstable "B-mesons." These particles are like fleeting fireflies; they exist for a split second before decaying (breaking apart) into other, lighter particles.

This paper is the story of the LHCb team finally catching a very rare, elusive firefly: the $B^+ \to p\Lambda$ decay.

Here is the breakdown of what they found, explained in everyday terms:

1. The Rare Event: Finding a Needle in a Haystack

Most of the time, when a B-meson decays, it turns into a pair of "pseudoscalar mesons" (think of them as two small, lightweight marbles). This happens often.

However, sometimes, a B-meson decides to turn into a baryon-antibaryon pair (a proton and a Lambda particle). Think of this as the B-meson suddenly deciding to turn into two heavy bowling balls instead of marbles. This is incredibly rare. Before this paper, scientists had only seen hints of this happening, but never with enough certainty to say, "Yes, we definitely saw it."

In this study, using data from 2016–2018, the LHCb team collected enough collisions to spot this rare event over 7 times more clearly than random noise would ever allow. In the world of particle physics, that's like hearing a whisper in a hurricane and being 99.99999% sure it wasn't just the wind. They have officially observed this decay for the first time.

2. The Measurement: How Often Does It Happen?

The team didn't just find it; they counted it. They compared the number of rare "bowling ball" decays ($B^+ \to p\Lambda$) to the number of common "marble" decays ($B^+ \to K^0_S \pi^+$).

• The Result: They found that for every 100 million times a B-meson decays, this specific rare event happens about 124 times.
• Why it matters: This number matches what theoretical physicists predicted. It's like checking a weather forecast that said "10% chance of rain," and then it actually rains 10% of the time. It confirms our current understanding of how the strong force (the glue holding atoms together) works in these extreme conditions.

3. The Mystery: The "Spin" of the Decay

Here is where it gets really interesting. When a particle decays, the pieces fly off in specific directions. The way they fly tells us about the "spin" or the internal dance of the particles involved.

The team measured a parameter called $\alpha_B$ (alpha-B).

• The Analogy: Imagine a spinning top falling apart. If it falls apart in a straight line, that's one type of motion. If it spins wildly as it breaks, that's another.
• The Finding: The value they measured ($\approx 0.87$) is very high. This suggests that the decay is a complex mix of two different types of motion happening at the same time: a "straight-line" motion (S-wave) and a "spinning" motion (P-wave). They are interfering with each other, like two waves in a pond crashing together.

Why do we care?
This interference is the key to a bigger mystery: CP Violation.

• The Big Question: Why does the universe prefer matter over antimatter? (If they were perfectly symmetrical, they would have annihilated each other at the Big Bang, and we wouldn't be here).
• The Puzzle: Scientists have seen strange behavior in other similar decays involving protons and kaons. They expected to see a big difference in how matter and antimatter behave, but they didn't.
• The Theory: Some physicists think the "S-wave" and "P-wave" motions might be canceling each other out, hiding the difference between matter and antimatter. By measuring this high $\alpha_B$ value, the LHCb team has confirmed that these two motions are indeed present and strong. This sets the stage for future experiments to see if they are hiding a secret "CP violation" (a difference between matter and antimatter) that we just haven't been able to see yet.

4. The "Magic" of the Data

To get this result, the team had to be incredibly clever:

• The Filter: They used a super-smart computer algorithm (a "Boosted Decision Tree") to act like a bouncer at a club, letting only the most likely candidates into the analysis and kicking out the millions of fake events.
• The Blind Test: To avoid bias (seeing what they wanted to see), they locked the final results in a digital safe. They didn't look at the final numbers until every single step of their analysis was finished and approved.

The Bottom Line

This paper is a major milestone. It's the first time we've definitively seen this specific particle transformation. It confirms our theories about how heavy particles break apart and, more importantly, it gives us the tools to hunt for the "smoking gun" of why our universe is made of matter.

Think of it as finding a new, rare species of bird. We know it exists, we know how often it flies, and now we know exactly how its wings move. The next step is to watch it closely to see if it sings a song that breaks the laws of physics.

Technical Summary

1. Problem and Motivation

The study of charmless two-body $B$-meson decays provides critical insights into strong interaction dynamics and CP violation. While decays into pseudoscalar-meson pairs ($B \to PP'$) are well-explored, decays into baryon-antibaryon pairs are significantly less understood.

• The Gap: Prior to this work, only two such processes had been observed ($B^0 \to p\bar{p}$ and $B^+ \to p\Lambda(1520)$), with imprecise measurements. The ground-state decay $B^+ \to p\Lambda$ had only been seen as "evidence" (4.1$\sigma$) by LHCb in Run 1 (2011–2012).
• Theoretical Context: Theoretical models suggest that two-body baryonic $B$ decays are suppressed relative to multibody counterparts due to threshold enhancement mechanisms. Furthermore, the underlying quark transition ($\bar{b} \to u\bar{u}\bar{s}$) is related to other decays like $B^0_s \to K^+K^-$ and $\Lambda_b^0 \to pK^-$.
• The Anomaly: There is a puzzling suppression of CP violation observed in $\Lambda_b^0 \to pK^-$ compared to mesonic decays. Theoretical studies suggest this might stem from the cancellation of CP asymmetries between different partial waves (S-wave and P-wave) in baryonic decays. To test this, one must measure the weak decay parameter $\alpha_B$, which characterizes the interference between S-wave ($L=0$) and P-wave ($L=1$) amplitudes.

2. Methodology

The analysis utilizes proton-proton collision data collected by the LHCb experiment during Run 2 (2016–2018) at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb$^{-1}$.

• Signal and Normalization Channels:

  • Signal: $B^+ \to p\Lambda$, with subsequent decays $\Lambda \to p\pi^+$.
  • Normalization: $B^+ \to K_S^0 \pi^+$, with $K_S^0 \to \pi^+\pi^-$.
  • The branching fraction is measured relative to the normalization channel to cancel systematic uncertainties related to production and detection efficiencies.

• Event Selection and Reconstruction:

  • Tracking: Candidates are reconstructed using "long" tracks (full tracking system) or "downstream" tracks (no vertex detector hits), creating four distinct data categories (LL, DD) combined with trigger categories (TOS, TIS).
  • Vertexing: Strict requirements are placed on the displacement of $V^0$ ($\Lambda, K_S^0$) and $B^+$ decay vertices from the primary interaction vertex (PV).
  • Particle Identification (PID): Ring-imaging Cherenkov (RICH) detectors are used to distinguish protons from pions and kaons, suppressing backgrounds from misidentified decays (e.g., $K_S^0 \to \pi^+\pi^-$ faking $\Lambda \to p\pi^+$).
  • Multivariate Analysis: A Boosted Decision Tree (BDT) classifier is trained on simulated signal and high-mass sideband data to separate signal from combinatorial background.

• Statistical Analysis:

  • Yield Extraction: A simultaneous unbinned maximum-likelihood fit is performed on the invariant mass distributions of both signal and normalization channels.
    • Signal shape: Sum of a Double-Sided Crystal Ball (DSCB) and a Gaussian.
    • Backgrounds: Exponential for combinatorial; Kernel Density Estimation (KDE) for partially reconstructed decays (e.g., $B^+ \to p\Lambda\pi^0$).
  • Angular Analysis: The weak decay parameter $\alpha_B$ is extracted from the angular distribution of the proton in the $\Lambda$ rest frame, described by $dN/d\cos\theta_p \propto (1 - \alpha_\Lambda \alpha_B \cos\theta_p)$. The acceptance function is modeled using simulation and validated with the control channel $B^+ \to K_S^0 \pi^+$.
  • Blinding: The analysis results were not examined until the full procedure was finalized to avoid experimenter bias.

3. Key Contributions

1. First Observation: This paper presents the first observation of the rare baryonic decay $B^+ \to p\Lambda$, upgrading the previous 4.1$\sigma$ evidence to a significance exceeding 7 standard deviations.
2. Precision Branching Fraction: It provides the most precise measurement of the branching fraction to date, combining Run 2 data with previous Run 1 results.
3. First Measurement of $\alpha_B$: It reports the first measurement of the weak decay parameter $\alpha_B$ for this channel, a crucial step in understanding the partial wave composition of the decay.
4. Systematic Control: The analysis rigorously addresses systematic uncertainties across four data categories, including fit biases, modeling choices, and efficiency corrections, treating correlations appropriately.

4. Results

• Branching Fraction:
  The combined branching fraction (Run 1 + Run 2) is measured as:
  $$\mathcal{B}(B^+ \to p\Lambda) = (1.24 \pm 0.17_{\text{stat}} \pm 0.05_{\text{syst}} \pm 0.03_{\text{norm}}) \times 10^{-7}$$
  This value is consistent with theoretical predictions and is more than 20 times lower than the three-body decay $B^+ \to p\Lambda\pi^0$, supporting the threshold enhancement hypothesis.

• Weak Decay Parameter:
  The weak decay parameter is measured to be:
  $$\alpha_B = 0.87^{+0.26}_{-0.29} \pm 0.09$$

  • Interpretation: The large value of $\alpha_B$ (close to 1) indicates comparable S-wave and P-wave decay amplitudes. This confirms the presence of strong interference between these amplitudes.

• Significance:
  The statistical significance of the signal yield exceeds 7$\sigma$, satisfying the criteria for a formal observation in particle physics.

5. Significance and Implications

• Resolving CP Anomalies: The measurement of $\alpha_B \approx 0.87$ supports the hypothesis that the small CP violation observed in $\Lambda_b^0 \to pK^-$ might be due to a cancellation between CP asymmetries in the S-wave and P-wave amplitudes. If both amplitudes are large and have different phases, their interference can suppress the net CP asymmetry.
• Testing QCD Dynamics: The result provides a stringent test for theoretical models of charmless baryonic $B$ decays, helping to constrain tree-level and penguin amplitudes.
• Future Prospects: The observation of this decay and the measurement of its angular parameters pave the way for future precision CP violation measurements in the $B^+ \to p\Lambda$ channel using the upgraded LHCb dataset. This will offer a powerful probe into the dynamics of heavy-flavor decays involving baryons, a sector previously less explored than mesonic decays.

In summary, this work marks a milestone in heavy-flavor physics by establishing the existence of the $B^+ \to p\Lambda$ decay and providing the first experimental handle on its angular structure, offering new clues to the mechanisms governing CP violation in baryonic systems.