First observation of the $\overline{B}_{s}^{0}\toΛ_{c}^{+}\overlineΛ_{c}{}^{-}$ decay and evidence for the $\overline{B}^{0}\toΛ_{c}^{+}\overlineΛ_{c}{}^{-}$ decay

Using LHCb data corresponding to 9 fb⁻¹ of integrated luminosity, this paper reports the first observation of the $\overline{B}_{s}^{0}\to\Lambda_{c}^{+}\overline{\Lambda}_{c}{}^{-}$ decay and evidence for the $\overline{B}^{0}\to\Lambda_{c}^{+}\overline{\Lambda}_{c}{}^{-}$ decay, providing the first measurements of their branching fractions to advance the theoretical understanding of two-body baryonic $B$ meson decays.

The Gist

Imagine the universe as a giant, high-speed racetrack where tiny particles zoom around at nearly the speed of light. At CERN, the European Organization for Nuclear Research, scientists use a massive machine called the Large Hadron Collider (LHC) to crash these particles together, creating a chaotic explosion of new, short-lived particles.

This paper is a report from the LHCb team, a group of scientists who act like forensic detectives at this racetrack. Their job is to sift through the debris of these collisions to find specific, rare "fingerprints" left behind by particles that shouldn't really exist or are very hard to catch.

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

1. The Mystery: The "Ghost" Particles

In the world of particle physics, there are particles called B-mesons. Think of them as heavy, unstable parents. Usually, when they die (decay), they break apart into lighter, simpler particles (like mesons).

However, sometimes they break apart into baryons (particles made of three quarks, like protons and neutrons). This is rare and tricky. The scientists were looking for a very specific, rare breakup: a B-meson parent splitting into two "charmed" children: a Lambda-c and an anti-Lambda-c.

It's like watching a heavy, complex toy car crash and expecting it to shatter into two specific, heavy, complex engines. Most theories said this crash would be so rare it would be invisible, or that the engines would be "handed" in a way that made them impossible to form.

2. The Theory vs. Reality

For a long time, physicists had a rulebook (the Standard Model) that predicted how these crashes happen.

• The Old Rule: One type of crash (called "W-emission") was expected to happen often. Another type (called "W-exchange") was thought to be "helicity suppressed."
• The Analogy: Imagine trying to throw a ball through a tiny, spinning hoop. If you throw it the "wrong" way (wrong spin), it bounces off. The "W-exchange" process was thought to be like throwing the ball the wrong way every time, making it nearly impossible to score.

Because of this, scientists thought the B-meson breaking into two Lambda-c particles would be incredibly rare. But some new theories suggested that maybe, just maybe, the "hoop" wasn't as strict as we thought, and the ball could get through.

3. The Hunt: Sifting Through the Noise

The LHCb team collected data from 2011 to 2018. This is like recording 9 billion hours of high-definition video of the racetrack.

• The Challenge: In every second, millions of particles fly by. The signal they were looking for (the B-meson breaking into two Lambda-cs) is like finding a single, specific grain of sand on a beach, while the rest of the beach is covered in similar-looking sand.
• The Method: They used a "filter" (mathematical algorithms) to ignore the boring, common crashes and focus only on the ones that looked like the rare event they wanted. They compared their rare finds against "control groups" (common, well-understood crashes) to make sure their measurements were accurate.

4. The Big Discovery

After crunching the numbers, the team found something amazing:

1. The First "Smoking Gun": They found clear evidence of the $B_s^0$ meson decaying into two Lambda-c particles.

   • Significance: They were 6.2 sigma sure. In the world of science, 5 sigma is the gold standard for a "discovery." This is like flipping a coin 100 times and getting heads every single time; the odds of it being a fluke are practically zero.
   • What it means: This proves that the "W-exchange" process (the one we thought was impossible) actually happens. The "ball" did get through the spinning hoop. This is the first time we've seen this specific mechanism work in baryonic decays.

2. The "Strong Hint": They also found evidence for the $B^0$ meson doing the same thing.

   • Significance: They were 4.3 sigma sure. This isn't a full discovery yet, but it's a very strong "evidence" that the event is happening. It's like seeing a shadow that is almost certainly a person, even if you haven't seen the face clearly yet.

5. Why Does This Matter?

The results are a bit of a shocker for the rulebook.

• The Surprise: The team measured how often these crashes happened. The rate for the $B^0$ decay was much lower than expected if only the "easy" mechanism was working.
• The Explanation: This suggests that the "easy" mechanism and the "hard" mechanism (W-exchange) are actually fighting each other. It's like two people pushing a car in opposite directions; the car moves, but much slower than if only one person was pushing.
• The Impact: This tells us that the "W-exchange" and "W-annihilation" forces are much more important than we thought. They are not just background noise; they are major players in how matter transforms.

The Bottom Line

The LHCb team has successfully caught a rare, elusive particle decay that was thought to be nearly impossible. They proved that nature has a more complex "dance" than we previously understood.

This discovery is a key piece of the puzzle for understanding why the universe is made of matter and not just energy. It opens the door to finding new physics beyond our current theories, potentially explaining mysteries like why there is more matter than antimatter in the universe.

In short: They found a ghost, proved it was real, and realized our map of the universe needs a few new roads drawn on it.

Technical Summary

1. Problem and Scientific Context

The study addresses the dynamics of two-body baryonic decays of $B$ mesons, specifically those involving a charm-anticharm pair ($\Lambda_c^+ \Lambda_c^-$). In the Standard Model, these decays proceed via tree-level quark diagrams:

• $W$-emission: The dominant mechanism for $B^0 \to \Lambda_c^+ \Lambda_c^-$.
• $W$-exchange: A topology expected to be helicity-suppressed and often neglected in theoretical models, but potentially significant for $B^0_s \to \Lambda_c^+ \Lambda_c^-$.

The Core Tension:
Previous theoretical predictions suggested that the $B^0 \to \Lambda_c^+ \Lambda_c^-$ branching fraction should be significantly larger than that of the $B^0_s$ counterpart due to the dominance of the $W$-emission diagram. However, previous experimental upper limits (from LHCb and Belle) suggested a tension with these predictions, hinting at the presence of non-negligible $W$-exchange contributions or interference effects. This paper aims to resolve this by measuring these branching fractions with high precision and observing the $B^0_s$ mode for the first time.

2. Methodology

Data Sample:

• Experiment: LHCb detector at the Large Hadron Collider (LHC).
• Period: Run 1 (2011–2012) and Run 2 (2015–2018).
• Integrated Luminosity: $9 \text{ fb}^{-1}$ of proton-proton collision data at center-of-mass energies of 7, 8, and 13 TeV.

Signal Reconstruction:

• Decay Chain: The analysis reconstructs the decay $B^{0(s)} \to \Lambda_c^+ \Lambda_c^-$, where each $\Lambda_c^+$ decays via $\Lambda_c^+ \to p K^- \pi^+$.
• Normalization Channels: To cancel systematic uncertainties related to detector efficiency and luminosity, the signal yields are normalized against topologically similar decays:
  • $B^0 \to D_s^- D^+$ (with $D_s^- \to K^+ K^- \pi^-$ and $D^+ \to K^- \pi^+ \pi^+$).
  • $B^0_s \to D_s^+ D_s^-$ (with $D_s^+ \to K^- K^+ \pi^+$).

Selection and Background Suppression:

• Trigger: Events required a high-transverse-energy hadron/photon/electron in the hardware trigger and a secondary vertex with significant displacement in the software trigger.
• Offline Selection:
  • Particle Identification (PID) requirements for protons, kaons, and pions.
  • Kinematic cuts: $p > 5 \text{ GeV}$ ($p > 10 \text{ GeV}$ for protons), $p_T > 500 \text{ MeV}$, and strict vertex quality ($\chi^2_{IP} > 4$).
  • Veto criteria to suppress cross-feed from misidentified $D$ mesons and $\Lambda_c$ candidates.
• Optimization: Selection criteria for $\chi^2_{IP}$ and a PID-based variable ($Q \Pi P_i$) were optimized using the Punzi figure of merit to maximize signal significance.

Analysis Strategy:

1. Two-Stage Fitting:
   • Stage 1: An unbinned maximum-likelihood fit to the 2D distribution of $[m(\Lambda_c^+), m(\Lambda_c^-)]$ to separate genuine $\Lambda_c^+ \Lambda_c^-$ pairs from singly charmed and charmless backgrounds.
   • Stage 2: A binned maximum-likelihood fit to the invariant mass $m(\Lambda_c^+ \Lambda_c^-)$ to extract the signal yields for $B^0$ and $B^0_s$.
2. Efficiency Correction: Data-driven corrections (using sPlot and gradient-boosting algorithms) were applied to simulation to match kinematic distributions and PID performance in data.
3. Systematic Uncertainties: Evaluated via alternative fit models, line shape variations (DSCB vs. Hypatia), background modeling, and simulation statistics.

3. Key Contributions

• First Observation of $B^0_s \to \Lambda_c^+ \Lambda_c^-$: This is the first experimental verification of this decay mode, providing direct evidence for the $W$-exchange mechanism in baryonic $B$ decays.
• Evidence for $B^0 \to \Lambda_c^+ \Lambda_c^-$: The analysis provides the first significant evidence for the $B^0$ mode, moving beyond previous upper limits.
• Precision Branching Fraction Measurements: The paper provides the first precise measurements of the branching fractions for both channels, replacing previous upper limits with central values and uncertainties.
• Theoretical Implications: The results challenge the assumption that $W$-exchange is negligible in these decays and suggest significant SU(3) flavor symmetry breaking and interference effects.

4. Results

Significance:

• $B^0_s \to \Lambda_c^+ \Lambda_c^-$: Observed with a statistical significance of 6.2$\sigma$.
• $B^0 \to \Lambda_c^+ \Lambda_c^-$: Observed with a statistical significance of 4.3$\sigma$ (evidence).

Branching Fractions:
The measured branching fractions are:

• $\mathcal{B}(B^0 \to \Lambda_c^+ \Lambda_c^-) = (1.01^{+0.27}_{-0.28} \pm 0.08 \pm 0.15) \times 10^{-5}$
• $\mathcal{B}(B^0_s \to \Lambda_c^+ \Lambda_c^-) = (5.0 \pm 1.3 \pm 0.5 \pm 0.8) \times 10^{-5}$

(Uncertainties are statistical, systematic, and due to external inputs, respectively.)

Key Observation:
Contrary to the naive expectation that the $B^0$ mode (dominated by $W$-emission) should be larger than the $B^0_s$ mode (dominated by suppressed $W$-exchange), the results show that the $B^0_s$ branching fraction is approximately 5 times larger than the $B^0$ branching fraction.

5. Significance

The findings have profound implications for the theoretical understanding of non-perturbative QCD in heavy flavor physics:

1. Validation of $W$-Exchange: The observation of the $B^0_s \to \Lambda_c^+ \Lambda_c^-$ decay confirms that the $W$-exchange topology, previously thought to be helicity-suppressed and negligible, is actually a dominant mechanism in this channel.
2. Interference Effects: The unexpectedly small branching fraction for $B^0 \to \Lambda_c^+ \Lambda_c^-$ (compared to theoretical predictions based solely on $W$-emission) suggests a destructive interference between the $W$-emission amplitude and the $W$-exchange amplitude.
3. SU(3) Symmetry Breaking: The large ratio between the $B^0_s$ and $B^0$ rates indicates significant SU(3) flavor symmetry breaking effects, which must be accounted for in theoretical models.
4. Future Physics: These results necessitate a reexamination of $W$-annihilation and $W$-exchange contributions in charmless, singly charmed, and doubly charmed baryonic $B$ decays. This is crucial for improving predictions of CP violation in baryonic systems, a key area for future LHCb Run 3 and upgrade studies.

In summary, this paper provides the first experimental proof that helicity-suppressed mechanisms play a critical role in two-body baryonic $B$ decays, fundamentally altering the theoretical landscape for these processes.