First evidence of $CP$ violation in beauty baryon to charmonium decays

Using LHCb data from 2015–2018, researchers observed the first evidence of CP violation in beauty baryon decays to charmonium, measuring a combined asymmetry difference of $4.31 \pm 1.06 \pm 0.28\%$ with a significance of $3.9\sigma$.

The Gist

Imagine the universe as a giant, chaotic kitchen where particles are the ingredients. For decades, physicists have been trying to solve a massive mystery: Why is there more matter (the stuff we are made of) than antimatter (the "anti-stuff" that should have annihilated everything in the Big Bang)?

If the universe were perfectly symmetrical, matter and antimatter would have canceled each other out, leaving nothing but light. But we are here. Something must have tipped the scales. That "something" is called CP Violation.

Think of CP Violation as the universe's way of saying, "I have a slight preference for left-handedness over right-handedness." If you look in a mirror, the reflection should be identical, but in the subatomic world, sometimes the mirror image behaves slightly differently.

The New Discovery: The "Beauty" Baryon

This paper from the LHCb collaboration at CERN is like a detective story. They were looking for evidence of this "mirror bias" in a specific type of particle decay.

• The Suspects: They studied a heavy particle called the $\Lambda_b^0$ baryon (think of it as a "Beauty" baryon because it contains a "beauty" or "bottom" quark).
• The Crime Scene: This heavy particle decays (breaks apart) into lighter particles. The team looked at two specific ways it broke apart:
  1. Path A: Breaking into a "charmonium" (a heavy charm-anticharm pair), a proton, and a pion (a light particle).
  2. Path B: Breaking into the same charmonium and proton, but with a kaon instead of a pion.

The Analogy: The Twin Brothers

Imagine two identical twin brothers, Particle A and Particle B. They are supposed to be perfect mirror images of each other.

• The Rule: If you flip a coin, heads and tails should appear 50/50.
• The Twist: In the subatomic world, sometimes the "heads" side of the coin is slightly heavier than the "tails" side.

The scientists wanted to see if the "Beauty" baryon had a favorite way to break apart. They compared how often the "matter" version of the particle broke into Path A vs. Path B, and compared that to how often the "antimatter" version did the same.

The Result: They found a difference!

• The "matter" version of the particle seemed to prefer one path slightly more than the "antimatter" version did.
• The difference was about 4%.
• In the world of particle physics, a 4% difference is huge. It's like flipping a coin 1,000 times and getting 520 heads and 480 tails. It's not a fluke; it's a pattern.

Why This Matters

Previously, scientists had seen this "mirror bias" in mesons (particles made of two quarks, like a married couple). But they had never seen it clearly in baryons (particles made of three quarks, like a family of three).

Think of mesons as a duet and baryons as a trio.

• We knew the duet had a rhythm that wasn't perfectly symmetrical.
• This paper is the first time we've proven the trio also has a broken rhythm.

This is a "smoking gun" for the Standard Model of physics. It confirms that the rules governing how these three-quark families behave are just as complex and asymmetrical as the two-quark couples. It helps us understand the "recipe" the universe used to create more matter than antimatter.

The "Triple-Product" Check

To make sure they weren't seeing ghosts, the scientists also looked at something called Triple-Product Asymmetry.

• The Metaphor: Imagine a spinning top. If you look at it from the front, it spins clockwise. If you look at it from the back, it spins counter-clockwise.
• The scientists checked if the "spin" of the debris from the explosion had a preferred direction that violated the laws of time reversal.
• The Verdict: No, the spin was symmetrical. This is actually good news! It means the asymmetry they found in the main measurement is real and not caused by some weird experimental glitch.

The Bottom Line

The LHCb team, using data from 2015–2018, found strong evidence (3.9 sigma) that the "Beauty" baryon treats matter and antimatter differently when it decays.

• Significance: In science, "3.9 sigma" means there is only a 1 in 10,000 chance this result is a random fluke. It's not quite the "5 sigma" (1 in 3.5 million) needed to officially claim a "discovery," but it is very close. It's the difference between "We are almost certain" and "We are 100% sure."
• The Future: This result, combined with older data, pushes us closer to solving the ultimate mystery: Why do we exist?

In short: The universe has a slight bias, and this paper proves that even the "three-quark family" particles have a favorite side, just like the "two-quark couples" we knew about before. We are one step closer to understanding why the kitchen didn't empty out after the Big Bang.

Technical Summary

1. Problem and Motivation

The primary goal of this study is to investigate CP violation (CPV) in the decay of the bottom baryon $\Lambda_b^0$ into charmonium final states. While CP violation has been well-established in neutral meson systems (kaons, B-mesons) and recently in charged B-meson decays to charmonium ($B^+ \to J/\psi \pi^+$ vs. $B^+ \to J/\psi K^+$), evidence in the baryon sector has been elusive.

• Theoretical Context: The Standard Model (SM) predicts CP violation via the interference of "tree-level" and "penguin" (loop) amplitudes in weak decays.
  • The decay $\Lambda_b^0 \to J/\psi p K^-$ is dominated by the $b \to c\bar{c}s$ transition (Cabibbo-favored), where penguin contributions are negligible. It serves as a reference channel with minimal expected CPV.
  • The decay $\Lambda_b^0 \to J/\psi p \pi^-$ proceeds via the $b \to c\bar{c}d$ transition (Cabibbo-suppressed). Here, penguin amplitudes are enhanced, making it sensitive to potentially larger CP asymmetries.
• The Observable: The paper focuses on the difference in CP asymmetries between these two modes:
  $$\Delta A_{CP} \equiv A_{CP}(\Lambda_b^0 \to J/\psi p \pi^-) - A_{CP}(\Lambda_b^0 \to J/\psi p K^-)$$
  Measuring $\Delta A_{CP}$ cancels out many systematic uncertainties related to production and detection, providing a clean probe of the weak phase and penguin contributions in baryonic decays.

2. Methodology

Data Sample

• Experiment: LHCb detector at CERN.
• Data Period: Proton-proton collisions collected during Run 2 (2015–2018).
• Center-of-Mass Energy: 13 TeV.
• Integrated Luminosity: $6 \text{ fb}^{-1}$.
• Total Dataset: Combined with previous Run 1 (2011–2012) data for the final combined result.

Candidate Selection and Reconstruction

• Decay Chain: $\Lambda_b^0 \to J/\psi (\to \mu^+\mu^-) p h^-$, where $h^-$ is either $\pi^-$ or $K^-$.
• Trigger: Hardware trigger requiring high-$p_T$ muons; software trigger reconstructing $J/\psi$ candidates or single high-$p_T$ muons with large impact parameters.
• Offline Selection:
  • Muons required to have $p_T > 500 \text{ MeV}/c$ and invariant mass within $[3049, 3140] \text{ MeV}/c^2$.
  • Proton and hadron candidates must have good track quality, high $p_T$, and be inconsistent with originating from the primary vertex (PV).
  • Particle Identification (PID): Neural networks using RICH, calorimeter, and muon system data distinguish pions from kaons.
  • Background Suppression:
    • Misidentified $B_s^0$ and $B^0$ decays are rejected using tight PID and invariant mass vetoes (e.g., rejecting candidates where assigning a kaon mass to the proton yields a $B^0$ mass).
    • Combinatorial background is suppressed using a Gradient Boosted Decision Tree (BDTG) classifier trained on kinematic and reconstruction variables.

Analysis Techniques

• Yield Extraction: An extended unbinned maximum-likelihood fit is performed on the $\Lambda_b^0$ invariant mass distributions for both decay modes simultaneously.
  • Signal shape: Modeled by a Hypatia function.
  • Background: Modeled by an exponential function.
  • Residual backgrounds (e.g., $\Lambda_b^0 \to J/\psi p K^-$ in the $\pi$ sample) are modeled using simulation.
• Asymmetry Correction:
  • Raw asymmetries ($A_{raw}$) are calculated from the yield differences between particle and antiparticle.
  • Detection Asymmetry: A crucial correction is applied for the difference in detection efficiency between pions and kaons ($A_D(K^-) - A_D(\pi^-)$). This is determined using calibration data from $D^+ \to K_S^0 \pi^+$ and $D^+ \to K^- \pi^+ \pi^+$ decays, weighted to match the kinematic distributions of the signal.
  • Production Asymmetry: Weighting techniques (using sPlot and hep_ml) are applied to the $\Lambda_b^0 \to J/\psi p K^-$ sample to match the kinematic distributions ($p, p_T, \eta$) of the $\Lambda_b^0 \to J/\psi p \pi^-$ sample, canceling production asymmetries.
• Triple-Product Asymmetry (TPA): To probe CPV via angular correlations, the TPA ($A_{T-odd}$) is measured. This observable is sensitive to the interference between different angular momenta and is defined using the scalar triple product of final-state momenta in the $\Lambda_b^0$ rest frame.
• Binned Analysis: The phase space is divided into bins (adaptive binning and resonance-based binning) to search for localized CPV variations.

3. Key Contributions

1. First Evidence in Baryons: This work provides the first evidence of CP violation in beauty baryon decays to charmonium final states.
2. Precision Measurement: It presents the most precise measurement of $\Delta A_{CP}$ to date, utilizing the full Run 2 dataset and advanced statistical techniques (sPlot, reweighting) to minimize systematic uncertainties.
3. Combined Result: It combines the new Run 2 result with the previous Run 1 measurement using the Best Linear Unbiased Estimate (BLUE) method, accounting for correlations in systematic uncertainties.
4. Complementary Observables: The simultaneous measurement of direct CP asymmetry and Triple-Product asymmetry offers a more comprehensive test of the SM, as TPA is sensitive to different phase combinations ($\cos \Delta\delta' \sin \Delta\phi'$) compared to direct CPV ($\sin \Delta\delta \sin \Delta\phi$).

4. Results

Primary Measurement (Run 2 Data)

The difference in CP asymmetries is measured as:
$$\Delta A_{CP} = (4.03 \pm 1.18 \text{ (stat)} \pm 0.23 \text{ (syst)})\%$$

• Significance: The deviation from zero (CP symmetry) is 3.3$\sigma$ when including systematic uncertainties.

Combined Measurement (Run 1 + Run 2)

Combining with the 2014 result ($5.7 \pm 2.4 \pm 1.2\%$):
$$\Delta A_{CP}^{\text{combined}} = (4.31 \pm 1.06 \text{ (stat)} \pm 0.28 \text{ (syst)})\%$$

• Significance: The combined result corresponds to a significance of 3.9$\sigma$ against the CP symmetry hypothesis. This constitutes "evidence" (typically defined as $>3\sigma$) but not yet "observation" ($>5\sigma$).

Triple-Product Asymmetry

The TPA for $\Lambda_b^0 \to J/\psi p \pi^-$ is measured as:
$$A_{T-odd} = (-1.37 \pm 1.15 \text{ (stat)} \pm 0.21 \text{ (syst)})\%$$

• This result is consistent with zero, showing no significant deviation from CP symmetry in the angular correlations.

Binned Results

• No significant variations in CP asymmetry or TPA were observed across the phase space (tested via $\chi^2$ tests on 4-bin, 128-bin, and resonance-based binning schemes). The data is consistent with a uniform asymmetry across the Dalitz plot.

5. Significance

• Standard Model Validation: The result is consistent with theoretical predictions that suggest large CP asymmetries in $b \to c\bar{c}d$ baryon transitions due to enhanced penguin contributions. It validates the SM description of CP violation in the baryon sector.
• New Physics Sensitivity: While consistent with the SM, the measurement constrains the magnitude of penguin-induced phase shifts. Any future deviation from the SM prediction in this channel could signal New Physics (NP) affecting the weak phase or loop diagrams.
• Baryon vs. Meson: This establishes that the mechanisms of CP violation observed in mesons (interference of tree and penguin amplitudes) are also active and measurable in baryons, despite the more complex hadronic environment.
• Future Outlook: The 3.9$\sigma$ significance suggests that with the full LHC Run 3 and Run 4 datasets, LHCb will likely reach the 5$\sigma$ threshold required for a definitive "observation" of CP violation in beauty baryon decays.

In summary, this paper marks a milestone in flavor physics by extending the discovery of CP violation to the baryon sector, providing a crucial test of the CKM mechanism and the Standard Model's ability to describe matter-antimatter asymmetry in complex hadronic systems.