Time-integrated CP asymmetries in meson and baryon decays

This paper reviews recent LHCb and Belle II measurements of time-integrated CP asymmetries in hadron decays, highlighting progress in determining the CKM angle $\gamma$, the first observation of CP violation in baryon decays, and new studies of direct CP violation in $D$ mesons, while also discussing future prospects.

The Gist

Imagine the universe as a giant, complex dance floor. In this dance, particles called "mesons" and "baryons" (types of matter) and their mirror-image partners, "antimatter," are supposed to move in perfect sync. If you play the music backward (a concept physicists call "CP symmetry"), the dance should look exactly the same.

However, for decades, physicists have known that sometimes the music plays slightly differently for the dancers and their mirror partners. This is called CP violation. It's a tiny glitch in the universe's choreography that helps explain why we have a universe made of matter instead of nothingness.

This paper, presented by Alex Gilman for the LHCb and Belle II experiments, is a report card on recent discoveries about these glitches. Here is what they found, explained simply:

1. The "Gold Standard" Check: Measuring the Angle $\gamma$

Think of the Standard Model (our current rulebook for physics) as a clock. The "CKM angle $\gamma$" is a specific setting on that clock. If the clock is set correctly, the hands should point exactly where the rulebook says they should.

• The Experiment: Scientists looked at how certain heavy particles ($B$ mesons) decay into lighter ones ($D$ mesons and pions or kaons). It's like watching a specific dance move and measuring the exact angle of the dancer's arm.
• The Result: By combining data from two massive detectors (LHCb in Europe and Belle II in Japan), they measured this angle with incredible precision. The result is $65.7 \pm 2.5$ degrees.
• Why it matters: This measurement is like checking if the clock is ticking true. So far, the clock is working perfectly according to the rulebook. There are no signs of a "broken gear" (new physics) yet, but the measurement is now so precise that if the clock does start ticking wrong in the future, we'll catch it immediately.

2. The Big Breakthrough: CP Violation in Baryons

For a long time, we only saw these "glitches" in mesons (particles made of two quarks). Baryons (particles made of three quarks, like protons) were the missing piece of the puzzle. It was like knowing the glitch happened in the living room but never finding it in the kitchen.

• The Search: Scientists looked at two types of baryon decays:
  1. Simple Decays: A baryon breaking into a proton and a pion/kaon.
  2. Complex Decays: A baryon breaking into a proton and three other particles, or a Lambda baryon and three other particles.
• The Discovery:
  • In the simple decays, they found nothing. The dance looked the same forward and backward. This was surprising because similar simple meson decays do show glitches. It suggests that in simple baryon dances, the "strong force" (the glue holding the particles together) is so dominant it hides the glitch.
  • In the complex decays (where multiple particles are created and interact), they found huge glitches. Specifically, in the decay of a $\Lambda_b^0$ baryon into a proton and three pions, they found a difference between matter and antimatter that was 5.2 standard deviations away from zero.
• The Metaphor: Imagine a simple two-person dance where the partners move perfectly in sync. Now imagine a chaotic group dance with four people spinning and bumping into each other. In the group dance, the "glitch" (CP violation) suddenly becomes visible. This is the first time we have ever seen CP violation in baryons, and it only shows up when the dance gets complicated enough to have "resonances" (interfering patterns).

3. The Charm Puzzle: $D$ Mesons

Charm quarks are the "middle child" of the particle world. They are heavy enough to be interesting but light enough that the Standard Model predicts the glitches should be tiny—almost invisible.

• The Mystery: Scientists have been measuring how often charm particles decay into pairs of pions or kaons. They found small differences between matter and antimatter that are slightly larger than the rulebook predicts. It's like seeing a clock gain a few seconds a day when it should be perfect.
• New Measurements:
  • LHCb used a super-upgraded detector to look at a very rare decay ($D^0 \to K_S^0 K_S^0$). They found no significant glitch, which is good for the rulebook, but their data collection speed improved by a factor of 15 compared to previous runs.
  • Belle II looked at other charm decays ($D^0 \to \pi^0 \pi^0$ and $D^+ \to \pi^+ \pi^0$). They found no evidence of a glitch in the $D^+$ decay (which the rulebook says shouldn't have one), and their measurements are getting incredibly precise.
• The Takeaway: The "charm" sector is a sensitive test. The current data is a bit puzzling—it hints that the rulebook might be slightly off, but it's not a slam-dunk proof yet. The scientists are now gathering more data to see if the tiny discrepancies grow into a big revelation.

Summary: What's Next?

The paper concludes that we are in a "golden age" of precision.

• We have confirmed the "clock" (CKM angle $\gamma$) is ticking correctly so far.
• We have finally found the "glitch" in the kitchen (baryon decays), but only when the dance gets complex.
• We are watching the "middle child" (charm quarks) closely, hoping to see if the tiny discrepancies grow.

With new data pouring in from LHCb and Belle II, the field is moving toward a level of precision where even the tiniest deviation from the rulebook could reveal a completely new layer of physics. For now, the universe is still dancing mostly to the tune of the Standard Model, but the music is getting more complex, and we are listening closer than ever before.

Technical Summary

Technical Summary: Time-integrated CP Asymmetries in Meson and Baryon Decays

Problem and Context
This proceedings paper reviews recent measurements of time-integrated CP asymmetries in hadron decays, focusing on the interplay between weak and strong interactions within the Standard Model (SM). While CP violation has been established in neutral meson systems (kaons, B-mesons) and recently in charm decays, its manifestation in baryon decays had remained unobserved until the work presented here. The paper addresses the challenge of isolating direct CP violation, which arises from the interference of at least two decay amplitudes with relative CP-odd weak phases ($\phi$) and CP-even strong phases ($\delta$). The goal is to test the SM's CKM mechanism, constrain the unitarity triangle (specifically the angle $\gamma$), and search for deviations that could indicate Beyond-Standard-Model (BSM) physics.

Methodology
The analysis relies on data from the LHCb experiment (proton-proton collisions at $\sqrt{s} = 7\text{--}13.6$ TeV) and the Belle II experiment ($e^+e^-$ collisions at the $\Upsilon(4S)$ resonance). The datasets include Run 1 and Run 2 data from LHCb (approx. 9 fb$^{-1}$) and early Run 3 data (up to 16 fb$^{-1}$ as of Aug 2025), alongside Belle (0.43 ab$^{-1}$) and Belle II (0.15 ab$^{-1}$) data.

Key methodological approaches include:

• CKM Angle $\gamma$ Determination: Utilizing $B^\pm \to D K^\pm$ and $B^\pm \to D K^{*\pm}$ decays where the $D$ meson decays to CP eigenstates or flavor-specific final states. The $D$ decay amplitude parameters are constrained by quantum-correlated measurements from BESIII and CLEO.
• Baryon CP Violation: Analyzing $\Lambda_b^0$ and $\Xi_b^0$ decays. To control for production and detection asymmetries, control modes such as $\Lambda_b^0 \to \Lambda_c^+ [\Lambda \pi^+] \pi^-$ are employed. The analysis involves integrating over time and, crucially, partitioning the phase space of multibody decays to isolate resonant regions where strong phases vary.
• Charm Sector ($D$ Mesons): Measuring direct CP asymmetries in $D^0 \to K_S^0 K_S^0$, $D^0 \to \pi^0 \pi^0$, and $D^+ \to \pi^+ \pi^0$. Flavor tagging is achieved via $D^{*+} \to D^0 \pi^+$ decays or event-wide algorithms. Detection asymmetries are controlled using control channels like $D^0 \to K^+ K^-$ or $D^0 \to K_S^0 \pi^+ \pi^-$.

Key Contributions and Results

1. Progress on the CKM Angle $\gamma$:

   • A combined analysis of LHCb Run 1 and 2 data for $B^\pm \to D K^{*\pm}$ decays yielded $\gamma = (63 \pm 13)^\circ$.
   • A 2024 LHCb combination of all measurements resulted in $\gamma = (64.6 \pm 2.8)^\circ$.
   • A 2024 Belle/Belle II combination found $\gamma = (75.2 \pm 7.6)^\circ$.
   • A 2025 global analysis incorporating over 100 observables from multiple experiments determined $\gamma = (65.7 \pm 2.5)^\circ$. This represents a significant improvement in precision from $\sim 7^\circ$ in 2015 to $\pm 2.5^\circ$ in 2025, showing excellent consistency across experiments.

2. First Observation of CP Violation in Baryon Decays:

   • Two-body decays: The analysis of $\Lambda_b^0 \to p K^-$ found $A_{CP} = (-1.4 \pm 0.7 \pm 0.4)\%$, consistent with zero. This contrasts with the $\sim 10\%$ asymmetry seen in analogous $B^0 \to K^- \pi^+$ meson decays, suggesting strong dynamics suppress CP violation in simple baryon topologies.
   • Multibody decays: A 2025 LHCb analysis of $\Lambda_b^0 \to \Lambda K^+ K^-$ observed $A_{CP} = (8.3 \pm 2.3 \pm 1.6)\%$ ($3.1\sigma$). In a specific resonant region ($m_{K^+K^-} > 2.2$ GeV, $m_{\Lambda K^+} < 2.9$ GeV), the asymmetry increased to $(16.5 \pm 4.8 \pm 1.7)\%$ ($3.2\sigma$).
   • Inclusive Observation: The analysis of $\Lambda_b^0 \to p K^- \pi^+ \pi^-$ yielded an inclusive asymmetry of $A_{CP} = (2.45 \pm 0.46 \pm 0.10)\%$, constituting a $5.2\sigma$ observation of CP violation in baryon decays.
   • Resonant Enhancement: The largest asymmetry was found in the resonant region of the $p \pi^+ \pi^-$ system: $A_{CP} = (5.4 \pm 0.9 \pm 0.1)\%$ ($6.0\sigma$). This confirms that interfering resonances in multibody final states provide favorable conditions for CP violation to manifest.

3. Direct CP Violation in Charm Decays:

   • $D^0 \to K_S^0 K_S^0$: Belle and Belle II combined analyses yielded $A_{CP} = (-0.6 \pm 1.1 \pm 0.1)\%$. LHCb, using 2024 data (Run 3), measured $A_{CP} = (1.86 \pm 1.04 \pm 0.41)\%$ with no significant evidence of CP violation. The Run 3 analysis demonstrated a factor of 15 improvement in signal collection per unit time compared to Run 2.
   • $D^0 \to \pi^0 \pi^0$: Belle II measured $A_{CP} = (0.30 \pm 0.72 \pm 0.20)\%$, a 15% improvement in precision over previous Belle results despite using half the luminosity.
   • $D^+ \to \pi^+ \pi^0$: Belle II measured $A_{CP} = (-1.8 \pm 0.9 \pm 0.1)\%$, consistent with the SM prediction of zero (as only a single weak amplitude contributes) and previous measurements.

Significance
The paper claims that these results represent major milestones in the field of flavor physics:

• Validation of the SM: The precise determination of $\gamma$ confirms the CKM mechanism's consistency across different decay modes and experiments.
• New Frontier in Baryons: The first observation of CP violation in baryon decays establishes a new testbed for understanding the interplay of weak and strong interactions. The results highlight that strong dynamics can either suppress CP violation (in two-body decays) or enhance it significantly (in resonant multibody decays).
• Charm Sector Sensitivity: The approach to sub-percent precision in charm CP asymmetries allows for stringent tests of the SM, where theoretical uncertainties are large but potential BSM signals are expected to be small.
• Future Prospects: The paper emphasizes that the upgraded detectors (LHCb Run 3, Belle II) and increasing datasets (targeting 23 fb$^{-1}$ for LHCb by 2026) will enable unprecedented precision. This positions the field to detect subtle deviations from SM predictions that could signal new physics.