Measurement of $C\!P$ asymmetry in $D^0 \to K^0_{\rm S} K^0_{\rm S}$ decays with Run 3 data

Using 2024 LHCb Run 3 proton-proton collision data, this paper reports the most precise single-experiment measurement of the time-integrated $C\!P$ asymmetry in $D^0 \to K^0_{\rm S} K^0_{\rm S}$ decays to date, yielding a value of $(1.86 \pm 1.04\pm 0.41)\%$.

The Gist

The Big Picture: A Cosmic Coin Flip

Imagine you have a magical coin. In our everyday world, if you flip a coin a million times, you expect roughly 50% heads and 50% tails. If the coin is "fair," the universe treats both sides exactly the same.

In particle physics, there is a rule called CP Symmetry. It's like saying the universe is a fair coin. If you create a particle (let's call it a "D-meson") and its anti-particle (the "anti-D-meson"), they should behave exactly the same way when they decay (fall apart).

However, the universe is a bit of a trickster. In 2019, scientists at CERN discovered that for certain particles, the coin isn't perfectly fair. The universe slightly prefers one side over the other. This is called CP Violation.

This paper is about a new, super-precise measurement of this unfairness in a specific type of particle decay: $D^0 \to K^0_S K^0_S$.

The Cast of Characters

To understand the experiment, let's meet the players:

1. The D-Meson ($D^0$): The main character. It's a heavy particle made of a charm quark. It lives for a tiny fraction of a second before it decays.
2. The $K^0_S$ (Kaon): The "child" particles. The $D^0$ decays into two of these. They are unstable and decay almost immediately into pions (which are like tiny, fast-moving ping-pong balls).
3. The LHCb Detector: The giant camera. It's a massive, high-tech spectrometer at CERN that watches protons smash into each other. Think of it as a high-speed camera capable of taking a photo of a bullet hitting another bullet, but at a scale a billion times smaller.
4. The "Tagging Pion": The ID badge. To know if the $D^0$ was a "boy" or a "girl" (matter or antimatter) when it was born, scientists look at a specific particle (a pion) that was born with it. If the pion is positive, the $D^0$ was a $D^0$; if negative, it was an anti-$D^0$.

The Challenge: Finding a Needle in a Haystack

The scientists wanted to count how many times the "boy" $D^0$ turned into two Kaons versus how many times the "girl" anti-$D^0$ did the same.

The Problem:

1. Rarity: This specific decay ($D^0 \to K^0_S K^0_S$) is very rare. It's like trying to find a specific grain of sand on a beach.
2. The Detector's Bias: The LHCb detector isn't perfect. It might be slightly better at catching "positive" particles than "negative" ones, or it might be built in a way that makes it easier to see particles moving left than right. If you just count the raw numbers, you might think the universe is unfair when it's actually just your camera being biased.
3. The "Calibration" Trick: To fix the camera bias, the scientists used a "control group." They looked at a different decay ($D^0 \to K^0_S \pi^+ \pi^-$) which is known to be perfectly fair (50/50). By comparing how the detector treated this fair group, they could calculate exactly how much the detector was "lying" and correct the numbers for the rare group.

The New Upgrade: The "Super Trigger"

This paper is special because it uses data from Run 3 of the Large Hadron Collider (LHC), which started in 2022.

Think of the LHC as a massive water hose spraying particles. In the past, the "trigger" (the system that decides which events to save) was like a sieve with big holes. It let most of the water through but missed the tiny, interesting droplets.

In this new experiment, they upgraded the trigger to be a high-tech digital sieve.

• Old Way: "If it looks like a big splash, save it."
• New Way: "If it looks like a specific, tiny, rare pattern, save it immediately."

This upgrade allowed them to catch three times more of the rare $D^0 \to K^0_S K^0_S$ events than before. It's like upgrading from a net that catches only fish to a net that catches fish and the specific plankton they eat.

The Results: The Verdict

After collecting data from 2024 (about 6.2 "inverse femtobarns" of data—a unit that basically means "a whole lot of collisions"), they did the math.

They found a tiny difference between the matter and antimatter decays:

• The Result: The asymmetry is 1.86%.
• The Uncertainty: They aren't 100% sure yet because the number is small. The "error bars" (the margin of doubt) are about 1.04%.

What does this mean?

• The result is compatible with zero. This means the universe might still be fair for this specific particle, or the unfairness is just too small to see clearly yet.
• However, this is the most precise measurement ever made of this specific quantity by a single experiment.
• It's like measuring the weight of a feather with a scale that is accurate to within a milligram. Even if the feather weighs nothing, you now know your scale is incredibly good.

Why Does This Matter?

The Standard Model (our current best theory of physics) predicts that CP violation in charm particles should be very small, but it's hard to calculate exactly how small.

• If the number is exactly zero: It confirms our current theories are working perfectly.
• If the number is bigger than expected: It's a smoking gun! It would mean there is "New Physics" hiding in the shadows—particles or forces we don't know about yet that are tipping the scales.

The Takeaway

This paper is a triumph of engineering and patience. The LHCb team upgraded their camera to catch rare events, built a clever mathematical trick to cancel out their own biases, and took the most precise "coin flip" measurement of its kind to date.

While they didn't find a massive new discovery in this specific run, they have sharpened their tools to a razor's edge. Now, when they look at the next batch of data, they will be able to see if the universe is truly fair, or if it's secretly favoring one side all along.

Technical Summary

1. Problem and Motivation

The primary objective of this work is to measure the time-integrated CP asymmetry ($A_{CP}$) in the decay of neutral D mesons into two neutral Kaons: $D^0 \to K^0_S K^0_S$.

• Context: CP violation has been observed in the charm sector, specifically in the difference between $D^0 \to K^+K^-$ and $D^0 \to \pi^+\pi^-$ decays. However, theoretical predictions for CP asymmetry in charm decays within the Standard Model (SM) are plagued by large uncertainties, making it difficult to distinguish SM effects from potential New Physics (NP).
• Specific Channel: The $D^0 \to K^0_S K^0_S$ mode is a Cabibbo-suppressed decay. Unlike the two-body charged modes, this decay proceeds only via tree-level exchange (vanishing in the flavor-SU(3) limit) and electroweak loops. Consequently, theoretical models predict that $A_{CP}(K^0_S K^0_S)$ could be significantly larger (up to the percent level) than in other channels, making it a sensitive probe for CP violation.
• Challenge: Previous measurements have been limited by the small branching fraction of the decay and the difficulty of reconstructing $K^0_S$ mesons (which have long lifetimes and decay into $\pi^+\pi^-$). The world average prior to this work was at the sub-percent level but with limited precision.

2. Methodology

Data Sample and Detector:

• Dataset: The analysis uses proton-proton collision data collected by the LHCb detector in 2024 (Run 3) at a center-of-mass energy of 13.6 TeV.
• Luminosity: The integrated luminosity is 6.2 fb$^{-1}$.
• Detector Upgrades: A key feature of this measurement is the use of the upgraded LHCb detector, which features an all-software trigger system. Crucially, the new trigger allows for the selection of $K^0_S$ candidates directly at the first-level trigger (HLT1), improving signal efficiency by a factor of three compared to previous runs.

Event Selection and Reconstruction:

• Signal: $D^0 \to K^0_S K^0_S$ candidates are reconstructed via the $K^0_S \to \pi^+\pi^-$ decay.
• Flavor Tagging: To determine the initial flavor of the $D^0$ meson, the analysis selects $D^0$ mesons produced in $D^{*+} \to D^0 \pi^+$ decays. The charge of the "tagging pion" ($\pi^+$) identifies the $D^0$ flavor.
• Calibration Channel: To cancel residual production and detection asymmetries (which arise from detector geometry and hadronization), the analysis uses a calibration sample of $D^0 \to K^0_S \pi^+ \pi^-$ decays. This channel has the same final-state particles as the signal but a negligible intrinsic CP asymmetry.
• Background Suppression:
  • A multivariate classifier (k-nearest-neighbours, kNN) is used to separate signal from combinatorial background.
  • Candidates are split into high-purity ($S/B \sim 20$) and low-purity ($S/B \sim 4$) samples to optimize sensitivity.
  • Specific cuts on flight distance significance and impact parameters are applied to suppress contamination from $D^0 \to K^0_S \pi^+ \pi^-$ and other background processes.

Correction of Nuisance Asymmetries:

• Weighting Scheme: The core of the analysis involves weighting signal candidates based on the kinematics of the tagging pion. Weights ($w_\pm$) are derived from the calibration sample to correct for production and detection asymmetries.
• Charge Symmetrization: Since the calibration channel ($D^0 \to K^0_S \pi^+ \pi^-$) is not self-conjugate and proceeds through intermediate resonances (like $K^{*-}$), the momentum distribution of pions is charge-asymmetric. To prevent detector response differences from biasing the result, the analysis applies a charge-symmetrization procedure to the calibration sample's pion momenta before calculating the weights.

Statistical Analysis:

• A binned maximum-likelihood fit is performed on the joint distribution of the mass difference $\Delta m = m(D^{*+}) - m(D^0)$ and the two $K^0_S$ invariant masses.
• The fit is performed separately for $D^0$ and $\bar{D}^0$ candidates across all data blocks and purity bins.
• Systematic uncertainties are evaluated via bootstrapping, varying the kNN parameters, and testing alternative fit models.

3. Key Contributions

1. Run 3 Efficiency: This is the first measurement utilizing the full capabilities of the LHCb Run 3 trigger system, specifically the HLT1 selection of $K^0_S$ candidates, which drastically improved the signal yield.
2. Novel Calibration Strategy: The paper introduces a refined calibration method using $D^0 \to K^0_S \pi^+ \pi^-$ with a specific charge-symmetrization correction for the pion kinematics, addressing a limitation of previous self-conjugate calibration channels.
3. Precision: The analysis achieves the most precise single-experiment determination of $A_{CP}(D^0 \to K^0_S K^0_S)$ to date.

4. Results

• Measured Asymmetry: The time-integrated CP asymmetry is measured to be:
  $$A_{CP}(D^0 \to K^0_S K^0_S) = (1.86 \pm 1.04 \text{ (stat)} \pm 0.41 \text{ (syst)})\%$$
• Significance: The result is compatible with CP symmetry (zero asymmetry) within approximately $1.8\sigma$. It is also compatible with the world average of previous measurements.
• Systematic Uncertainties: The dominant systematic uncertainties arise from the calibration sample size (0.24%), the weighting procedure (0.20%), and the fit model choice (0.27%).
• Combined Result: When combined with previous LHCb measurements, the world average for LHCb becomes $A_{CP} = (-0.37 \pm 0.78 \pm 0.29)\%$.

5. Significance

• Theoretical Discrimination: While the result does not currently show a statistically significant deviation from the SM, the improved precision (reaching the sub-percent level) is crucial. It constrains theoretical models that predict large CP violation in the charm sector, helping to discriminate between competing approaches (e.g., those involving long-distance effects vs. short-distance New Physics).
• Benchmark for Run 3: This paper demonstrates the effectiveness of the LHCb Run 3 upgrades, particularly the software trigger, in measuring rare charm decays with high precision.
• Future Prospects: The methodology established here, particularly the handling of non-self-conjugate calibration channels and the use of high-purity/low-purity splitting, sets a standard for future high-precision CP violation measurements in the charm sector at the LHC.

In summary, this paper represents a significant step forward in the experimental characterization of CP violation in charm physics, providing the most precise single measurement of the $D^0 \to K^0_S K^0_S$ asymmetry and validating the capabilities of the upgraded LHCb detector.