Measurement of CP asymmetries in $\kern 0.18em\overline{\kern -0.18em B}^0 \to D_s^- D^+$ and $\kern 0.18em\overline{\kern -0.18em B}_s^0 \to D_s^+ D^-$ decays

Using 9 fb$^{-1}$ of proton-proton collision data from the LHCb experiment, this paper presents the first measurement of the CP asymmetry in $\kern 0.18em\overline{\kern -0.18em B}_s^0 \to D_s^+ D^-$ decays and the most precise measurement to date for $\kern 0.18em\overline{\kern -0.18em B}^0 \to D_s^- D^+$ decays, with both results being consistent with CP symmetry.

The Gist

Imagine the universe as a giant, high-speed racetrack where particles zoom around at nearly the speed of light. At the LHCb experiment (part of the massive CERN lab in Switzerland), scientists are like detectives trying to solve a cosmic mystery: Why does the universe prefer matter over antimatter?

In a perfect, symmetrical world, if you created a particle, you should also create its "anti-twin" (antimatter), and they should behave exactly the same way, just with opposite charges. This is called CP Symmetry. If this symmetry held true perfectly, the Big Bang should have created equal amounts of matter and antimatter, which would have annihilated each other instantly, leaving nothing but light. But here we are, so clearly, something broke that symmetry.

This paper is about the LHCb team measuring a very specific "crack" in that symmetry using two types of heavy particles called B-mesons (specifically $B^0$ and $B^0_s$).

The Cast of Characters

Think of these B-mesons as unstable, heavy "parents" that decay (fall apart) into lighter "children."

• The Parents: $B^0$ and $B^0_s$ mesons.
• The Children: Pairs of "Charm" mesons ($D_s$ and $D$).
• The Mystery: When a parent decays, does it behave exactly the same as its antimatter twin decaying into the opposite children?

The Experiment: A Cosmic Coin Flip

The scientists collected data from 9 "inverse femtobarns" of collisions. To put that in perspective, imagine they watched trillions of these particle collisions happen in the LHC accelerator.

They looked at two specific decay scenarios:

1. Scenario A: A $B^0$ meson decays into a $D^-_s$ and a $D^+$.
2. Scenario B: A $B^0_s$ meson decays into a $D^+_s$ and a $D^-$.

They then compared these to the "mirror image" events where the charges were flipped (antimatter versions). They counted how many times each happened.

The Analogy: The Biased Coin

Imagine you have two coins.

• Coin 1 ($B^0$): You flip it 43,000 times. You count how many times it lands on "Heads" (matter decay) vs. "Tails" (antimatter decay).
• Coin 2 ($B^0_s$): You flip it 430 times. You do the same count.

If the universe is perfectly fair, the coins should land 50/50. If there is a bias (CP violation), one side will come up slightly more often.

The Results: What Did They Find?

1. The "Boring" Coin ($B^0$):
For the first type of decay, the scientists found the coin was perfectly fair.

• Result: The difference between matter and antimatter decays was essentially zero (0.0009).
• Significance: This is the most precise measurement of this specific coin flip ever made. It confirms that for this specific process, the universe plays by the rules of symmetry. It's like checking a coin 43,000 times and finding it's not weighted at all.

2. The "Exciting" Coin ($B^0_s$):
For the second type of decay, this is the first time anyone has ever measured this coin.

• Result: They found a small tilt! The matter version happened about 10% more often than the antimatter version (0.103).
• The Catch: While 10% sounds huge in particle physics, the "wobble" in their measurement (uncertainty) was about 5%. So, while it looks like a bias, it's not statistically strong enough yet to say, "Aha! We found a new law of physics!" It's consistent with the Standard Model's prediction that this coin might be slightly biased, but we need more flips to be sure.

Why Does This Matter?

Think of the Standard Model (our current best theory of physics) as a map.

• The "Boring" result confirms the map is accurate for that region.
• The "Exciting" result is a tiny smudge on the map. It doesn't prove the map is wrong, but it's a place where we might find a hidden path to New Physics (like Dark Matter or extra dimensions) if we look closer.

The "Noise" Problem

One of the hardest parts of this experiment was dealing with "noise."

• The Detector Bias: The LHCb machine itself might be slightly better at catching positive particles than negative ones (like a net with a slightly larger hole on one side).
• The Production Bias: The machine might create more $B^0$ particles than $B^0_s$ particles naturally.

The scientists had to act like master accountants, subtracting all these "machine errors" and "production quirks" to find the true physical difference. They used calibration data (like testing the net with known objects) to ensure their final numbers were clean.

The Bottom Line

This paper is a triumph of precision.

1. They confirmed that one type of B-meson decay is perfectly symmetrical (no surprise, but a very precise check).
2. They took the first-ever measurement of CP asymmetry in the $B^0_s$ decay.
3. They found a hint of asymmetry (10%), but it's not yet "smoking gun" evidence of new physics.

It's like finding a tiny scratch on a perfect mirror. It doesn't mean the mirror is broken, but it tells us exactly where to look if we want to find a crack in the universe's foundation. The LHCb team is now ready to collect even more data to see if that 10% tilt grows into a giant wave of new physics or settles down to a tiny ripple.

Technical Summary

1. Problem and Motivation

The study of CP violation in hadronic $B$ meson decays is a critical test of the Cabibbo–Kobayashi–Maskawa (CKM) paradigm within the Standard Model (SM) and a sensitive probe for Beyond Standard Model (BSM) physics.

• Physics Context: The decays $B^0 \to D_s^- D^+$ and $B_s^0 \to D_s^+ D^-$ are mediated by $b \to c\bar{c}d$ and $b \to c\bar{c}s$ transitions, respectively. These processes are crucial for determining the CKM angles $\beta$ and $\beta_s$.
• Theoretical Challenge: Precise determination of these angles requires controlling subleading loop-level contributions (penguin diagrams) to the decay amplitudes. Time-integrated CP asymmetry measurements in these specific channels provide constraints on these loop contributions.
• The Gap: Prior to this work, the CP asymmetry for $B^0 \to D_s^- D^+$ had only been measured with limited precision by the Belle collaboration ($-0.01 \pm 0.02$), and the asymmetry for $B_s^0 \to D_s^+ D^-$ had never been measured. Theoretical predictions suggest the $B^0$ asymmetry is very small, while the $B_s^0$ asymmetry could be as large as 18%.

2. Methodology

The analysis utilizes proton-proton collision data collected by the LHCb experiment at center-of-mass energies of $\sqrt{s} = 7, 8,$ and $13$ TeV, corresponding to a total integrated luminosity of 9 fb$^{-1}$.

Data Selection and Reconstruction

• Decay Channels: Both charm mesons are reconstructed in charged three-body Cabibbo-favored decays:
  • $D_s^- \to K^- K^+ \pi^-$
  • $D^+ \to K^- \pi^+ \pi^+$
• Candidate Selection: A multivariate classifier (Multilayer Perceptron, MLP) trained on simulated signal events and data sidebands is used to suppress combinatorial background. The selection retains ~80% of the signal while removing >90% of the background.
• Yields: The fit to the invariant mass distributions yields:
  • $N(B^0 \to D_s^- D^+) = (43.0 \pm 0.2) \times 10^3$
  • $N(B_s^0 \to D_s^+ D^-) = (0.43 \pm 0.02) \times 10^3$

Asymmetry Measurement Framework

The raw asymmetry ($A_{raw}$) is measured and corrected for detection and production asymmetries to extract the physical CP asymmetry ($A_{CP}$):
$$A_{raw} = A_{CP} + A_{det} + A_{prod}$$

• Raw Asymmetry ($A_{raw}$): Calculated from the difference in yields of particle and antiparticle decays.
• Detection Asymmetry ($A_{det}$): Arises from charge-dependent efficiencies in tracking, particle identification (PID), and triggering.
  • Decomposed into tracking ($A_{K\pi}$), PID ($A_{PID}$), and trigger ($A_{trigger}$) components.
  • Calibrated using control samples: $D^+ \to K^- \pi^+ \pi^+$, $D^+ \to K_S^0 \pi^+$, and $D^{*+} \to D^0(K^- \pi^+)\pi^+$.
  • Key values: $A_{K\pi} = -0.0126 \pm 0.0019$, $A_{PID} = 0.0003 \pm 0.0011$, $A_{trigger} = 0.0002 \pm 0.0017$.
• Production Asymmetry ($A_{prod}$):
  • For $B_s^0$, the effective production asymmetry is negligible due to rapid oscillation relative to its lifetime.
  • For $B^0$, the production asymmetry is measured using $B^0 \to J/\psi K^{*0}$ decays and corrected for oscillation dilution ($\kappa = 0.449$). The resulting effective asymmetry is $A_{prod}(B^0) = 0.0011 \pm 0.0007$.

Statistical Analysis

A binned maximum-likelihood fit is performed simultaneously on the invariant mass distributions ($m(D_s^\mp D^\pm)$) for both decay modes. The signal shape is modeled by a bifurcated Gaussian with asymmetric tails, while background is modeled by an exponential distribution. Partially reconstructed decays (e.g., $B^0 \to D_s^{*-} D^+$) are included as separate components.

3. Key Contributions

1. First Measurement of $A_{CP}(B_s^0 \to D_s^+ D^-)$: This paper presents the world's first measurement of the CP asymmetry in the $B_s^0 \to D_s^+ D^-$ channel.
2. Precision Improvement: The measurement of $A_{CP}(B^0 \to D_s^- D^+)$ improves the precision of the existing world best measurement (from Belle) by a factor of more than three.
3. Comprehensive Systematic Control: The analysis meticulously accounts for charge-dependent detection biases using multiple calibration channels and kinematic reweighting techniques (Gradient Boosted Reweighting) to match signal and calibration kinematics.
4. Global Consistency Checks: The analysis was repeated across independent data subsets (magnet polarity, collision energy, trigger categories) to ensure the robustness of the corrections and the stability of the results.

4. Results

The measured time-integrated CP asymmetries are:

• $B^0 \to D_s^- D^+$:
  $$A_{CP} = 0.0009 \pm 0.0053 \text{ (stat)} \pm 0.0040 \text{ (syst)}$$
• $B_s^0 \to D_s^+ D^-$:
  $$A_{CP} = 0.103 \pm 0.053 \text{ (stat)} \pm 0.010 \text{ (syst)}$$

Observations:

• Both measurements are consistent with CP symmetry (zero asymmetry) within approximately 2 standard deviations.
• The $B_s^0$ result, while showing a central value of 0.103, is not statistically significant enough to claim a discovery of CP violation, but it provides the first constraint on this parameter.
• The correlation between the two measurements is negligible ($-0.0023$).

5. Significance

• Standard Model Validation: The results are consistent with SM predictions, reinforcing the current understanding of CP violation in the $b \to c\bar{c}q$ sector.
• BSM Constraints: By providing precise measurements of these asymmetries, the results significantly constrain global fits of $B \to DD$ decays. This helps in isolating potential contributions from new physics models (such as those involving supersymmetry or extra generations of quarks) that might alter the loop-level amplitudes.
• Future Physics: These measurements serve as essential inputs for the global determination of CKM parameters and will be crucial for future high-precision tests of the SM at the High-Luminosity LHC.

In conclusion, this paper establishes a new benchmark for CP violation measurements in $B \to D_s D$ decays, offering the most precise determination to date for the $B^0$ mode and the inaugural measurement for the $B_s^0$ mode, all while demonstrating the LHCb experiment's capability to control systematic uncertainties at the sub-percent level.