Quantum correlation of neutral charmed mesons at BESIII

This paper reports new measurements of strong-phase differences in neutral $D$ meson decays using BESIII's large $20\text{ fb}^{-1}$ dataset near the $\psi(3770)$ threshold, alongside the first observation of correlated $D\bar{D}$ pairs above this threshold, which enables novel techniques for determining strong phases essential for CP violation studies.

The Gist

Imagine a particle physics experiment as a giant, high-speed dance hall. In this hall, the BESIII detector (a massive, high-tech camera system) watches as electrons and positrons (tiny particles of matter and antimatter) crash into each other. When they collide, they create pairs of "charmed mesons," which are short-lived particles that immediately decay into other particles.

The paper by Alex Gilman and the BESIII collaboration describes two major discoveries made in this dance hall, focusing on how these particles behave when they are born together.

1. The "Mirror Dance" at the Threshold

The first part of the study looks at collisions happening at a very specific energy level, called the $\psi(3770)$ threshold. Think of this as a dance floor where the music is so specific that the dancers (the charmed mesons) are forced to move in a very strict, synchronized pattern.

• The Rule: Because of the laws of physics (specifically something called "charge conjugation"), these two particles are born in a quantum entangled state. They are like a pair of dancers who must always do the opposite of each other. If one spins left, the other must spin right. If one decays into a specific set of particles, the other is constrained to decay in a way that balances the first one out.
• The Problem: Scientists want to know the "strong phase" of these decays. In everyday terms, imagine two dancers performing a routine. The "strong phase" is the exact timing difference between their moves. If they are perfectly in sync, the timing is 0. If one is slightly ahead or behind, the timing changes. This timing is crucial because it helps scientists solve a bigger mystery: Why does the universe have more matter than antimatter? (This is known as CP violation).
• The New Data: The team collected a massive amount of data (20.3 "inverse femtobarns," which is like recording 20 years of high-definition video of these dances). This is five times more data than they had before.
• The Result: By watching thousands of these "mirror dances," they were able to measure the timing differences (strong phases) for various decay routines, including a complex four-particle routine ($D \to K^+K^-\pi^+\pi^-$). They found the exact "beat" of these decays, which helps other scientists (like those at the LHCb experiment) calculate the "CKM angle gamma," a key number in understanding the universe's matter-antimatter imbalance.

2. The "Surprise Dance" Above the Threshold

The second, more surprising discovery happened at higher energy levels (above 4.13 GeV). Usually, when you turn up the volume (energy) in a dance hall, you expect the dancers to move differently, but you don't expect them to suddenly change their synchronization rules.

• The Expectation: At these higher energies, the collisions produce not just simple pairs, but pairs accompanied by extra particles (like a photon or a pion). Scientists thought that because of these extra guests, the strict "opposite dance" rule might break down, or at least become messy.
• The Discovery: The team observed that even with these extra guests, the pairs still danced in a synchronized, quantum-correlated way. In fact, they found that some of these new processes forced the dancers to move in a different kind of synchronization (a "C-even" state) compared to the "C-odd" state seen at the lower energy threshold.
• The Analogy: Imagine you usually see two dancers who always do opposite moves. Suddenly, you see a new routine where they are forced to do the same move at the same time, but only because a specific third person (an extra particle) joined the dance. The paper confirms this "same-move" synchronization exists for the first time in these specific high-energy collisions.
• Why it Matters: This new type of synchronization acts like a different kind of microscope. It allows scientists to measure the timing differences (strong phases) of the decays in a completely new way. The team used this to measure the timing difference for a specific decay ($D \to K\pi$) and found it matched their previous measurements, proving the new method works.

Summary of the Impact

Think of the "strong phase" as the secret code that unlocks the door to understanding why our universe exists as it does.

• Before: Scientists had a few keys (data points) to try to open the door.
• Now: With this new paper, they have a whole new keyring. They have:
  1. Measured the timing of complex dances with much higher precision.
  2. Discovered a new way to watch the dancers (using higher energy collisions) that confirms the rules of the dance hall are even more robust than thought.

The paper concludes that with this massive new dataset, the "timing" of these particle decays will no longer be the bottleneck holding back our understanding of the universe's fundamental secrets. They have provided the precise measurements needed for other experiments to finish the puzzle.

Technical Summary

Technical Summary: Quantum Correlation of Neutral Charmed Mesons at BESIII

Problem and Motivation
Neutral $D^0\bar{D}^0$ pairs produced at the $\psi(3770)$ resonance in $e^+e^-$ collisions exist in a $C$-odd correlated state due to charge-conjugation conservation. This quantum entanglement creates a unique laboratory for measuring strong-phase differences between $D^0$ and $\bar{D}^0$ decays to specific final states. These strong-phase parameters are critical inputs for determining the CKM angle $\gamma$ (via $B^\pm \to D K^\pm$ decays) and for understanding neutral-charm meson mixing. While previous measurements have been limited by statistics, the BESIII experiment has recently accumulated a significantly larger dataset to improve the precision of these hadronic parameters. Furthermore, the existence of quantum correlations in $D\bar{D}$ pairs produced above the $\psi(3770)$ threshold (involving processes like $e^+e^- \to D^*D$ and $D^*D^*$) had not been experimentally verified, despite theoretical predictions that such states could exhibit both $C$-odd and $C$-even correlations.

Methodology
The analysis utilizes two primary datasets collected by the BESIII detector at the BEPCII collider:

1. Threshold Data: A sample of 20.3 fb$^{-1}$ collected at the $\psi(3770)$ resonance (including 17.4 fb$^{-1}$ from 2022–2024 and 2.9 fb$^{-1}$ from 2011).
2. Above-Threshold Data: A sample of 7.3 fb$^{-1}$ collected at center-of-mass energies between 4.13 and 4.23 GeV.

The methodology relies on "tagging" techniques where one $D$ meson in the pair is reconstructed in a specific decay mode (the tag), and the properties of the recoiling $D$ meson are studied. The analysis categorizes tags into flavor/quasi-flavor, CP/quasi-CP, and indefinite modes. For multi-body decays like $D^0 \to K^+K^-\pi^+\pi^-$, the phase space is coarse-grained into bins to define effective amplitude ratios ($r_D$) and strong phases ($\delta_D$), or alternatively, using $c_i$ and $s_i$ parameters defined by integrals over the phase space.

For the above-threshold analysis, the study examines five specific production mechanisms ($D\bar{D}$, $D^*D \to \gamma D\bar{D}$, $D^*D \to \pi^0 D\bar{D}$, $D^*D^* \to \gamma \pi^0 D\bar{D}$, and $D^*D^* \to \gamma\gamma/\pi^0\pi^0 D\bar{D}$) to test for $C$-definite correlations. Yields are determined via fits to the beam-constrained mass ($M_{BC}$) for fully reconstructed events and missing mass squared ($M^2_{miss}$) for partially reconstructed events.

Key Contributions and Results

• Strong-Phase Measurements in $D^0 \to K^+K^-\pi^+\pi^-$:
  Using the full 20.3 fb$^{-1}$ dataset, the collaboration performed the first measurement of $c_i$ and $s_i$ parameters in regions of the $D^0 \to K^+K^-\pi^+\pi^-$ phase space optimized for sensitivity to the CKM angle $\gamma$. The analysis also provided an updated measurement of the CP-even fraction ($F_+$) for this decay.

  • Result: $F_+ = 0.754 \pm 0.010 \text{ (stat)} \pm 0.008 \text{ (syst)}$.
  • Result: Branching fraction $\mathcal{B}(D^0 \to K^+K^-\pi^+\pi^-) = (2.863 \pm 0.028 \pm 0.045) \times 10^{-3}$.
  • These results have already been utilized by the LHCb collaboration to determine the CKM angle $\gamma$.

• First Observation of Above-Threshold Correlations:
  The paper reports the first experimental observation of correlated $D\bar{D}$ pairs produced at energies above the $\psi(3770)$ threshold. The analysis confirmed the presence of quantum correlations in five distinct production mechanisms, distinguishing between $C$-odd and $C$-even states.

  • Result: The corrected yields of $D\bar{D}$ final states in these channels were found to deviate significantly from uncorrelated expectations, matching the predictions for quantum correlations.

• Measurement of the $K\pi$ Strong Phase ($\delta_{K\pi}$):
  Using the above-threshold data, the collaboration analyzed $D\bar{D} \to K^\mp\pi^\pm$ vs. $Y$ decays (where $Y$ is a CP eigenstate) to determine the strong phase difference between $D^0 \to K^-\pi^+$ and $\bar{D}^0 \to K^-\pi^+$.

  • Result: \delta_{K\pi} = 192.8^{+11.0+1.9}_{-12.4-2.4}^\circ (stat+syst).
  • This was combined with the $\psi(3770)$ resonance measurement to yield a world-average-like result of $\delta_{K\pi} = (189.2^{+6.9+3.4}_{-7.4-3.8})^\circ$. The mixed $C$-even and $C$-odd sample provided robust control over systematic uncertainties.

Significance
The paper claims that these results represent a significant step forward in the precision of strong-phase measurements, which are essential for reducing uncertainties in the determination of the CKM angle $\gamma$ and charm-mixing parameters. Specifically:

1. The large 20.3 fb$^{-1}$ dataset allows for significantly increased precision on strong-phase parameters, with future results expected to ensure that strong-phase uncertainties no longer limit the knowledge of $\gamma$ or mixing parameters.
2. The observation of $C$-even correlations above threshold opens new measurement techniques using previously unused datasets.
3. The demonstration of $C$-even correlations is particularly significant for the study of neutral charm meson mixing, as $C$-even pairs are theoretically more sensitive to mixing effects than $C$-odd pairs. The paper notes that sensitivity to charm-mixing parameters at a proposed Super-Tau Charm facility, utilizing similar $C$-even correlations, is estimated to reach current world-average levels.