Search for the rare decays of $D\to h(h^{(')})e^{+}e^{-}$

Using 20.3 fb$^{-1}$ of $e^+e^-$ collision data collected by the BESIII detector, this study searches for 15 rare $D$ meson decays into hadrons accompanied by an electron-positron pair, setting new upper limits on their branching fractions at the $10^{-6}$ to $10^{-7}$ level, including first-time measurements for five channels and significant improvements for others.

The Gist

Imagine the universe is a giant, bustling cosmic construction site. In the center of this site, there's a special machine called BESIII (part of the BEPCII accelerator in China) that smashes tiny particles together, creating a shower of new particles, much like a high-speed collision of two cars creating a cloud of debris.

The scientists in this paper are like cosmic detectives. Their job is to look through the debris of these collisions to find a very specific, extremely rare type of "accident" that happens when a particle called a D meson falls apart.

The Mystery: The "Forbidden" Breakup

Usually, when a D meson breaks apart, it follows the standard rules of physics (the Standard Model). It might split into a few other common particles. But the detectives are looking for a "ghost" event: a D meson that splits into a hadron (a heavy particle like a pion or kaon) and a pair of electrons (one positive, one negative).

In the language of physics, this is written as $D \to h(h')e^+e^-$.

Why is this a big deal?

• The "Forbidden" Zone: According to our current best theories, this specific breakup is supposed to be incredibly rare. It's like trying to win the lottery twice in a row. The "Standard Model" says it should happen maybe once in a billion tries.
• The New Physics Hope: If the detectives find more of these breakups than expected, it would be a smoking gun! It would mean there are "ghosts in the machine"—new, undiscovered particles or forces (New Physics) helping to make this happen. It's like finding a secret shortcut in a maze that shouldn't exist.

The Investigation: The "Double-Tag" Trick

The problem is that these rare events are so rare, and the "noise" (other common particle breakups) is so loud, that it's hard to spot them. It's like trying to hear a single whisper in a rock concert.

To solve this, the BESIII team uses a clever trick called Double-Tagging (DT).

Imagine you are at a party where everyone comes in pairs.

1. The First Tag: You spot one person from a pair (let's call him "Tag Man") and identify exactly who he is and what he's wearing. Because you know he came in a pair, you know his partner ("Signal Man") must be somewhere nearby.
2. The Second Tag: You look at the rest of the room to find "Signal Man." Since you know exactly who "Tag Man" is, you can calculate exactly how much energy and momentum "Signal Man" should have if he's the real partner.

By using this "Tag Man" method, the scientists can filter out the noise. They ignore the millions of random breakups and only look at the specific cases where the "Signal Man" fits the perfect profile of the rare decay they are hunting.

The Search: 20.3 "Femtobarns" of Data

The team didn't just look at a few collisions; they analyzed a massive amount of data—20.3 inverse femtobarns. To use an analogy, if one femtobarn is like a single grain of sand, they sifted through a mountain of sand to find a specific type of grain.

They looked for 15 different types of these rare breakups. Some involved particles like pions, some involved kaons, and some involved heavier, more complex particles like the $\rho$ (rho) or $\omega$ (omega).

The Verdict: No Ghosts Found (Yet)

After sifting through all that data, the result is: Silence.

• No Significant Signals: They didn't find any "ghosts." The number of rare breakups they saw was exactly what you would expect from background noise and known physics.
• Setting the Limits: Even though they didn't find the "New Physics," they didn't come up empty-handed. They set a speed limit on how often these events could be happening.
  • They said: "If this rare event is happening, it's happening less than once in every 10 million to 100 million tries."
  • For some of the 15 types they looked at, this is the very first time anyone has ever set a limit. For others, they improved the limit by a factor of 4 to 14, making the "searchlight" much brighter and sharper than before.

Why Does This Matter?

Think of the Standard Model as a map of the world. We know most of the continents, but there are blank spots labeled "Here Be Dragons."

• Lepton Flavor Universality: The scientists are also checking if electrons and muons (a heavier cousin of the electron) behave exactly the same way. If they don't, the map is wrong.
• The Future: By proving that these rare events are even rarer than we thought, they are telling theorists: "The dragons aren't here. You need to redraw the map or look in a different direction."

Summary

The BESIII collaboration acted as the ultimate cosmic detectives. They used a massive dataset and a clever "double-tag" strategy to hunt for a ghostly, forbidden particle breakup. They didn't find the ghost, but they successfully proved that if the ghost is real, it's hiding much better than we thought. This tightens the rules of the universe and helps scientists know exactly where not to look, so they can focus their energy on finding the new physics that is there.

Technical Summary

1. Problem and Motivation

The paper addresses the search for rare flavor-changing neutral current (FCNC) decays of $D$ mesons into a hadron (or hadrons) and an electron-positron pair ($D \to h(h')e^+e^-$).

• Standard Model (SM) Context: In the SM, FCNC processes are suppressed by the GIM mechanism and occur only at the loop level. In the charm sector, the absence of a heavy top quark in the loop makes the short-distance (SD) contribution extremely small (branching fractions $\mathcal{B} \sim 10^{-9}$).
• Long-Distance (LD) Effects: The decay rates are dominated by long-distance contributions via intermediate vector meson resonances (e.g., $D \to hV, V \to e^+e^-$ where $V = \rho, \omega, \phi$), yielding branching fractions around $10^{-6}$.
• Physics Goal: These decays serve as clean channels to search for New Physics (NP). Deviations from SM predictions could indicate NP contributions. Furthermore, comparing electron and muon channels tests Lepton Flavor Universality (LFU).
• Previous Status: Previous searches by BESIII (using 2.93 fb$^{-1}$) and other collaborations (LHCb, BABAR, Belle II) had set upper limits, but many channels involving neutral mesons ($\pi^0, \eta, K_S^0$) lacked precise measurements or had not been studied at all.

2. Methodology

The analysis utilizes a Double-Tag (DT) technique, which significantly reduces background and systematic uncertainties compared to single-tag methods.

• Dataset: The study uses 20.3 fb$^{-1}$ of $e^+e^-$ collision data collected at the BESIII detector at the BEPCII collider, corresponding to the center-of-mass energy $\sqrt{s} = 3.773$ GeV (the $\psi(3770)$ resonance).
• Event Reconstruction Strategy:
  1. Single Tag (ST): One $D$ meson in the event is fully reconstructed via hadronic decay modes (e.g., $\bar{D}^0 \to K^+\pi^-$, $D^- \to K^+\pi^-\pi^-$, etc.). This defines the event kinematics and provides the total number of produced $D$ mesons ($N_{tag}$).
  2. Signal Tag: The remaining particles in the event (recoiling against the ST $D$) are used to reconstruct the rare decay $D \to h(h')e^+e^-$.
• Selection Criteria:
  • Particle Identification (PID): Electrons/positrons are identified using a combined likelihood from the MDC, TOF, and EMC, with an $E/p$ ratio requirement.
  • Vertexing: To suppress backgrounds from photon conversions ($\gamma \to e^+e^-$), the $e^+e^-$ pair vertex must be reconstructed outside a cylindrical region ($R_{xy} \in 2.0-8.0$ cm) around the beam pipe.
  • Kinematic Constraints: The beam-constrained mass ($M_{BC}$) and energy difference ($\Delta E$) are calculated for signal candidates.
  • Vetos: Specific vetoes are applied to suppress backgrounds from $\pi^0 \to \gamma e^+e^-$ and $\eta \to \gamma e^+e^-$ by reconstructing missing photons and checking invariant masses.
• Background Estimation:
  • Sideband (SB): Events in the sideband region of the ST $M_{BC}$ distribution are used to estimate backgrounds from incorrectly reconstructed ST candidates.
  • Monte Carlo (MC): Inclusive MC samples are used to estimate backgrounds from mis-reconstructed signal candidates (e.g., $D \to h(h')\pi^+\pi^-$ faking $e^+e^-$).
• Statistical Analysis: A Profile Likelihood method is employed to calculate upper limits (ULs) on branching fractions at the 90% confidence level (CL), incorporating both statistical and systematic uncertainties.

3. Key Contributions

• Dataset Scale: This analysis uses a dataset nearly 7 times larger than the previous BESIII study on similar channels, allowing for significantly improved sensitivity.
• First-Time Measurements: The paper reports the first-ever upper limits for five decay channels:
  • $D^+ \to \rho^+ e^+e^-$
  • $D^+ \to K^{*+} e^+e^-$
  • $D^0 \to K_S^0 K_S^0 e^+e^-$
  • $D^0 \to \pi^0 \pi^0 e^+e^-$
  • $D^0 \to \eta' e^+e^-$
• Improved Limits: For eight other channels (e.g., $D^0 \to \pi^0 e^+e^-$, $D^0 \to \omega e^+e^-$, $D^+ \to \pi^+ \pi^0 e^+e^-$), the upper limits on branching fractions are improved by a factor of 4 to 14 compared to previous PDG values.
• Specific Results:
  • $D^0 \to \rho^0 e^+e^-$: $\mathcal{B} < 0.7 \times 10^{-6}$ (improved from $< 1.0 \times 10^{-5}$).
  • $D^0 \to \phi e^+e^-$: $\mathcal{B} < 4.6 \times 10^{-6}$.

4. Results

• Observation: No significant signals were observed for any of the 15 searched decay channels. The number of observed events ($n_{obs}$) is consistent with the estimated background yields ($n_{bkg}$) derived from sidebands and MC simulations.
• Upper Limits: The 90% CL upper limits on the branching fractions are determined to be in the range of $10^{-6}$ to $10^{-7}$.
  • Example: For $D^+ \to \pi^+ \pi^0 e^+e^-$, the limit is $< 2.4 \times 10^{-6}$.
  • Example: For $D^0 \to \pi^0 e^+e^-$, the limit is $< 0.7 \times 10^{-6}$.
• Systematics: The total systematic uncertainties range from roughly 3.3% to 6.6% for $D^0$ modes and 4.8% to 5.2% for $D^+$ modes. The dominant sources include MC modeling, particle identification, and reconstruction efficiencies for neutral mesons ($\pi^0, \eta, K_S^0$).

5. Significance

• Theoretical Impact: These results provide crucial constraints for theoretical models. The improved limits help disentangle short-distance (NP-sensitive) contributions from long-distance (resonant) effects, which are currently difficult to calculate precisely.
• New Physics Search: By pushing the sensitivity to the $10^{-7}$ level, the analysis tightens the constraints on potential New Physics contributions to charm FCNC processes.
• Lepton Flavor Universality: The results complement existing muon-channel measurements (e.g., from LHCb), providing a necessary dataset to test LFU in the charm sector.
• Experimental Benchmark: The study demonstrates the power of the Double-Tag method with large datasets at the $\psi(3770)$ resonance for studying rare decays involving neutral particles, setting a new standard for precision in charm physics.