Search for the radiative decay $D^+_s \to γK^*(892)^+$

Using 7.33 fb$^{-1}$ of $e^+e^-$ collision data collected by the BESIII detector, this study reports the first search for the radiative decay $D_s^+\to\gamma K^*(892)^+$, finding no significant signal and setting an upper limit on its branching fraction of $2.3\times10^{-4}$ at the 90% confidence level.

The Gist

Imagine the universe as a giant, high-speed racetrack where tiny particles called "charm mesons" (specifically the $D_s^+$) zoom around at nearly the speed of light. Physicists at the BESIII detector in China act like ultra-fast photographers, trying to catch these particles in the act of doing something very specific and rare: spitting out a flash of light (a photon) while changing into a different particle.

Here is a breakdown of what the paper does, using everyday analogies:

The Big Picture: The "Ghostly" Transformation

The scientists were looking for a specific event: A $D_s^+$ meson turning into a $K^*$ meson (a different type of particle) and a photon ($\gamma$).

• The Analogy: Imagine a magician (the $D_s^+$) who suddenly transforms into a rabbit ($K^*$) and a flash of light.
• Why it's hard: In the world of particle physics, this kind of transformation is supposed to be very rare. It's like trying to find a specific needle in a haystack, but the needle is made of light and the haystack is made of billions of other particles crashing into each other.

The Setup: The "Double-Tag" Strategy

To find this rare event, the team used a clever trick called the "Double-Tag" method.

• The Analogy: Imagine you are at a crowded party where couples are dancing. You want to find a specific couple where the man suddenly disappears and leaves a glowing balloon behind.
  1. Single Tag (The Woman): First, you spot the woman (the $D_s^-$ partner) and confirm exactly who she is by looking at what she is holding (her decay products). Once you identify her, you know her partner must be the man you are looking for, because they were created together.
  2. Double Tag (The Man): Now, you look at the empty space where the man should be. You check if he turned into the specific rabbit and the glowing balloon you were hoping for.
• The Benefit: By confirming the partner first, you eliminate a lot of the "noise" from the crowd. You know exactly what the missing piece should look like, making it much easier to spot if it actually happened.

The Search: Sifting Through the Noise

The team analyzed 7.33 fb⁻¹ of data.

• The Analogy: This is like watching 7.33 million hours of high-definition security footage from the particle collider.
• The Process: They used powerful computers to filter out the billions of "boring" crashes and focus only on the events where the "woman" (the tagged particle) was identified correctly. Then, they looked at the "man's" side to see if the "rabbit and balloon" (the $K^*$ and photon) appeared.

The Result: The "Silent" Room

After all that searching, the result was quiet.

• The Finding: They did not find the specific transformation they were looking for. The "rabbit and balloon" never appeared in the way they predicted.
• The Conclusion: It's not that the event is impossible; it just means it happens less often than the most optimistic theories suggested.
• The Limit: Because they didn't see it, they set a "speed limit" on how often it could be happening. They calculated that if this event happens at all, it occurs less than 2.3 times out of every 10,000 attempts. (In scientific terms, the "branching fraction" is less than $2.3 \times 10^{-4}$).

Why This Matters

The paper compares their "speed limit" to what different math models (theories) predicted.

• The Comparison: Some theories said, "It happens 1 to 10 times out of 10,000." Others said, "It happens 0.1 to 0.5 times."
• The Verdict: The new limit (less than 2.3) is higher than the most optimistic predictions but lower than the most pessimistic ones. It's like saying, "We looked for a unicorn, didn't find one, but we know for sure that if unicorns exist, they are rarer than we thought."
• The Outcome: None of the current theories are proven wrong yet, but the scientists have narrowed down the search area. It's a "null result" that helps refine the map of how the universe works.

Summary

The BESIII team took a massive snapshot of particle collisions, used a clever "partner-checking" technique to isolate specific events, and looked for a rare light-emitting transformation. They didn't find it, but they successfully proved that if it does happen, it is extremely rare—helping physicists rule out some of the more optimistic guesses about how these particles behave.

Technical Summary

Technical Summary: Search for the Radiative Decay $D_s^+ \to \gamma K^*(892)^+$

Problem and Motivation
This work addresses the experimental measurement of the radiative decay $D_s^+ \to \gamma K^*(892)^+$. In the study of weak radiative decays of charged charmed mesons, short-range interactions are suppressed by the GIM mechanism, yielding inclusive branching fractions (BFs) on the order of $10^{-8}$ from penguin diagrams. Consequently, long-range non-perturbative processes, such as final-state interactions (FSIs) and vector meson dominance (VMD), are expected to dominate, potentially enhancing BFs to the $10^{-4}$ level. While various theoretical models (including hard spectator interaction, weak annihilation, light-cone sum rules, and VMD) predict the BF for this Cabibbo-suppressed process to range between $O(10^{-5})$ and $O(10^{-4})$, the decay $D_s^+ \to \gamma K^*(892)^+$ had not been experimentally measured prior to this study. Previous experiments have measured other radiative charm decays (e.g., $D_s^+ \to \gamma \rho(770)^+$, $D^0 \to \gamma \bar{K}^*(892)^0$), but the specific channel $D_s^+ \to \gamma K^*(892)^+$ remained unobserved.

Methodology
The analysis utilizes $7.33 \text{ fb}^{-1}$ of $e^+e^-$ collision data collected by the BESIII detector at center-of-mass energies ($E_{cm}$) between 4.128 and 4.226 GeV. In this energy region, $D_s^\pm$ mesons are produced predominantly via the process $e^+e^- \to D_s^{*\pm} D_s^{\mp}$.

The analysis employs the double-tag (DT) method:

1. Single Tag (ST): A $D_s^-$ meson is fully reconstructed in one of three hadronic decay modes: $D_s^- \to K_S^0 K^-$, $D_s^- \to K^+ K^- \pi^-$, or $D_s^- \to K_S^0 K^+ \pi^- \pi^-$. The recoil mass ($M_{rec}$) against the ST candidate is required to be consistent with the $D_s^+$ mass.
2. Signal Search: In the system recoiling against the tagged $D_s^-$, the signal decay $D_s^+ \to \gamma K^*(892)^+$ is searched for via two decay chains of the $K^*(892)^+$:
   • $K^*(892)^+ \to K^+ \pi^0$ (with $\pi^0 \to \gamma\gamma$)
   • $K^*(892)^+ \to K_S^0 \pi^+$ (with $K_S^0 \to \pi^+ \pi^-$)

Selection criteria include strict particle identification (PID), kinematic fits for $\pi^0$ and $K_S^0$, and specific mass windows for the $K^*(892)^+$ candidates ($0.83 < M < 0.94 \text{ GeV}/c^2$). To suppress backgrounds involving $\pi^0$ and $\eta$ mesons, cuts are applied on the energy of the radiative photon ($E_\gamma > 0.55 \text{ GeV}$) and on the invariant masses of extra photon pairs ($M_{\gamma\gamma}$).

The branching fraction is calculated using the formula:
$$\mathcal{B}(D_s^+ \to \gamma K^*(892)^+) = \frac{N_{DT}^{total}}{\sum_{\alpha, i} N_{ST}^{\alpha, i} \cdot (\epsilon_{DT}^{\alpha, i} / \epsilon_{ST}^{\alpha, i}) \cdot \mathcal{B}_{sub}}$$
where $N_{DT}$ is the signal yield, $N_{ST}$ is the single-tag yield, $\epsilon$ represents efficiencies, and $\mathcal{B}_{sub}$ accounts for the sub-decay branching fractions. A simultaneous fit is performed on the two-dimensional distribution of the signal invariant mass ($M_{sig}$) versus the helicity angle ($\cos \theta_H$) for both decay channels. The signal shape is modeled using Monte Carlo (MC) simulations convolved with a Gaussian, while backgrounds are modeled using MC-derived shapes and Chebyshev polynomials.

Key Contributions and Results

• First Search: This paper reports the first experimental search for the radiative decay $D_s^+ \to \gamma K^*(892)^+$.
• Signal Observation: No significant signal is observed in the data. The fitted signal yields are $0.2^{+2.0}_{-1.5}$ for the $K^+ \pi^0$ channel and $0.1^{+1.2}_{-1.0}$ for the $K_S^0 \pi^+$ channel.
• Upper Limit: Based on the absence of a signal, an upper limit on the branching fraction is set at the 90% confidence level (CL). The result is:
  $$\mathcal{B}(D_s^+ \to \gamma K^*(892)^+) < 2.3 \times 10^{-4}$$
• Systematic Uncertainties: The analysis includes a comprehensive evaluation of systematic uncertainties, categorized as additive (signal shape modeling, background yields) and multiplicative (tracking, PID, reconstruction efficiencies, MC statistics). The total multiplicative systematic uncertainty is 4.0% for the $K^+ \pi^0$ channel and 2.4% for the $K_S^0 \pi^+$ channel.

Significance
The paper claims that while the obtained upper limit ($2.3 \times 10^{-4}$) is above the range predicted by most theoretical models (which generally predict values between $0.1 \times 10^{-4}$ and $1.4 \times 10^{-4}$), it approaches the upper end of these expectations. Consequently, the result does not exclude any of the existing theoretical models (HSI+WA, LCSR, Hybrid, VMD). The authors note that the data collected by the Belle Collaboration may be sufficient for a similar search, and they suggest that future facilities with larger data samples, such as the Super Tau-Charm Facility and Belle II, will be required to perform more stringent tests of these theoretical predictions.