Measurement of the branching fraction of $D_{s}^{*+}\to e^{+}e^{-}D_{s}^{+}$

Using 7.33 fb⁻¹ of $e^{+}e^{-}$ collision data collected by the BESIII experiment, the paper reports a measurement of the branching fraction for the electromagnetic Dalitz decay $D_{s}^{*+}\to e^{+}e^{-}D_{s}^{+}$ as $(7.28\pm0.61_{\mathrm{stat}}\pm0.31_{\mathrm{syst}})\times10^{-3}$, achieving a 2.5-fold improvement in precision over previous results and providing crucial constraints for theoretical models and related absolute branching fractions.

The Gist

Imagine the subatomic world as a bustling, high-speed dance floor where particles are constantly pairing up, spinning, and sometimes breaking apart. In this paper, a massive team of scientists (the BESIII Collaboration) acts like a group of ultra-observant bouncers and photographers, trying to catch a very specific, rare dance move performed by a particle called the $D^*_s$ meson.

Here is the story of what they found, explained simply:

The Main Event: A Rare "Split"

Usually, when a heavy particle like the $D^*_s$ meson decays (breaks down), it might shoot out a photon (a particle of light) or a pion (a lighter particle). But the scientists were looking for something much more unusual: a process where the $D^*_s$ meson splits into a regular $D_s$ meson and a pair of electrons (one positive, one negative) that fly off together.

Think of it like this: Imagine a spinning top (the $D^*_s$) that suddenly slows down and releases a smaller, slower top (the $D_s$) while simultaneously shooting out a tiny, glowing firework (the electron-positron pair). This specific "firework" event is called an electromagnetic Dalitz decay. It's a rare occurrence, happening only about 7 times out of every 1,000 times this particle decays.

The Detective Work: The "Tagging" Technique

The problem is that these particles live for a split second and are created in a chaotic environment where billions of other things are happening. To find this rare event, the scientists used a clever trick called "tagging."

Imagine you are at a crowded party, and you are looking for a specific person (the signal). Instead of scanning the whole crowd, you ask a friend to stand next to that person and hold a bright sign (the "tag").

1. The Tag: The scientists first looked for the "sibling" of the particle they were studying. They found a $D_s$ meson that was created alongside the $D^*_s$.
2. The Signal: Once they found that sibling, they knew exactly where to look for the rare decay. They checked if the partner particle had performed that special "firework" split (turning into an electron pair).

By using this "tagging" method, they could ignore the noise of the rest of the party and focus entirely on the specific couples they were interested in.

The Data: A Massive Dataset

The team used a giant particle collider (the BEPCII) to smash electrons and positrons together. They collected a massive amount of data—equivalent to 7.33 "inverse femtobarns" (a unit of data volume in particle physics). To put that in perspective, it's like watching millions of hours of high-definition particle collisions to find just a few hundred of these specific rare events.

They analyzed data from eight different energy settings, like tuning a radio to different frequencies to make sure they didn't miss the signal.

The Result: A Sharper Picture

After crunching the numbers and filtering out the background noise, the team calculated the "branching fraction." In simple terms, this is the probability of this specific event happening.

• Their Finding: They found that this rare decay happens 7.28 times out of every 1,000 decays.
• The Improvement: A previous experiment (CLEO-c) had guessed this number, but with a wide margin of error (like guessing a distance is "between 5 and 10 miles"). This new measurement is much sharper (like saying "it's 7.3 miles, give or take a tiny bit"). They improved the precision by 2.5 times.

Why Does This Matter?

The paper explains that this measurement is like a crucial piece of a puzzle for theoretical physicists.

• Testing Models: Scientists have mathematical models (like the Vector Meson Dominance model) that try to predict how particles interact with light. This new, precise number helps them check if their models are correct.
• Calibrating Other Measurements: Because this decay is so well-understood theoretically, measuring it precisely helps scientists figure out the rates of other decays that are harder to measure directly. It acts as a "ruler" to measure the size of other things.

The Bottom Line

The BESIII team successfully caught a rare glimpse of a subatomic particle performing a unique dance move. By using a clever "tagging" strategy and analyzing a huge amount of data, they measured the frequency of this event with much greater accuracy than ever before. This doesn't change how we live our daily lives, but it helps the scientists who study the fundamental building blocks of the universe refine their understanding of how matter and light interact.

Technical Summary

Technical Summary: Measurement of the Branching Fraction of $D^*_s \to e^+e^- D_s$

Problem and Motivation
The paper addresses the measurement of the branching fraction for the electromagnetic (EM) Dalitz decay $D^*_s \to e^+e^- D_s$. This process, where a vector meson ($V$) decays into a pseudoscalar meson ($P$) and a lepton pair via a virtual photon ($V \to \gamma^* P \to l\bar{l}P$), serves as a stringent test for theoretical models of hadron structure and the interaction mechanism between photons and hadrons. Specifically, these measurements allow for the exploration of charmed meson structures and the testing of chiral perturbation theory in the flavor sector.

While EM Dalitz decays of light vector mesons (e.g., $\omega, \phi$) and charmonia (e.g., $J/\psi, \psi(3686)$) have been studied extensively, measurements involving charmed mesons remain limited. Previous measurements of $D^*_s \to e^+e^- D_s$ by the CLEO-c experiment and the BESIII experiment provided initial data, but with limited precision. The branching fraction of this decay is a critical input for constraining theoretical parameters (such as those in the Vector Meson Dominance model) and for determining the absolute branching fractions of $D^*_s \to \pi^0 D_s$ and $D^*_s \to \gamma D_s$ when relative normalization methods are employed.

Methodology
The analysis utilizes an electron-positron collision data sample collected by the BESIII detector at the BEPCII storage ring. The data corresponds to center-of-mass energies ($\sqrt{s}$) ranging from 4.128 GeV to 4.226 GeV, near the $D^*_s D_s$ production threshold, with a total integrated luminosity of 7.33 fb$^{-1}$.

The measurement employs a "tagging" technique to reconstruct the $e^+e^- \to D^*_s D_s$ events:

1. Tagging: One $D_s$ meson (the "tag") is fully reconstructed using 11 specific decay modes with large branching fractions (e.g., $K^0_S K^\pm$, $K^+K^-\pi^\pm$, $\pi^\pm \eta$). The recoil mass against this tag is used to identify the presence of the partner $D^*_s$.
2. Signal Selection: The signal $D^*_s \to e^+e^- D_s$ is identified by reconstructing the remaining $e^+e^-$ pair and the associated $D_s$ meson (either the daughter or the bachelor particle relative to the tag).
3. Kinematic Constraints: To suppress backgrounds from misidentified pions/kaons and photon conversions, strict particle identification (PID) criteria are applied using the Time-of-Flight (TOF) and drift chamber (MDC) $dE/dx$ information. Photon conversions are rejected by calculating the distance between the interaction point and the conversion vertex.
4. Yield Extraction: The signal yields are extracted via a simultaneous unbinned maximum likelihood fit to the invariant mass distributions of the $e^+e^- D_s$ system. The analysis distinguishes between cases where the tagged $D_s$ is the daughter of the $D^*_s$ decay and cases where it is the bachelor particle. The eleven tag modes are grouped into five categories based on their signal-to-background ratios to optimize the fit.

Key Contributions and Results
The primary contribution of this work is a precise measurement of the branching fraction for the decay $D^*_s \to e^+e^- D_s$. The analysis yields:
$$\mathcal{B}(D^*_s \to e^+e^- D_s) = (7.28 \pm 0.61_{\text{stat}} \pm 0.31_{\text{syst}}) \times 10^{-3}$$

Key aspects of the result include:

• Precision: The measurement represents a 2.5-fold improvement in precision compared to the previous BESIII result and is consistent with the earlier CLEO-c measurement of $(6.7^{+1.4}_{-1.2} \pm 0.9) \times 10^{-3}$.
• Systematic Uncertainties: The total systematic uncertainty is 4.3%, dominated by contributions from photon conversion rejection (2.8%), tracking of the $e^+e^-$ pair (1.7%), and PID (1.4%).
• Theoretical Comparison: Using the Particle Data Group (PDG) value for $\mathcal{B}(D^*_s \to \gamma D_s) = 0.936 \pm 0.004$, the ratio of the branching fractions $\mathcal{B}(D^*_s \to e^+e^- D_s) / \mathcal{B}(D^*_s \to \gamma D_s)$ is calculated to be $(7.78 \pm 0.73) \times 10^{-3}$. This result is consistent with the theoretical prediction of $6.5 \times 10^{-3}$ (derived from the Vector Meson Dominance model) within 1.8 standard deviations.

Significance
The paper claims that this improved measurement provides a crucial input for constraining the parameters of theoretical models describing the hadron structure and photon-hadron interactions. Furthermore, the result aids in determining the absolute branching fractions of $D^*_s \to \pi^0 D_s$ and $D^*_s \to \gamma D_s$, which are often measured using relative methods. The consistency with the Vector Meson Dominance model, despite the slight tension (1.8$\sigma$), supports the current understanding of these electromagnetic transitions in the charm sector.