Dₛ⁺ Radiative Decay: γK*(892)⁺ Insights

• The paper presents the first dedicated search for Dₛ⁺→γK*(892)⁺ decay, setting an upper limit on the branching fraction at 2.3×10⁻⁴ using advanced double-tag techniques.
• It explains how the short-distance c→uγ transition is suppressed by the GIM mechanism while long-distance weak annihilation and VMD effects can enhance the decay rate.
• The study employs rigorous signal extraction and systematic uncertainty analysis, laying the groundwork for future high-luminosity experiments in charm physics.

The radiative decay $D_s^+\to\gamma K^*(892)^+$ is a flavor-changing electromagnetic transition in the charm sector, representing a key probe of Standard Model (SM) processes and their long-distance and short-distance dynamics. This decay arises from $c\to u\gamma$ transitions, with potential enhancements from weak annihilation and vector-meson dominance (VMD) mechanisms. The first dedicated experimental search for $D_s^+\to\gamma K^*(892)^+$ has been performed by the BESIII Collaboration, utilizing a substantial $e^+e^-$ collision dataset and advanced double-tagging techniques to set an upper limit on the branching fraction at the $10^{-4}$ level (Collaboration et al., 23 Jan 2026).

1. Theoretical Framework and Physics Motivation

In the SM, the short-distance $c\to u\gamma$ transition is highly suppressed by Glashow–Iliopoulos–Maiani (GIM) mechanism, yielding a radiative branching ratio from perturbative “penguin” diagrams of only $$\mathcal{B}_{\mathrm{peng}}(D_s^+\to\gamma K^*(892)^+)\sim\mathcal{O}(10^{-8})$$ [Fajfer et al., Eur. Phys. J. C 6 (1999) 471]. However, long-range effects—predominantly from weak annihilation topologies with VMD or final-state rescattering—can enhance the rate by up to four orders of magnitude, leading to SM predictions for $\mathcal{B}(D_s^+\to\gamma K^*(892)^+)$ in the range $\mathcal{O}(10^{-4})$ [Altmannshofer & Archilli (2022), de Boer & Hiller JHEP 08 (2017) 091, Lyon & Zwicky Phys. Rev. D 106 (2022) 053001, Burdman et al. Phys. Rev. D 52 (1995) 6383]. The dominant long-distance mechanism proceeds via a weak annihilation ($c\bar{s}\to u\bar{d}$) followed by emission of a virtual vector meson that converts to a real photon via VMD. Specific model predictions (in units of $10^{-4}$) for $\mathcal{B}$ include:

• HSI+WA: $1.0$–$1.4$ [de Boer–Hiller]
• LCSR: $0.17$ [Lyon–Zwicky]
• Hybrid long-distance: $0.1$–$0.5$ [Fajfer–Singer]
• VMD: $0.1$–$0.3$ [Burdman et al.]

No observation at or above these levels would constrain the non-local hadronic mechanisms in the SM.

2. Experimental Dataset and Detector Description

The search for $D_s^+\to\gamma K^*(892)^+$ exploits an integrated luminosity of $\mathcal{L} = 7.33\,\mathrm{fb}^{-1}$, collected by BESIII at center-of-mass energies of 4.128–4.226 GeV, partitioned into four data groups (4.128/4.157, 4.178, 4.189–4.219, and 4.226 GeV). The BESIII detector features:

• A 1 T solenoidal magnet.
• A multilayer drift chamber (MDC), providing momentum resolution ($\sigma_p/p\approx0.5\%$ at 1 GeV/$c$) and $dE/dx$ for charged particle identification.
• Time-of-flight (TOF) counters, with time resolutions of $\sim68\,\mathrm{ps}$ (barrel) and $\sim110\,\mathrm{ps}$ (endcap).
• A CsI(Tl) electromagnetic calorimeter (EMC), with energy resolution $\sigma_E/E\approx2.5\%$ (barrel) and $5\%$ (endcap) at 1 GeV.
• Muon detection in the instrumented flux return.

These subsystems provide the necessary kinematic and PID information for high-efficiency charm hadron reconstruction.

3. Event Selection and Decay Reconstruction

BESIII employs a double-tag (DT) technique. On the tag side, $D_s^-$ candidates are fully reconstructed via standard hadronic decay modes, using tight vertexing and PID in the MDC and TOF, as well as $K_S^0$ and $\pi^0$ reconstruction with EMC information. The recoil mass against the single-tag $D_s^-$ ensures selection of events consistent with $D_s^\ast D_s$ production:

$$M_{\rm rec} = \sqrt{(E_{\rm cm}-E_{D_s^-})^2 - |\vec{p}_{D_s^-}|^2}$$

requiring $M_{\rm rec}$ to match $m(D_s^*)$ within specific windows.

On the signal side, candidate events require:

• The highest-energy photon in EMC not matched to a track ($E_\gamma>0.55$ GeV).
• $K^*(892)^+$ reconstruction via $K^+\pi^0$ ($M(K^+\pi^0)\in[0.83,0.94]$ GeV/$c^2$) or $K_S^0\pi^+$ ($M(K_S^0\pi^+)\in[0.83,0.94]$ GeV/$c^2$).
• Veto of extra $\pi^0$ or $\eta$ candidates to suppress backgrounds from $D_s^+\to\pi^+\pi^0\eta$ and $D_s^+\to K^+\eta$.

The analysis does not rely on the more common $M_{\rm bc}$ and $\Delta E$ variables, but uses $M_{\rm rec}$ and tag mass.

4. Signal Extraction and Statistical Procedure

A simultaneous unbinned maximum-likelihood fit is performed in the two-dimensional space of $(M_{\rm sig} = M(\gamma K\pi),\,\cos\theta_H)$ for both $K^*$ decay channels, with the isospin-constrained ratio $$\mathcal{B}(K^*\to K_S^0 \pi^+)/\mathcal{B}(K^*\to K^+\pi^0) = 2$$. The total probability density function (PDF) is:

$$\mathcal{P}(M,\cos\theta_H) = N_s\,\mathrm{PDF}_s(M,\cos\theta_H) + N_{b1}\mathrm{PDF}_{D_s^*D_s}(M,\cos\theta_H) + N_{b2}\mathrm{PDF}_{\text{other}}(M,\cos\theta_H)$$

where:

• $\mathrm{PDF}_s$ is derived from MC and convolved with a double-Gaussian resolution function.
• $\mathrm{PDF}_{D_s^*D_s}$ models backgrounds from $D_s^*D_s$ events.
• $\mathrm{PDF}_{\text{other}}$ accounts for continuum and combinatorial backgrounds.

The helicity angle $\theta_H$ distribution for the signal ($1-\cos^2\theta_H$) provides additional discrimination power. Signal efficiencies are determined by large-scale exclusive MC simulations for each tag mode and energy group, yielding an average double-tag efficiency of $\epsilon_{\rm avg} = (21.76 \pm 0.04)\%$ (inclusive of $K^*$ and $\pi^0/K_S^0$ branching fractions).

5. Systematic Uncertainties

Multiplicative systematic uncertainties originate from tracking ($1.0\%$ for $\pi^+$), PID ($1.0\%$ for $\pi^+$), photon reconstruction ($1.0\%$), $\pi^0$ and $K_S^0$ reconstruction ($2.0\%$, $1.5\%$ respectively), MC statistics ($0.4\%$), and selection mass windows for $\gamma\gamma$ and $K^*$ candidates. The overall relative uncertainties sum to $4.0\%$ ($K^+\pi^0$ mode) and $2.4\%$ ($K_S^0 \pi^+$ mode). Additive uncertainties are estimated by varying fitting procedures, background shapes, and yields; the most conservative limit is adopted.

6. Results and Implications

No statistically significant signal is observed, with fit yields of $0.2^{+2.0}_{-1.5}$ ($K^+\pi^0$) and $0.1^{+1.2}_{-1.0}$ ($K_S^0 \pi^+$) events. The $90\%$ confidence-level upper limit on the branching fraction is

$$\mathcal{B}(D_s^+\to\gamma K^*(892)^+) < 2.3\times10^{-4}$$

as determined by integration of the profile likelihood ($L(\mathcal{B})$) convolved with the systematic uncertainty [Stenson physics/0605236]. This bound is above, but approaches, the upper edge of the predicted SM range for long-distance dominated processes ($0.1$–$1.4\times10^{-4}$). No theoretical scenario is excluded.

A plausible implication is that future high-luminosity flavor factories (Belle II, Super τ-Charm Facility) will be required to decisively access the SM-calculable regime for this decay. Progress in both experimental precision and theoretical control of long-distance contributions will be necessary for conclusive SM tests (Collaboration et al., 23 Jan 2026).