Observation of the radiative decay $D_s (2317)^+ \to D_s^* γ$

Abstract

We observe the radiative decay $D^{*}_{s0}(2317)^{+} \to D_{s}^{*+} γ$ for the first time, with a significance exceeding $10$ standard deviations. The signal is found in the continuum $e^+ e^- \to c\bar{c}$ process with the combined data samples of 980.4~$\rm fb^{-1}$ and 427.9~$\rm fb^{-1}$ collected by the Belle and Belle~II detectors operating at the KEKB and SuperKEKB asymmetric-energy $e^+e^-$ colliders, respectively. The branching fraction ratio ${\cal B}(D^{*}_{s0}(2317)^{+} \to D_{s}^{*+} γ)/{\cal B}(D^{*}_{s0}(2317)^{+} \to D_{s}^{+} π^{0})$ is measured to be $[7.14 \pm 0.70({\rm stat.}) \pm 0.23({\rm syst.})]\%$. This result provides significant new experimental input for the determination of the quark structure of the $D^{*}_{s0}(2317)^{+}$, which remains unknown.

Figures (3)

• Figure 1: Fits to the $M( D_{s}^{+} \pi^{0})$ spectra from (a) Belle and (b) Belle II data. The data samples are represented by the dots with error bars. The blue curves, green dotted curves, and green filled areas are the fitted total pdfs, total backgrounds, and combinatorial backgrounds, respectively. The areas between total and combinatorial backgrounds are from the fitted cross-feed contributions. The distributions from the normalized $D_{s}^{+}$ and $\pi^{0}$ mass sidebands are shown with yellow blank and red slash filled histograms, respectively.
• Figure 2: Simultaneous fits to the $M(D_{s}^{*+}\gamma)$ distributions from (a) Belle and (b) Belle II data samples. The blue and violet curves are the best fit results and the fitted total background pdfs, respectively. The filled green areas are the fitted combinatorial backgrounds. The histograms in red slashes represent the normalized $D_{s}^{*+}$ sidebands.
• Figure 3: Comparison between the measured ${\cal B}(D^{*}_{s0}(2317)^{+} \to D_{s}^{*+} \gamma)/{\cal B}(D^{*}_{s0}(2317)^{+} \to D_{s}^{+} \pi^{0})$ in this work and the theoretical predictions. The theoretical approaches of the references are traditional quark model for Godfrey Godfrey:2003kg, light front quark model for Ke Ke:2013zs, effective Lagrangian with with chiral symmetry for Bardeen Bardeen:2003kt, effective Lagrangian for Faessler Faessler:2007gv, heavy quark flavor symmetry for Fu Fu:2021wde, and chiral lagrangian with coupled-channel dynamics for Lutz Lutz:2007sk. The prediction of Ke Ke:2013zs is a lower limit. The uncertainty of the experimental measurement is the combination of statistical and systematic uncertainties.