Study of the decay $D^{+}\to K^{*}(892{)}^{+}{K}_S^0$ in $D^{+}\to K^{+}{K}_S^0{\pi }^0$

Based on an $e^{+}{e}^{-}$ collision data sample corresponding to an integrated luminosity of $2.93{\mathrm{fb}}^{-1}$ collected with the BESIII detector at $\sqrt{s}=3.773\mathrm{GeV}$, the first amplitude analysis of the singly Cabibbo-suppressed decay $D^{+}\to K^{+}{K}_S^0{\pi }^0$ is performed. From the amplitude analysis, the $K^{*}(892{)}^{+}{K}_S^0$ component is found to be dominant with a fraction of $(57.1\pm 2.6\pm 4.2)\%$, where the first uncertainty is statistical and the second systematic. In combination with the absolute branching fraction $\mathcal{B}(D^{+}\to K^{+}{K}_S^0{\pi }^0)$ measured by BESIII, we obtain $\mathcal{B}(D^{+}\to K^{*}(892{)}^{+}{K}_S^0)=(8.69\pm 0.40\pm 0.64\pm 0.51)\times {10}^{-3}$, where the third uncertainty is due to the branching fraction $\mathcal{B}(D^{+}\to K^{+}{K}_S^0{\pi }^0)$. The precision of this result is significantly improved compared to the previous measurement. This result also differs from most of theoretical predictions by about $4\sigma$, which may help to improve the understanding of the dynamics behind.

Figure 1

Topological diagrams contributing to the decay $D^{+}\to K^{*}(892{)}^{+}{K}_S^0$ with (a) color-favored tree diagram, (b) $W$-annihilation diagram, (c) color-favored QCD penguin diagram and (d) QCD penguin exchange diagram.

Figure 2

Distributions of $\mathrm{\Delta }{E}_{\mathrm{sig}}$ (a) and $M_{\mathrm{rec}}$ (b) in data and the scaled inclusive MC sample. The points with uncertainties denote data and the unshaded (shaded) histogram denotes the signal (background) events from the scaled inclusive MC sample. The arrows indicate the $\mathrm{\Delta }{E}_{\mathrm{sig}}$ and $M_{\mathrm{rec}}$ requirements.

Figure 3

Dalitz plot for (a) the reconstructed distribution of the PHSP MC sample and (b) the corresponding smoothed distribution. The projections on (c) $M_{K^{+}{\pi }^0}^2$ and (d) $M_{K_S^0{\pi }^0}^2$, where the dots with uncertainties denote the reconstructed and the solid lines denote the corresponding smoothed distributions.

Figure 4

The Dalitz plot distributions of (a) data and (b) nominal fit, along with the projections and corresponding pull distributions on (c) $M_{K^{+}{\pi }^0}$, (d) $M_{K_S^0{\pi }^0}$, and (e) $M_{K^{+}{K}_S^0}$ of the nominal fit, where the black points with error bars denote data, the blue solid lines denote the fit results, and the other colored curves denote the different resonances components.