Study of the decays $D_s^{+}\to K_S^0{K}^{+}$ and $K_L^0{K}^{+}$

Using an $e^{+}{e}^{-}$ annihilation data sample corresponding to an integrated luminosity of $3.19{\mathrm{fb}}^{-1}$ and collected at a center-of-mass energy $\sqrt{s}=4.178\mathrm{GeV}$ with the BESIII detector, we measure the absolute branching fractions $\mathcal{B}(D_s^{+}\to K_S^0{K}^{+})=(1.425\pm 0.038_{\mathrm{stat}.}\pm 0.031_{\mathrm{syst}.})\%$ and $\mathcal{B}(D_s^{+}\to K_L^0{K}^{+})=(1.485\pm 0.039_{\mathrm{stat}.}\pm 0.046_{\mathrm{syst}.})\%$. The branching fraction of $D_s^{+}\to K_S^0{K}^{+}$ is compatible with the world average and that of $D_s^{+}\to K_L^0{K}^{+}$ is measured for the first time. We present the first measurement of the $K_S^0\text{−}{K}_L^0$ asymmetry in the decays $D_s^{+}\to K_{S,L}^0{K}^{+}$, and $R(D_s^{+}\to K_{S,L}^0{K}^{+})=\frac{\mathcal{B}(D_s^{+}\to K_S^0{K}^{+})-\mathcal{B}(D_s^{+}\to K_L^0{K}^{+})}{\mathcal{B}(D_s^{+}\to K_S^0{K}^{+})+\mathcal{B}(D_s^{+}\to K_L^0{K}^{+})}=(-2.1\pm 1.9_{\mathrm{stat}.}\pm 1.6_{\mathrm{syst}.})\%$. In addition, we measure the direct $CP$ asymmetries $A_{CP}(D_s^{\pm }\to K_S^0{K}^{\pm })=(0.6\pm 2.8_{\mathrm{stat}.}\pm 0.6_{\mathrm{syst}.})\%$ and $A_{\mathrm{CP}}(D_s^{\pm }\to K_L^0{K}^{\pm })=(-1.1\pm 2.6_{\mathrm{stat}.}\pm 0.6_{\mathrm{syst}.})\%$.

Figure 1

Fits to $M_{\mathrm{tag}}$ distributions for each ST mode. The dots with error bars are data, the blue solid curves are the overall fit results, the red dashed curves are the signal, and the green dotted curves are the background.

Figure 2

Distribution of $M_{\mathrm{tag}}$ vs $M_{K_S^0{K}^{+}}$ for $D_s^{+}\to K_S^0{K}^{+}$ candidates in data, summed over the 13 tag modes.

Figure 3

(a) Distributions of $M_{K_S^0{K}^{+}}$ and (b) $M_{\mathrm{tag}}$, summed over the 13 tag modes, with the projection of the fit result superimposed. The data are shown as the black dots with error bars, the blue solid line is the total fit projection, the red short-dashed line is the projection of the signal component, the green long-dashed line is the projection of the BKGI component, the blue dotted line is the projection of the BKGII component, and the magenta dotted-dashed line is the projection of the BKGIII component. The residual $\chi$ between the data and the total fit result, normalized by the uncertainty, is shown beneath the figures.

Figure 4

Distribution of $M{M}^2$ summed over 13 tag modes with the fit result superimposed. The data are shown as the dots with error bars, the blue solid line is the total fit result, the red short-dashed line is the signal component of the fit, the magenta dotted-dashed line is the component of the peaking background from $D_s^{+}\to K_S^0{K}^{+}$ decays, the grey dotted line is the component of the peaking background from $D_s^{+}\to \eta K^{+}$ decays, and the green long-dashed line is the nonpeaking background component. The residual $\chi$ between the data and the total fit result, normalized by the uncertainty, is shown beneath the figures.