# Study of the Decays $D_{s}^{+} \rightarrow K_{S}^{0}K^{+}$ and $K_{L}^{0}K^{+}$

## TL;DR

This study measures the branching fractions, asymmetries, and CP violation parameters in $D_s^+$ decays to $K_{S,L}^0 K^+$ using BESIII data, providing first measurements for some quantities and confirming previous results.

## Contribution

First measurement of the $D_s^+
ightarrow K_L^0 K^+$ branching fraction and $K_{S}^0$-$K_{L}^0$ asymmetry, with improved precision on decay parameters.

## Key findings

- Branching fraction for $D_s^+
ightarrow K_{S}^0 K^+$ is consistent with world average.
- First measurement of $D_s^+
ightarrow K_{L}^0 K^+$ branching fraction.
- Asymmetry $R(D_s^+
ightarrow K_{S,L}^0 K^+)$ measured as $-2.1 ext{ extpm}1.9_{
m stat} ext{ extpm}1.6_{
m syst} ext{ extpm}$.

## Abstract

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 $\mathcal{B}(D_{s}^{+} \rightarrow K_{S}^{0}K^{+}) = (1.425\pm0.038_{\rm stat.}\pm0.031_{\rm syst.})\%$ and $\mathcal{B}(D_{s}^{+} \rightarrow K_{L}^{0}K^{+}) =(1.485\pm0.039_{\rm stat.}\pm0.046_{\rm syst.})\%$. The branching fraction of $D_{s}^{+} \rightarrow K_{S}^{0}K^{+}$ is compatible with the world average and that of $D_{s}^{+} \rightarrow K_{L}^{0}K^{+}$ is measured for the first time. We present the first measurement of the $K_{S}^{0}$-$K_{L}^{0}$ asymmetry in the decays $D_{s}^{+} \rightarrow K_{S,L}^{0}K^{+}$, and $R(D_{s}^{+} \rightarrow K_{S,L}^{0}K^{+})=\frac{\mathcal{B}(D_{s}^{+} \rightarrow K_{S}^{0}K^{+}) -\mathcal{B}(D_{s}^{+} \rightarrow K_{L}^{0}K^{+})}{\mathcal{B}(D_{s}^{+} \rightarrow K_{S}^{0}K^{+}) +\mathcal{B}(D_{s}^{+} \rightarrow K_{L}^{0}K^{+})}= (-2.1\pm1.9_{\rm stat.}\pm1.6_{\rm syst.})\%$. In addition, we measure the direct $CP$ asymmetries $A_{\rm CP}(D_{s}^{\pm} \rightarrow K_{S}^{0}K^{\pm}) = (0.6\pm2.8_{\rm stat.}\pm0.6_{\rm syst.})\%$ and $A_{\rm CP}(D_{s}^{\pm} \rightarrow K_{L}^{0}K^{\pm}) = (-1.1\pm2.6_{\rm stat.}\pm0.6_{\rm syst.})\%$.