Comparison of $D\to K_S^0\pi$ and $D\to K_L^0\pi$ Decay Rates

We present measurements of $D\to K_S^0\pi$ and $D\to K_L^0\pi$ branching fractions using $281{\mathrm{pb}}^{-1}$ of $\psi (3770)$ data at the CLEO-$c$ experiment. We find that $\mathcal{B}(D^0\to K_S^0{\pi }^0)$ is larger than $\mathcal{B}(D^0\to K_L^0{\pi }^0)$, with an asymmetry of $R(D^0)=0.108\pm 0.025\pm 0.024$. For $\mathcal{B}(D^{+}\to K_S^0{\pi }^{+})$ and $\mathcal{B}(D^{+}\to K_L^0{\pi }^{+})$, we observe no measurable difference; the asymmetry is $R(D^{+})=0.022\pm 0.016\pm 0.018$. The $D^0$ asymmetry is consistent with the value based on the U-spin prediction $A(D^0\to K^0{\pi }^0)/A(D^0\to {\overline{K}}^0{\pi }^0)=-{tan}^2{\theta }_C$, where ${\theta }_C$ is the Cabibbo angle.

Figure 1

Missing mass squared distribution, with all tag modes combined, for $D^0\to X{\pi }^0$, after removing events with extra tracks, ${\pi }^0$’s, or $\eta$’s. The points with error bars are data, and the solid line is a Monte Carlo simulation. The dashed, colored lines represent simulations of the peaking backgrounds $D^0\to {\pi }^0{\pi }^0$, $K_S^0{\pi }^0$, $\eta {\pi }^0$, and $K^{*0}{\pi }^0$. The difference in the peak position is due to a minor discrepancy in our calorimeter simulation at large photon energies; the signal region, marked with arrows, encompasses the peak in both distributions.

Figure 2

Missing mass squared distribution, with all tag modes combined, for $D^{+}\to X{\pi }^{+}$, after removing events with extra tracks or ${\pi }^0$’s. The solid line shows a fit for the $D^{+}\to K_L^0{\pi }^{+}$ yield. The many dashed lines represent the various components of the fit, added cumulatively. The small peak under the signal is the contribution of $D^{+}\to K_S^0{\pi }^{+}$ events that are not removed by the extra track and ${\pi }^0$ vetoes.