Comparison ofD→KS0πandD→KL0πDecay Rates

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