Measurement of the ratio of branching fractions $ {\cal B}(D^0 \to K^+ \pi^-)/{\cal B}(D^0 \to K^- \pi^+)$ using the CDF II Detector

We present a preliminary measurement of the ratio, $R_D$, of the branching fraction for the doubly Cabibbo-suppressed decay $D^0 \to K^+ \pi^-$ to that for the Cabibbo-favored decay $D^0 \to K^- \pi^+$. Charge conjugate decays are implicitly included. A signal of $2005 \pm 104$ events for the decay $D^0 \to K^+ \pi^-$ is obtained using the CDF II detector at the Fermilab Tevatron collider. The data set corresponds to an integrated luminosity of 0.35 $fb^{-1}$ produced in $\bar{p}p$ collisions at $\sqrt{s}=1.96$ TeV. Assuming no mixing and no CP violation, we find $R_D = 4.05 \pm 0.21 (\mbox{stat.}) \pm 0.12 (\mbox{syst.}) \times 10^{-3}$. This measurement is consistent with the world average, and comparable in accuracy with the best measurements from other experiments.