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

We present a measurement of $R_{\mathcal{B}}$, the ratio of the branching fraction for the rare 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 $0.35{\mathrm{fb}}^{-1}$ produced in $\overline{p}p$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. Assuming no mixing, we find $R_{\mathcal{B}}=[4.05\pm 0.21(\mathrm{stat})\pm 0.11(\mathrm{syst})]\times {10}^{-3}$. This measurement is consistent with the world average, and comparable in accuracy with the best measurements from other experiments.

Figure 1

$K\pi$ invariant mass distribution for candidates reconstructed as $D^0\to K^{+}{\pi }^{-}$ (DCS), requiring $5\mathrm{MeV}/c^2<\delta m<7\mathrm{MeV}/c^2$. The shaded regions are projections from the overall fit onto this distribution. This mass plot illustrates the relative contributions from the DCS signal and the three types of background, as described in the text.

Figure 2

The number of $D^0\to K^{+}{\pi }^{-}$ (DCS) decays as a function of $\delta m$. The data points and statistical uncertainty bars are taken from the $K\pi$ slice fits. The shaded regions are determined from a least-squares fit and show the contributions from signal (dark gray) and random tagging pion background (light gray) as explained in the text.

Figure 3

Comparison of this measurement of $R_D$ with other recent results. All the experimental fits assume no mixing or $CP$ violation. The inner set of bars indicate statistical uncertainty; the outer set indicates the quadratic sum of statistical and systematic uncertainties. The shaded region spans the PDG average and uncertainty [1]. That average includes measurements from E791 [16], CLEO [17], FOCUS(2001) [18], and BABAR [7]. The Belle [8], FOCUS(2005) [19] and current CDF measurements are not included in the PDG average.