Measurement of absolute hadronic branching fractions of $D$ mesons and $e^{+}{e}^{-}\to D\overline{D}$ cross sections at the $\psi (3770)$

Using $281{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collisions recorded at the $\psi (3770)$ resonance with the CLEO-c detector at CESR (Cornell Electron Storage Ring), we determine absolute hadronic branching fractions of charged and neutral $D$ mesons using a double tag technique. Among measurements for three $D^0$ and six $D^{+}$ modes, we obtain reference branching fractions $\mathcal{B}(D^0\to K^{-}{\pi }^{+})=(3.891\pm 0.035\pm 0.059\pm 0.035)\%$ and $\mathcal{B}(D^{+}\to K^{-}{\pi }^{+}{\pi }^{+})=(9.14\pm 0.10\pm 0.16\pm 0.07)\%$, where the first uncertainty is statistical, the second is all systematic errors other than final-state radiation (FSR), and the third is the systematic uncertainty due to FSR. We include FSR in these branching fractions by allowing for additional unobserved photons in the final state. Using an independent determination of the integrated luminosity, we also extract the cross sections $\sigma (e^{+}{e}^{-}\to D^0{\overline{D}}^0)=(3.66\pm 0.03\pm 0.06)\mathrm{nb}$ and $\sigma (e^{+}{e}^{-}\to D^{+}{D}^{-})=(2.91\pm 0.03\pm 0.05)\mathrm{nb}$ at a center-of-mass energy, $E_{\mathrm{cm}}=3774\pm 1\mathrm{MeV}$.

Figure 1

(a) The efficiency $ϵ({\pi }^{\pm })$ for identifying a pion as a function of the momentum $p$ and, on a highly expanded vertical axis scale, (b) the probability $\eta (K^{\pm }\to {\pi }^{\pm })$ that a kaon is misidentified as a pion. The reason for behavior of the data above $p=0.7\mathrm{GeV}/c$ is discussed in the text.

Figure 2

(a) The efficiency $ϵ(K^{\pm })$ for identifying a kaon as a function of the momentum $p$ and, on a highly expanded vertical axis scale, (b) the probability $\eta ({\pi }^{\pm }\to K^{\pm })$ that a pion is misidentified as a kaon. The reason for behavior of the data above $p=0.7\mathrm{GeV}/c$ is discussed in the text.

Figure 3

Scatter plot of $M_{\mathrm{BC}}(\overline{D})$ vs $M_{\mathrm{BC}}(D)$ for $D^0{\overline{D}}^0$ double tag candidates. Signal candidates are concentrated at $M_{\mathrm{BC}}(\overline{D})=M_{\mathrm{BC}}(D)=M_D$. Beam energy smearing [$\sigma (E_0)$] smears candidates along the $M_{\mathrm{BC}}(\overline{D})$ vs $M_{\mathrm{BC}}(D)$ diagonal. Initial-state radiation spreads candidates further along the diagonal above the concentration of signal candidates. Detector resolution smears a candidate parallel to the $M_{\mathrm{BC}}(\overline{D})$ axis [$\sigma ({\overline{D}}^0)$] and parallel to the $M_{\mathrm{BC}}(D)$ axis [$\sigma (D^0)$]. Since the $D^0$ and ${\overline{D}}^0$ resolutions are equal, the resulting distribution is isotropic. Candidates with either the $D^0$ or ${\overline{D}}^0$ properly reconstructed and the other particle (${\overline{D}}^0$ or $D^0$, respectively) improperly reconstructed are spread along the lines $M_{\mathrm{BC}}(\overline{D})=M_D$ or $M_{\mathrm{BC}}(D)=M_D$. Candidates that are mispartitioned (i.e., where some particles are interchanged between the $D^0$ and the ${\overline{D}}^0$) are spread along the diagonal. Finally, some of the candidates smeared along the diagonal are from continuum events (i.e., annihilations to $u\overline{u}$, $d\overline{d}$, and $s\overline{s}$ quark pairs) where all particles in the final state are found and used.

Figure 4

Projections of double tag candidate masses on the $M_{\mathrm{BC}}(D)$ axis for (a) all double tag $D^0{\overline{D}}^0$ modes and (b) all double tag $D^{+}{D}^{-}$ modes. In each plot, the lines are projections of the fit results, the dashed line is the background contribution, and the solid line is the sum of signal and background.

Figure 5

Projections of double tag $D^0{\overline{D}}^0$ candidate masses on the $M_{\mathrm{BC}}(D^0)$ axis, with the ${\overline{D}}^0$ reconstructed in any of the three neutral tag modes. The number of events in each bin is plotted on a square-root scale. The lines are projections of the fit results; the dashed line is the background contribution and the solid line is the sum of signal and background. Projections of the candidate masses on the orthogonal $M_{\mathrm{BC}}({\overline{D}}^0)$ axis are nearly identical to those on the $M_{\mathrm{BC}}(D^0)$ axis illustrated here.

Figure 6

Projections of double tag $D^{+}{D}^{-}$ candidate masses on the $M_{\mathrm{BC}}(D^{+})$ axis, with the $D^{-}$ reconstructed in any of the six charged tag modes. The number of events in each bin is plotted on a square-root scale. The lines are projections of the fit results; the dashed line is the background contribution and the solid line is the sum of signal and background. Projections of the candidate masses on the orthogonal $M_{\mathrm{BC}}(D^{-})$ axis are nearly identical to those on the $M_{\mathrm{BC}}(D^{+})$ axis illustrated here.

Figure 7

Distributions of measured $M_{\mathrm{BC}}(D)$ or $M_{\mathrm{BC}}(\overline{D})$ values for single tag $D^0$ and $D^{+}$ candidates with $D$ and $\overline{D}$ candidates combined in each mode. The points are data and the curves are fits to the data. In each plot, the dashed curve shows the contribution of the ARGUS background function and the solid curve shows the sum of this background and the signal peak function. The number of events in each bin is plotted on a square-root scale. The ST $D^0$ decays are illustrated in the left column and the ST $D^{+}$ decays are illustrated in the other two columns. The reference modes $D^0\to K^{+}{\pi }^{-}$ and $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ are illustrated in the first two plots from the left in the top row.

Figure 8

Histograms of and fits to $M_{\mathrm{miss}}^2$ distributions from $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ decays to determine the charged pion efficiency for $p_{{\pi }^{+}}>0.2\mathrm{GeV}/c$. (a) and (c) are from events in data, and (b) and (d) are from events in Monte Carlo simulation. (a) and (b) are from decays in which the pion was found, while (c) and (d) are from decays in which the pion was not found. The solid curves are fits to the data or Monte Carlo sample; the dashed curves in (c) and (d) are background contributions.

Figure 9

Histograms of and fits to $M_{\mathrm{miss}}^2$ distributions from $D^0\to K^{-}{\pi }^{+}$ decays to determine the charged kaon efficiency. (a) and (c) are from events in data, and (b) and (d) are from events in Monte Carlo simulation. (a) and (b) are from decays in which the kaon was found, while (c) and (d) are from decays in which the kaon was not found. The solid curves are fits to the data or Monte Carlo sample; the dashed curves in (c) and (d) are background contributions.

Figure 10

Histograms of and fits to $M_{\mathrm{miss}}^2$ distributions to determine the $K_S^0$ efficiency. (a) and (c) are from events in data, and (b) and (d) are from events in Monte Carlo simulation. (a) and (b) are from decays in which the $K_S^0$ was found, while (c) and (d) are from decays in which the $K_S^0$ was not found. The background peak and deficit are determined by searching for $K_S^0$ candidates in high and low sidebands of the $K_S^0$ mass. In (a) and (b), the dashed curves are the contributions from fake $K_S^0$ candidates. In (c) and (d), the dashed curve is the background—a linear function with a deficit due to events in which a fake $K_S^0$ candidate was found—and the solid curve is the total fit function including the signal peak. The area between the curves is proportional to the number of $K_S^0$ mesons not found.

Figure 11

Distributions of ${\pi }^0$ missing mass squared in candidate $\psi (2S)\to J/\psi {\pi }^0{\pi }^0$ events for data (points) and Monte Carlo events (histogram). The predicted background level is also shown. The vertical arrows demarcate the signal region. Events in which the second ${\pi }^0$ was found are shown in (a) whereas the events where the second ${\pi }^0$ was not found are shown in (b).

Figure 12

Distributions of CLEO-c $E_{\mathrm{cm}}=3.774\mathrm{GeV}$ data (solid circles) and Monte Carlo simulations (histogram) for the polar angles of the positive lepton (upper two plots) in $e^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{-}$ events, respectively, and the mean value of $|\cos {\theta }_{\gamma }|$ of the two photons in $\gamma \gamma$ events. In each case, the Monte Carlo histograms are normalized to the numbers of data events.