Measurement of the $D^{*}(2010{)}^{\mathbf{+}}$ natural linewidth and the $D^{*}(2010{)}^{\mathbf{+}}\mathbf{-}{D}^0$ mass difference

We measure the mass difference, $\Delta m_0$, between the $D^{*}(2010{)}^{+}$ and the $D^0$ and the natural linewidth, $\Gamma$, of the transition $D^{*}(2010{)}^{+}\to D^0{\pi }^{+}$. The data were recorded with the BABAR detector at center-of-mass energies at and near the ${\rm Y}(4S)$ resonance, and correspond to an integrated luminosity of approximately $477{\mathrm{fb}}^{-1}$. The $D^0$ is reconstructed in the decay modes $D^0\to K^{-}{\pi }^{+}$ and $D^0\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$. For the decay mode $D^0\to K^{-}{\pi }^{+}$ we obtain $\Gamma =(83.4\pm 1.7\pm 1.5)\mathrm{keV}$ and $\Delta m_0=(145425.6\pm 0.6\pm 1.8)\mathrm{keV}$, where the quoted errors are statistical and systematic, respectively. For the $D^0\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ mode we obtain $\Gamma =(83.2\pm 1.5\pm 2.6)\mathrm{keV}$ and $\Delta m_0=(145426.6\pm 0.5\pm 2.0)\mathrm{keV}$. The combined measurements yield $\Gamma =(83.3\pm 1.2\pm 1.4)\mathrm{keV}$ and $\Delta m_0=(145425.9\pm 0.4\pm 1.7)\mathrm{keV}$; the width is a factor of approximately 12 times more precise than the previous value, while the mass difference is a factor of approximately 6 times more precise.

Figure 1

Disjoint sets of $D^0\to K^{-}{\pi }^{+}$ candidates illustrating the candidates that fail the tracking requirements have worse $\Delta m$ resolution. Each histogram is normalized to its peak. The events that populate the narrowest peak are the nominal $D^{*+}$ candidates that pass all selection criteria. The events that populate the intermediate and widest peaks pass all selection criteria except either the slow pion candidates or $D^0$ daughters fail the SVT requirements or fail the DCH requirements, respectively.

Figure 2

Events with $D^{*+}$ candidates from $D^0\to K^{-}{\pi }^{+}$ that pass all selection criteria, but the slow pion candidate fails the $dE/dx$ requirement.

Figure 3

Events with $D^{*+}$ candidates from $D^0\to K^{-}{\pi }^{+}$ that pass all selection criteria, but the slow pion candidate is identified by the algorithms as either a photon conversion in the detector material or a ${\pi }^0$ Dalitz decay.

Figure 4

Illustrations of the $(m^{\prime },\Delta m^{\prime })$ system in (a) MC with the $D^{*+}$ correctly reconstructed, (b) MC with the slow pion and a $D^0$ daughter pion swapped during reconstruction, and (c) in data. The majority of correctly reconstructed decays are located outside of the shown $(m^{\prime },\Delta m^{\prime })$ range.

Figure 5

Sample of $K_S^0\to {\pi }^{+}{\pi }^{-}$ candidates from $D^{*+}\to D^0{\pi }_s^{+}\to (K_S^0{\pi }^{-}{\pi }^{+}){\pi }_s^{+}$ decay where the $K_S^0$ daughter pions satisfy the same tracking criteria as the slow pions of the $D^{*+}$ analysis.

Figure 6

Mass value of the $K_S^0$ obtained by fitting the invariant ${\pi }^{+}{\pi }^{-}$ mass distribution shown as a function of the slower pion laboratory momentum before (open squares) and after (closed circles) all energy-loss and momentum corrections have been applied. Note that the horizontal scale is logarithmic.

Figure 7

Binned maximum likelihood fit to the $\Delta m$ resolution distribution of MC samples for both $D^0$ decay modes. The interval size is 50 keV, and the high mass tails are dominated by low statistics. Normalized residuals are defined as $(N_{\mathrm{observed}}-N_{\mathrm{predicted}})/\sqrt{N_{\mathrm{predicted}}}$. The shapes in the distribution of the normalized residuals are from dominance by Poisson statistics. In the peak region the total PDF is visually indistinguishable from the Gaussian component of the resolution function.

Figure 8

The results of the fits to data for each $D^0$ decay mode. The fitted parameter values are summarized in Table 2. The solid curve is the sum of the signal (dashed curve) and background (dotted curve) PDFs. The total PDF and signal component are visually indistinguishable in the peak region.

Figure 9

The values of $\Gamma$ (left) and $\Delta m_0$ (right) obtained from fits to data divided into ten disjoint subsets in laboratory momentum $p$ (top row), reconstructed $D^0$ mass (center row), and azimuthal angle (bottom row). The quantities $p$ and $\varphi$ are defined by the $D^{*+}$ momentum. Each point represents an individual fit and each horizontal line is the nominal fit result (i.e. integrating over the variable). The correlation value of $\Gamma$ (or $\Delta m_0$) measured from the $D^0\to K^{-}{\pi }^{+}$ and $D^0\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ samples for each of the variables chosen is given above each plot. The widths from the nominal fits and the weighted average agree well and the corresponding lines are visually indistinguishable.

Figure 10

The values of the scale factor ($1+ϵ$) obtained from fits to data divided into ten disjoint subsets in laboratory momentum $p$, reconstructed $D^0$ mass, and azimuthal angle. The quantities $p$ and $\varphi$ are defined by the $D^{*+}$ laboratory momentum. Each point represents an individual fit and each horizontal line is the nominal fit result (i.e. integrating over the variable).