Improved search for $D^0$-${\overline{D}}^0$ mixing using semileptonic decays at Belle

A search for mixing in the neutral $D$ meson system has been performed using semileptonic $D^0\to K^{(*)-}{e}^{+}\nu$ and $D^0\to K^{(*)-}{\mu }^{+}\nu$ decays. Neutral $D$ mesons from $D^{*+}\to D^0{\pi }_s^{+}$ decays are used and the flavor at production is tagged by the charge of the slow pion. The measurement is performed using $492{\mathrm{fb}}^{-1}$ of data recorded by the Belle detector. From the yield of right-sign and wrong-sign decays arising from nonmixed and mixed events, respectively, we measure the ratio of the time-integrated mixing rate to the unmixed rate to be $R_M=(1.3\pm 2.2\pm 2.0)\times {10}^{-4}$. This corresponds to an upper limit of $R_M<6.1\times {10}^{-4}$ at the 90% C.L.

Figure 1

$\Delta M$ distribution for MC-simulated signal events in different $p_{K\ell }^{*}$ bins: $p_{K\ell }^{*}<2.0\mathrm{GeV}/c$ (dashed line), $2.0\mathrm{GeV}/c<p_{K\ell }^{*}<3.2\mathrm{GeV}/c$ (solid line), and $p_{K\ell }^{*}>3.2\mathrm{GeV}/c$ (dotted line). The histograms are normalized to the same area. The resolution is improved at higher values of momentum. The left plot is for the electron decay mode and the right one for the muon decay mode.

Figure 2

MC-simulated distribution of $p_{K\ell }^{*}$ for signal (solid line) and background events ($b\overline{b}$, $c\overline{c}$, and $uds$ components of background are shown). The arrow shows the value of the $p_{K\ell }^{*}$ requirement.

Figure 3

The distribution of $M(K\ell )$ for signal (solid line) and for background events (dashed line), normalized to the same number of entries. The arrows show the values of the selection criteria. The left plot is for the electron decay mode and the right one for the muon decay mode.

Figure 4

Left: the $\Delta M$ distribution of $\gamma \to e^{+}{e}^{-}$ events, where one of the electrons is selected as the slow pion candidate and the other as the electron candidate, before applying the selection on $M_{ee}({\pi }_s{e}_{\mathrm{signal}})$. Right: the $M_{ee}({\pi }_s{e}_{\mathrm{signal}})$ distribution for these events (solid line), for signal events (dotted line), and for the total WS background (dashed line). The arrow shows the value of the selection criterion.

Figure 5

Distribution of $\Delta M$ for signal (left) and background events (right): with the first approximation for the neutrino four-momentum (dashed line), after applying the constraint on the $D^0$ mass (dotted line) and with the final neutrino momentum, obtained as described in the text (solid line). Selection criteria on $M^2(K\ell \nu )$ and $M_{\nu }^2$ have been omitted. The plot is for the electron decay mode; the distributions in the muon decay mode are similar.

Figure 6

Left: distribution of $M^2(K\ell \nu )$, calculated using the first approximation neutrino momentum. Right: distribution of $M_{\nu }^2$, calculated with the neutrino momentum obtained after applying the constraint on $M^2(K\ell \nu )$. The solid line is for signal and the dotted line for the background. The distributions are shown for the electron decay mode; in the muon decay mode they are similar with a slightly smaller root mean square value.

Figure 7

Left: distribution of the scale factor $\xi$ obtained by the constraint on $M^2(K\ell \nu )$. Right: distribution of the rotation angle for ${\overrightarrow{p}}_{\mathrm{rest}}^{*}$, obtained by the constraint on $M_{\nu }^2$. Both are for signal events; the solid line shows the distributions for electron decays and the dotted line for muon decays.

Figure 8

Left: the fraction of RS background events in 15 proper decay time intervals (error bars) and the result of the fit, described in the text (dotted lines). Note that the $t_{xy}$ intervals are not equidistant, which causes the apparently nonsmooth shape of the function. The first and the last interval include events with $t_{xy}<-10$ and $t_{xy}>10$, respectively. Right: the $t_{xy}$ distribution of RS events (error bars) with the result of the fit (solid line) for the $e-2$ subsample. The dashed line shows the RS background distribution, ${\mathcal{F}}_{\mathrm{bkg}}^{\mathrm{RS}}$, obtained from the data as explained in the text.

Figure 9

Left: the proper decay time distribution of the WS data events (error bars) and the distribution for the WS signal events (solid line), obtained from the data according to Eq. (16). The distributions are for the $e-2$ subsample. Right: the figure-of-merit dependence on the lower and upper limit of the selected $t_{xy}$ interval. When plotting the dependence on the lower limit, the upper limit was set at its optimal value and vice versa. The arrows show the value of the selection criterion, Eq. (17). Distributions for the other three subsamples are similar.

Figure 10

The simulated $\Delta M$ distribution for the signal decays (solid line) and for the associated signal decays (dotted line), for both the electron (left) and muon (right) decay modes.

Figure 11

The simulated $\Delta M$ distribution for WS background events. The solid line shows the total background, the dotted line shows the uncorrelated background, and the dashed line shows the correlated background, multiplied by a factor of 15 and 5 in the electron and muon samples, respectively. The plots are for the selected proper decay time interval. The left plot is for the electron decay mode and the right one for the muon decay mode.

Figure 12

The $\Delta M$ distribution of the RS events for $1.6<t_{xy}<9.0$, SVD-2. The dashed line represents the background, the solid line is the result of the fit, described in the text, and the points with error bars are the data. The left plot is for the $e-2$ subsample; the right plot is for the $\mu -2$ subsample.

Figure 13

The $\Delta M$ distribution of WS events in the six proper decay time intervals for the $e-1$ (left) and $e-2$ (right) subsamples. The points with error bars are the data, the histogram represents the result of the fit, described in the text, and the small contribution on the horizontal axis shows the fitted signal yield.

Figure 14

Same as Fig. 13 for the $\mu -1$ and $\mu -2$ subsamples.

Figure 15

The resulting $R_M^i$ values for the four subsamples and their average value (dashed line). The dotted lines represent the $\pm 1\sigma$ interval. The solid line corresponds to no mixing.

Figure 16

Left: the $R_M$ values of the four subsamples with the statistical uncertainty only, and the result of the fit to these four values (dashed line, ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=2.5/3$). Right: the four $R_M$ values with the systematic uncertainty included and the combined result (dashed line), obtained as described in Sec. 5a7. The dotted lines represent the $\pm 1\sigma$ interval. The solid line corresponds to no mixing.