An investigation of $D^{+}\to {\tau }^{+}\nu$

We test whether or not the $\tau$ lepton manifests the same couplings as the $\mu$ lepton by investigating the relative decay rates in purely leptonic $D^{+}$ meson decays. We use $281{\mathrm{pb}}^{-1}$ of data accumulated at the $\psi (3770)$ resonance with the CLEO-c detector, to limit $\mathcal{B}(D^{+}\to {\tau }^{+}\nu )<2.1\times {10}^{-3}$ at 90% confidence level (C.L.), thus allowing us to place the first upper limit on the ratio $R=\Gamma (D^{+}\to {\tau }^{+}\nu )/\Gamma (D^{+}\to {\mu }^{+}\nu )$. The ratio of $R$ to the standard model expectation of 2.65 then is $<1.8$ at 90% C.L., consistent with the prediction of lepton universality.

Figure 1

The decay diagram for $D^{+}\to {\ell }^{+}\nu$.

Figure 2

Beam-constrained mass distributions for different fully reconstructed $D^{-}$ decay candidates in the final states: (a) $K^{+}{\pi }^{-}{\pi }^{-}$, (b) $K^{+}{\pi }^{-}{\pi }^{-}{\pi }^0$, (c) $K_S{\pi }^{-}$, (d) $K_S{\pi }^{-}{\pi }^{-}{\pi }^{+}$, (e) $K_S{\pi }^{-}{\pi }^0$, and (f) $K^{+}{K}^{-}{\pi }^{-}$. The solid curves show the sum of signal and background functions. The dashed curves indicate the background fits. Events between the arrows are selected for further analysis.

Figure 3

Missing mass-squared distribution for $D^{+}\to {\tau }^{+}\nu$, ${\tau }^{+}\to {\pi }^{+}\overline{\nu }$ from Monte Carlo simulation.

Figure 4

The ${\mathrm{MM}}^2$ distributions from data using $D^{-}$ tags and one additional opposite-sign charged track and no extra energetic showers (see text). For the case when the single track (a) deposits $<300\mathrm{MeV}$ of energy in the calorimeter, case (i). The peak near zero is from $D^{+}\to {\mu }^{+}\nu$ events. (b) Track deposits $>300\mathrm{MeV}$ in crystal calorimeter but is not consistent with being an electron, case (ii). The arrows indicate the signal regions. The insets show the signal regions with a finer binning of $0.002{\mathrm{GeV}}^2$.

Figure 5

The ${\mathrm{MM}}^2$ distribution obtained using $D^{-}$ tags and one additional opposite-sign charged track and no extra energetic showers (see text). The track is required to deposit $>300\mathrm{MeV}$ of energy in the calorimeter and be consistent with an electron. The solid curve is data and the dashed curve Monte Carlo.

Figure 6

The ${\mathrm{MM}}^2$ distribution from data events with a single $D^0$ or ${\overline{D}}^0$ tag and the other neutral $D$ decaying into two tracks, most likely $K^{\mp }{\pi }^{\pm }$, where the kaon information is ignored. For the two cases: (a) track deposits $<300\mathrm{MeV}$ of energy in the crystal calorimeter and (b) track deposits $>300\mathrm{MeV}$ in the calorimeter. The arrows delineate the relevant signal regions.