Observation of the Leptonic Decay $D^{+}\to {\tau }^{+}{\nu }_{\tau }$

We report the first observation of $D^{+}\to {\tau }^{+}{\nu }_{\tau }$ with a significance of $5.1\sigma$. We measure $\mathcal{B}(D^{+}\to {\tau }^{+}{\nu }_{\tau })=(1.20\pm {0.24}_{\text{stat}}\pm {0.12}_{\text{syst}})\times {10}^{-3}$. Taking the world average $\mathcal{B}(D^{+}\to {\mu }^{+}{\nu }_{\mu })=(3.74\pm 0.17)\times {10}^{-4}$, we obtain $R_{\tau /\mu }=\mathrm{\Gamma }(D^{+}\to {\tau }^{+}{\nu }_{\tau })/\mathrm{\Gamma }(D^{+}\to {\mu }^{+}{\nu }_{\mu })=3.21\pm {0.64}_{\text{stat}}\pm {0.43}_{\text{syst}}$., which is consistent with the standard model expectation of lepton flavor universality. Using external inputs, our results give values for the $D^{+}$ decay constant $f_{D^{+}}$ and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ that are consistent with, but less precise than, other determinations.

Figure 1

Fits to $M_{\mathrm{BC}}$ distributions of single-tag $D^{-}$ candidates for the full data sample for tag modes $D^{-}\to$ (a) $K^{+}{\pi }^{-}{\pi }^{-}$, (b) $K^{+}{\pi }^{-}{\pi }^{-}{\pi }^0$, (c) $K_S^0{\pi }^{-}$, (d) $K_S^0{\pi }^{-}{\pi }^0$, (e) $K_S^0{\pi }^{-}{\pi }^{-}{\pi }^{+}$, and (f) $K^{+}{K}^{-}{\pi }^{-}$. Red lines are the overall fits, while the yellow-dashed (blue-dotted) lines are the fitted signals (backgrounds).

Figure 2

$M_{\text{miss}}^2$ distributions of $D^{+}\to {\pi }^0{\pi }^{+}$ (a), (c) and $D^{+}\to K_S^0(\to {\pi }^{+}{\pi }^{-}){\pi }^{+}$ (b), (d) events from data (black points) for the $\mu$-like (a), (b) and $\pi$-like (c), (d) samples. The blue lines are the PDFs derived from the black points, while the red-shaded histograms are true $D^{+}\to {\pi }^0{\pi }^{+}$ and $D^{+}\to K_L^0{\pi }^{+}$ MC events with all selection criteria applied.

Figure 3

Fits to $M_{\text{miss}}^2$ distributions of the $\mu$-like (left) and $\pi$-like (right) samples. The black points are data and gray-shaded histograms are MC-predicted smooth background components scaled to the data size based on the known production cross sections and measured integrated luminosity. The insets show the same distributions with logarithmic scales.