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 $B\left({D}^{+}\to {\tau }^{+}{\nu }_{\tau }\right)=\phantom{\rule{0ex}{0ex}}\left(1.20±{0.24}_{\text{stat}}±{0.12}_{\text{syst}}\right)×{10}^{-3}$. Taking the world average $B\left({D}^{+}\to {\mu }^{+}{\nu }_{\mu }\right)=\left(3.74±0.17\right)×{10}^{-4}$, we obtain ${R}_{\tau /\mu }=\Gamma \left({D}^{+}\to {\tau }^{+}{\nu }_{\tau }\right)/\Gamma \left({D}^{+}\to {\mu }^{+}{\nu }_{\mu }\right)=3.21±{0.64}_{\text{stat}}±{0.43}_{\text{syst}}$., 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.