Observation of the leptonic decay $D^+ to tau^+ u_tau$

We report the first observation of $D^+totau^+ u_tau$ with a significance of $5.1sigma$. We measure ${cal B}(D^+totau^+ u_tau) = (1.20pm0.24_{text{stat.}}pm0.12_{text{syst.}})times10^{-3}$. Taking the world average ${cal B}(D^+tomu^+ u_mu) = (3.74pm0.17)times10^{-4}$, we obtain $R_{tau/mu} =Gamma(D^+totau^+ u_tau)/Gamma(D^+tomu^+ u_mu) = 3.21pm0.64_{text{stat.}}pm0.43_{text{syst.}}$, 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 CKM matrix element $|V_{cd}|$ that are consistent with, but less precise than, other determinations.