Measurement of the $D_s^{+}\to {\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ branching fractions and the decay constant $f_{D_s^{+}}$

Using 482~pb${}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of $\sqrt{s}=4.009$ GeV with the BESIII detector, we measure the branching fractions of the decays $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ and $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$. By constraining the ratio of decay rates of $D_s^{+}$ to ${\tau }^{+}{\nu }_{\tau }$ and to ${\mu }^{+}{\nu }_{\mu }$ to the Standard Model prediction, the branching fractions are determined to be $$\mathcal{B}$(D_s^+ \to \mu^+\nu_\mu) = (0.495 \pm 0.067 \pm 0.026)%$and$$\mathcal{B}$(D_s^+ \to \tau^+\nu_\tau) = (4.83 \pm 0.65 \pm 0.26)%$. Using these branching fractions, we obtain a value for the decay constant $f_{D_s^{+}}$ of $(241.0\pm 16.3\pm 6.5)\text{ MeV}$, where the first error is statistical and the second systematic.