Abstract
Using 482\~pb\$^-1\$ of \$e^+e^-\$ collision data collected at a center-of-mass
energy of \$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 \$B(D\_s^+ \mu^+\nu\_\mu) =
(0.495 0.067 0.026)\%\$ and \$B(D\_s^+ \tau^+\nu\_\tau) =
(4.83 0.65 0.26)\%\$. Using these branching fractions, we obtain a value
for the decay constant \$f\_D\_s^+\$ of \$(241.0 16.3 6.5)\~MeV\$,
where the first error is statistical and the second systematic.
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