Measurement of the $D_s^+ to ell^+ u_ell$ 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 $D_s^+tomu^+ u_mu$ and $D_s^+totau^+ u_tau$. By constraining the ratio of decay rates of $D_s^+$ to $tau^+ u_tau$ and to $mu^+ u_mu$ to the Standard Model prediction, the branching fractions are determined to be $mathcal{B}(D_s^+ to mu^+ u_mu) = (0.495 pm 0.067 pm 0.026)%$ and $mathcal{B}(D_s^+ to tau^+ u_tau) = (4.83 pm 0.65 pm 0.26)%$. 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.