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Measurement of the $D_s^+ \to \ell^+ν_\ell$ 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 $D_s^+\toμ^+ν_μ$ and $D_s^+\toτ^+ν_τ$. By constraining the ratio of decay rates of $D_s^+$ to $τ^+ν_τ$ and to $μ^+ν_μ$ to the Standard Model prediction, the branching fractions are determined to be $\mathcal{B}(D_s^+ \to μ^+ν_μ) = (0.495 \pm 0.067 \pm 0.026)\%$ and $\mathcal{B}(D_s^+ \to τ^+ν_τ) = (4.83 \pm 0.65 \pm 0.26)\%$. 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.