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

Abstract

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.

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