Determination of the pseudoscalar decay constant $f_{D_s^{+}}$ via $D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$

Abstract

Using a $3.19{\mathrm{fb}}^{-1}$ data sample collected at an $e^{+}{e}^{-}$ center-of-mass energy of $E_{\mathrm{cm}}=4.178$ GeV with the BESIII detector, we measure the branching fraction of the leptonic decay $D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ to be ${\mathcal{B}}_{D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼}=(5.49\pm 0.16_{stat.}\pm 0.15_{syst.})\times 10^{-3}$. Combining our branching fraction with the masses of the $D_s^{+}$ and $\hat{I}{¼}^{+}$ and the lifetime of the $D_s^{+}$, we determine $f_{D_s^{+}}|V_{cs}|=246.2\pm 3.6_{stat.}\pm 3.5_{syst.}\mathrm{MeV}$. Using the $c\to s$ quark mixing matrix element $|V_{cs}|$ determined from a global standard model fit, we evaluate the $D_s^{+}$ decay constant $f_{D_s^{+}}=252.9\pm 3.7_{stat.}\pm 3.6_{syst.}$\,MeV. Alternatively, using the value of $f_{D_s^{+}}$ calculated by lattice quantum chromodynamics, we find $|V_{cs}|=0.985\pm 0.014_{stat.}\pm 0.014_{syst.}$. These values of ${\mathcal{B}}_{D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼}$, $f_{D_s^{+}}|V_{cs}|$, $f_{D_s^{+}}$ and $|V_{cs}|$ are each the most precise results to date.