Measurement of the branching fraction of $D_s^{+}\to {\ell }^{+}\hat{I}{½}_{\ell }$ via $e^{+}{e}^{-}\to D_s^{\ast +}{D}_s^{\ast -}$

Abstract

Based on $10.64{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data taken at center-of-mass energies between 4.237 and 4.699 GeV with the BESIII detector, we study the leptonic $D_s^{+}$ decays using the $e^{+}{e}^{-}\to D_s^{\ast +}{D}_s^{\ast -}$ process. The branching fractions of $D_s^{+}\to {\ell }^{+}\hat{I}{½}_{\ell }(\ell =\hat{I}¼,\ddot{I}„)$ are measured to be $\mathcal{B}(D_s^{+}\to \hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)=(0.547\pm 0.026_{\mathrm{stat}}\pm 0.016_{\mathrm{syst}})\%$ and $\mathcal{B}(D_s^{+}\to \ddot{I}{„}^{+}\hat{I}{½}_{\ddot{I}}„)=(5.60\pm 0.16_{\mathrm{stat}}\pm 0.20_{\mathrm{syst}})\%$, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined to be $f_{D_s^{+}}|V_{cs}|=(246.5\pm 5.9_{\mathrm{stat}}\pm 3.6_{\mathrm{syst}}\pm 0.5_{\mathrm{input}}{)}_{\hat{I}¼\hat{I}½}\mathrm{MeV}$ and $f_{D_s^{+}}|V_{cs}|=(252.7\pm 3.6_{\mathrm{stat}}\pm 4.5_{\mathrm{syst}}\pm 0.6_{\mathrm{input}}){)}_{\ddot{I}„\hat{I}½}\mathrm{MeV}$, respectively. Taking the value of $|V_{cs}|$ from a global fit in the Standard Model, we obtain $f_{D_s^{+}}=(252.8\pm 6.0_{\mathrm{stat}}\pm 3.7_{\mathrm{syst}}\pm 0.6_{\mathrm{input}}{)}_{\hat{I}¼\hat{I}½}$ MeV and $f_{D_s^{+}}=(259.2\pm 3.6_{\mathrm{stat}}\pm 4.5_{\mathrm{syst}}\pm 0.6_{\mathrm{input}}{)}_{\ddot{I}„\hat{I}½}$ MeV, respectively. Conversely, taking the value for $f_{D_s^{+}}$ from the latest lattice quantum chromodynamics calculation, we obtain $|V_{cs}|=(0.986\pm 0.023_{\mathrm{stat}}\pm 0.014_{\mathrm{syst}}\pm 0.003_{\mathrm{input}}{)}_{\hat{I}¼\hat{I}½}$ and $|V_{cs}|=(1.011\pm 0.014_{\mathrm{stat}}\pm 0.018_{\mathrm{syst}}\pm 0.003_{\mathrm{input}}{)}_{\ddot{I}„\hat{I}½}$, respectively.

27 pages, 13 figures