Precision Measurements of $D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$ and $D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e$

Abstract

Precision measurements of the semileptonic decays $D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$ and $D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e$ are performed with 7.33\,fb${}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector. The branching fractions obtained are $\mathcal{B}(D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e)$ = $(2.255\pm 0.039_{\mathrm{stat}}\pm 0.051_{\mathrm{syst}})\%$ and $\mathcal{B}(D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e)$ = $(0.810\pm 0.038_{\mathrm{stat}}\pm 0.024_{\mathrm{syst}})\%$. Combining these results with the $\mathcal{B}(D^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e)$ and $\mathcal{B}(D^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e)$ obtained from previous BESIII measurements, the $\hat{I}\cdot -\hat{I}{\cdot }^{\prime }$ mixing angle in the quark flavor basis is determined to be $\ddot{I}{•}_{\mathrm{P}}=(40.0\pm 2.0_{\mathrm{stat}}\pm 0.6_{\mathrm{syst}}{)}^{\circ }$. Moreover, from the fits to the partial decay rates of $D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$ and $D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e$, the products of the hadronic transition form factors $f_{+}^{\hat{I}{\cdot }^{(\prime )}}(0)$ and the modulus of the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ are determined by using different hadronic transition form factor parametrizations. Based on the two-parameter series expansion, the products $f^{\hat{I}}{\cdot }_{+}(0)|V_{cs}|=0.4519\pm 0.0071_{\mathrm{stat}}\pm 0.0065_{\mathrm{syst}}$ and $f_{+}^{\hat{I}{\cdot }^{\prime }}(0)|V_{cs}|=0.525\pm 0.024_{\mathrm{stat}}\pm 0.009_{\mathrm{syst}}$ are extracted. All results determined in this work supersede those measured in the previous BESIII analyses based on the 3.19 fb${}^{-1}$ subsample of data at 4.178 GeV.