Measurement of the Dynamics of the Decays $D_s^{+}\to \hat{I}{\cdot }^{(\prime )}{e}^{+}\hat{I}{½}_e$

Abstract

Using $e^{+}{e}^{-}$ annihilation data corresponding to an integrated luminosity of 3.19\,fb${}^{-1}$ collected at a center-of-mass energy of 4.178~GeV with the BESIII detector, we measure the absolute branching fractions ${\mathcal{B}}_{D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e}$ = $(2.323\pm 0.063_{\mathrm{stat}}\pm 0.063_{\mathrm{syst}})\%$ and ${\mathcal{B}}_{D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e}$ = $(0.824\pm 0.073_{\mathrm{stat}}\pm 0.027_{\mathrm{syst}})\%$ via a tagged analysis technique, where one $D_s$ is fully reconstructed in a hadronic mode. Combining these measurements with previous BESIII measurements of ${\mathcal{B}}_{D^{+}\to \hat{I}{\cdot }^{(\prime )}{e}^{+}\hat{I}{½}_e}$, the $\hat{I}\cdot -\hat{I}{\cdot }^{\prime }$ mixing angle in the quark flavour basis is determined to be $\ddot{I}{•}_{\mathrm{P}}=(40.1\pm 2.1_{\mathrm{stat}}\pm 0.7_{\mathrm{syst}}{)}^{\circ }$. From the first measurements of the dynamics of $D_s^{+}\to \hat{I}{\cdot }^{(\prime )}{e}^{+}\hat{I}{½}_e$ decays, the products of the hadronic form factors $f_{+}^{\hat{I}{\cdot }^{(\prime )}}(0)$ and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ are determined with different form factor parameterizations. For the two-parameter series expansion, the results are $f^{\hat{I}}{\cdot }_{+}(0)|V_{cs}|=0.4455\pm 0.0053_{\mathrm{stat}}\pm 0.0044_{\mathrm{syst}}$ and $f_{+}^{\hat{I}{\cdot }^{\prime }}(0)|V_{cs}|=0.477\pm 0.049_{\mathrm{stat}}\pm 0.011_{\mathrm{syst}}$.

10pages, 3 figures