Measurement of the Dynamics of the Decays $D_s^{+}\to {\eta }^{(\prime )}{e}^{+}{\nu }_e$

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 ${\mathcal{B}}_{D_s^{+}\to \eta e^{+}{\nu }_e}$ = $(2.323\pm 0.063_{\mathrm{stat}}\pm 0.063_{\mathrm{syst}})\%$ and ${\mathcal{B}}_{D_s^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e}$ = $(0.824\pm 0.073_{\mathrm{stat}}\pm 0.027_{\mathrm{syst}})\%$ via a tagged analysis technique, where one $D_s$ is fully reconstructed in a hadronic mode. Combining these measurements with previous BESIII measurements of ${\mathcal{B}}_{D^{+}\to {\eta }^{(\prime )}{e}^{+}{\nu }_e}$, the $\eta -{\eta }^{\prime }$ mixing angle in the quark flavour basis is determined to be ${\varphi }_{\mathrm{P}}=(40.1\pm 2.1_{\mathrm{stat}}\pm 0.7_{\mathrm{syst}}{)}^{\circ }$. From the first measurements of the dynamics of $D_s^{+}\to {\eta }^{(\prime )}{e}^{+}{\nu }_e$ decays, the products of the hadronic form factors $f_{+}^{{\eta }^{(\prime )}}(0)$ 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 $f_{+}^{\eta }(0)|V_{cs}|=0.4455\pm 0.0053_{\mathrm{stat}}\pm 0.0044_{\mathrm{syst}}$ and $f_{+}^{{\eta }^{\prime }}(0)|V_{cs}|=0.477\pm 0.049_{\mathrm{stat}}\pm 0.011_{\mathrm{syst}}$.

arXiv comment10pages, 3 figures

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