Measurement of the Dynamics of the Decays ${ D_s^+ \rightarrow η^{(\prime)} e^{+} ν_e}$

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 $\mathcal{B}_{D_s^+ \rightarrow ηe^{+} ν_e }$ = $(2.323\pm0.063_{\rm stat}\pm0.063_{\rm syst})\%$ and $\mathcal{B}_{D_s^+ \rightarrow η^{\prime} e^{+} ν_e}$ = $(0.824\pm0.073_{\rm stat}\pm0.027_{\rm syst})\%$ via a tagged analysis technique, where one $D_s$ is fully reconstructed in a hadronic mode. Combining these measurements with previous BESIII measurements of $\mathcal{B}_{D^+\toη^{(\prime)} e^{+} ν_e}$, the $η-η^\prime$ mixing angle in the quark flavour basis is determined to be $ϕ_{\rm P} = (40.1\pm2.1_{\rm stat}\pm0.7_{\rm syst})^\circ$. From the first measurements of the dynamics of $D^+_s\to η^{(\prime)}e^+ν_e$ decays, the products of the hadronic form factors $f_+^{η^{(\prime)}}(0)$ 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 $f^η_+(0)|V_{cs}| = 0.4455\pm0.0053_{\rm stat}\pm0.0044_{\rm syst}$ and $f^{η^{\prime}}_+(0)|V_{cs}| = 0.477\pm0.049_{\rm stat}\pm0.011_{\rm syst}$.

10pages, 3 figures