Precision measurements of Ds+→ηe+νe and Ds+→η′e+νe

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Abstract

Precision measurements of the semileptonic decays ${D}_{s}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{e}^{+}{\ensuremath{\nu}}_{e}$ and ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{e}^{+}{\ensuremath{\nu}}_{e}$ are performed with $7.33\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of ${e}^{+}{e}^{\ensuremath{-}}$ collision data collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector. The branching fractions obtained are $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{e}^{+}{\ensuremath{\nu}}_{e})=(2.255\ifmmode\pm\else\textpm\fi{}0.03{9}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.05{1}_{\mathrm{syst}})%$ and $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{e}^{+}{\ensuremath{\nu}}_{e})=(0.810\ifmmode\pm\else\textpm\fi{}0.03{8}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.02{4}_{\mathrm{syst}})%$. Combining these results with the $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{e}^{+}{\ensuremath{\nu}}_{e})$ and $\mathcal{B}({D}^{+}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{e}^{+}{\ensuremath{\nu}}_{e})$ obtained from previous BESIII measurements, the $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing angle in the quark flavor basis is determined to be ${\ensuremath{\phi}}_{\mathrm{P}}=(40.0\ifmmode\pm\else\textpm\fi{}{2.0}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{0.6}_{\mathrm{syst}})\ifmmode^\circ\else\textdegree\fi{}$. Moreover, from the fits to the partial decay rates of ${D}_{s}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{e}^{+}{\ensuremath{\nu}}_{e}$ and ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{e}^{+}{\ensuremath{\nu}}_{e}$, the products of the hadronic transition form factors ${f}_{+}^{{\ensuremath{\eta}}^{(\ensuremath{'})}}(0)$ and the modulus of the $c\ensuremath{\rightarrow}s$ 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 ${f}_{+}^{\ensuremath{\eta}}(0)|{V}_{cs}|=0.4519\ifmmode\pm\else\textpm\fi{}0.007{1}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.006{5}_{\mathrm{syst}}$ and ${f}_{+}^{{\ensuremath{\eta}}^{\ensuremath{'}}}(0)|{V}_{cs}|=0.525\ifmmode\pm\else\textpm\fi{}0.02{4}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.00{9}_{\mathrm{syst}}$ are extracted. All results determined in this work supersede those measured in the previous BESIII analyses based on the $3.19\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ subsample of data at 4.178 GeV.

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