Measurements of the branching fractions of semileptonic ${D}_{s}^{+}$ decays via ${e}^{+}{e}^{-}\to {D}_{s}^{*+}{D}_{s}^{*-}$

We measure the absolute branching fractions of semileptonic ${D}_{s}^{+}$ decays via the ${e}^{+}{e}^{-}\to {D}_{s}^{*+}{D}_{s}^{*-}$ process using ${e}^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of $10.64\text{}\text{}{\mathrm{fb}}^{-1}$ collected by the BESIII detector at center-of-mass energies between 4.237 and 4.699 GeV. The branching fractions are $B\left({D}_{s}^{+}\to \eta {e}^{+}{\nu }_{e}\right)=\left(2.35±{0.11}_{\mathrm{stat}}±{0.10}_{\mathrm{syst}}\right)%$, $B\left({D}_{s}^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_{e}\right)=\left(0.82±{0.09}_{\mathrm{stat}}±{0.04}_{\mathrm{syst}}\right)%$, $B\left({D}_{s}^{+}\to \varphi {e}^{+}{\nu }_{e}\right)=\left(2.21±{0.16}_{\mathrm{stat}}±{0.11}_{\mathrm{syst}}\right)%$, $B\left({D}_{s}^{+}\to {f}_{0}\left(980\right){e}^{+}{\nu }_{e},{f}_{0}\left(980\right)\to {\pi }^{+}{\pi }^{-}\right)=\left(0.15±\phantom{\rule{0ex}{0ex}}{0.02}_{\mathrm{stat}}±{0.01}_{\mathrm{syst}}\right)%$, $B\left({D}_{s}^{+}\to {K}^{0}{e}^{+}{\nu }_{e}\right)=\left(0.24±0.0{4}_{\mathrm{stat}}±0.0{1}_{\mathrm{syst}}\right)%$, and $B\left({D}_{s}^{+}\to {K}^{*0}{e}^{+}{\nu }_{e}\right)=\left(0.19±\phantom{\rule{0ex}{0ex}}0.0{3}_{\mathrm{stat}}±0.0{1}_{\mathrm{syst}}\right)%$. These results are consistent with those measured via the ${e}^{+}{e}^{-}\to {D}_{s}^{*±}{D}_{s}^{\mp }$ process by BESIII and CLEO. Using two-parameter series expansion, the hadronic transition form factors of ${D}_{s}^{+}\to \eta {e}^{+}{\nu }_{e}$, ${D}_{s}^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_{e}$, and ${D}_{s}^{+}\to {K}^{0}{e}^{+}{\nu }_{e}$ are determined to be ${f}_{+}^{\eta }\left(0\right)=0.442±0.02{2}_{\mathrm{stat}}±\phantom{\rule{0ex}{0ex}}0.01{7}_{\mathrm{syst}}$, ${f}_{+}^{{\eta }^{\prime }}\left(0\right)=0.557±0.06{2}_{\mathrm{stat}}±0.02{4}_{\mathrm{syst}}$, and ${f}_{+}^{{K}^{0}}\left(0\right)=0.677±0.09{8}_{\mathrm{stat}}±0.02{3}_{\mathrm{syst}}$.