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Search for ${D}^{0}\to {K}^{-}\eta {e}^{+}{\nu }_{e}$, ${D}^{+}\to {K}_{S}^{0}\eta {e}^{+}{\nu }_{e}$ and ${D}^{+}\to \eta \eta {e}^{+}{\nu }_{e}$ decays

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    <subfield code="a">&lt;p&gt;&lt;/p&gt;&lt;p&gt;By analyzing ${e}^{+}{e}^{-}$ annihilation data corresponding to an integrated luminosity of $7.93\text{}\text{}{\mathrm{fb}}^{-1}$, collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we search for the semileptonic decays ${D}^{0}\to {K}^{-}\eta {e}^{+}{\nu }_{e}$, ${D}^{+}\to {K}_{S}^{0}\eta {e}^{+}{\nu }_{e}$ and ${D}^{+}\to \eta \eta {e}^{+}{\nu }_{e}$ for the first time. We present evidence for ${D}^{0}\to {K}^{-}\eta {e}^{+}{\nu }_{e}$ with a significance of $3.3\sigma $. The branching fraction of ${D}^{0}\to {K}^{-}\eta {e}^{+}{\nu }_{e}$ is measured to be $\left(0.8{4}_{-0.34}^{+0.29}±0.22\right)×{10}^{-4}$. No significant signals are observed for the decays ${D}^{+}\to {K}_{S}^{0}\eta {e}^{+}{\nu }_{e}$ and ${D}^{+}\to \eta \eta {e}^{+}{\nu }_{e}$ and we set the upper limits on their branching fractions.&lt;/p&gt;&lt;p&gt;&lt;/p&gt;</subfield>
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    <subfield code="v">110</subfield>
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