Abstract By analyzinge
+e
−annihilation data corresponding to an integrated luminosity of 2.93 fb
−1collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the first observation of the semileptonic decays$$$$ {D}^0\to {K}_S^0{\pi}^{-}{\pi}^0{e}^{+}{\nu}_e $$$$
and$$$$ {D}^{+}\to {K}_S^0{\pi}^{+}{\pi}^{-}{e}^{+}{\nu}_e $$$$
is reported. In the hypothesis that all events correspond toK
1(1270) decays, the branching fractions are measured to be$$$$ \mathcal{B}\left({D}^0\to {K}_1{(1270)}^{-}\left(\to {K}_S^0{\pi}^{-}{\pi}^0\right){e}^{+}{\nu}_e\right)=\left({1.69}_{-0.46}^{+0.53}\pm 0.15\right)\times {10}^{-4} $$$$
and$$$$ \mathcal{B}\left({D}^{+}\to {\overline{K}}_1{(1270)}^0\left(\to {K}_S^0{\pi}^{+}{\pi}^{-}\right){e}^{+}{\nu}^e\right)=\left({1.47}_{-0.40}^{+0.45}\pm 0.14\right)\times {10}^{-4} $$$$
with statistical significance of 5.4σand 5.6σ, respectively. When combined with measurements of theK
1(1270)→ K
+π
−πdecays, the absolute branching fractions are determined to be$$$$ \mathcal{B}\left({D}^0\to {K}_1{(1270)}^{-}{e}^{+}{\nu}_e\right)=\left({1.08}_{-0.13-0.10}^{+0.14+0.08}\pm 0.21\right)\times {10}^{-3} $$$$
and$$$$ \mathcal{B}\left({D}^{+}\to {\overline{K}}_1{(1270)}^0{e}^{+}{\nu}_e\right)=\left({1.70}_{-0.23}^{+0.26}\pm 0.13\pm 0.35\right)\times {10}^{-3} $$$$
. The first and second uncertainties are statistical and systematic, respectively, and the third uncertainties originate from the assumed branching fractions of theK
1(1270)→ Kππdecays.
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