Observation of the semileptonic decays $$ {\textrm{D}}^0\to {\textrm{K}}_{\textrm{S}}^0{\pi}^{-}{\pi}^0{\textrm{e}}^{+}{\nu}_{\textrm{e}} $$ and $$ {\textrm{D}}^{+}\to {\textrm{K}}_{\textrm{S}}^0{\pi}^{+}{\pi}^{-}{\textrm{e}}^{+}{\nu}_{\textrm{e}} $$
Abstract By analyzinge + e − annihilation data corresponding to an integrated luminosity of 2.93 fb −1 collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the first observation of the semileptonic decays$$ {D}^0\to {K}_S^0{\pi}^{-}{\pi}^0{e}^{+}{\nu}_e $$ D 0 → K S 0 π − π 0 e + ν e and$$ {D}^{+}\to {K}_S^0{\pi}^{+}{\pi}^{-}{e}^{+}{\nu}_e $$ D + → K S 0 π + π − e + ν e is reported. In the hypothesis that all events correspond toK 1 (1270) decays, the branching fractions are measured to be$$ \mathcal{B}\left({D}^0\to {K}_1{(1270)}^{-}\left(\to {K}_S^0{\pi}^{-}{\pi}^0\right){e}^{+}{\nu}_e\right)=\left({1.69}_{-0.46}^{+0.53}\pm 0.15\right)\times {10}^{-4} $$ B D 0 → K 1 1270 − → K S 0 π − π 0 e + ν e = 1.69 − 0.46 + 0.53 ± 0.15 × 10 − 4 and$$ \mathcal{B}\left({D}^{+}\to {\overline{K}}_1{(1270)}^0\left(\to {K}_S^0{\pi}^{+}{\pi}^{-}\right){e}^{+}{\nu}^e\right)=\left({1.47}_{-0.40}^{+0.45}\pm 0.14\right)\times {10}^{-4} $$ B D + → K ¯ 1 1270 0 → K S 0 π + π − e + ν e = 1.47 − 0.40 + 0.45 ± 0.14 × 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$$ \mathcal{B}\left({D}^0\to {K}_1{(1270)}^{-}{e}^{+}{\nu}_e\right)=\left({1.08}_{-0.13-0.10}^{+0.14+0.08}\pm 0.21\right)\times {10}^{-3} $$ B D 0 → K 1 1270 − e + ν e = 1.08 − 0.13 − 0.10 + 0.14 + 0.08 ± 0.21 × 10 − 3 and$$ \mathcal{B}\left({D}^{+}\to {\overline{K}}_1{(1270)}^0{e}^{+}{\nu}_e\right)=\left({1.70}_{-0.23}^{+0.26}\pm 0.13\pm 0.35\right)\times {10}^{-3} $$ B D + → K ¯ 1 1270 0 e + ν e = 1.70 − 0.23 + 0.26 ± 0.13 ± 0.35 × 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.