Observation of the semileptonic decays D0→KS0π−π0e+νe and D+→KS0π+π−e+νe

By analyzing e⁺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 D⁰→K_S⁰π⁻π⁰e⁺ν_e and D⁺→K_S⁰π⁺π⁻e⁺ν_e is reported. In the hypothesis that all events correspond to K₁(1270) decays, the branching fractions are measured to be BD⁰→K₁1270⁻→K_S⁰π⁻π⁰e⁺ν_e=1.69_−0.46^+0.53±0.15×10⁻⁴ and BD⁺→K¯₁1270⁰→K_S⁰π⁺π⁻e⁺ν^e=1.47_−0.40^+0.45±0.14×10⁻⁴ with statistical significance of 5.4σ and 5.6σ, respectively. When combined with measurements of the K₁(1270) → K⁺π⁻π decays, the absolute branching fractions are determined to be BD⁰→K₁1270⁻e⁺ν_e=1.08_{−0.13−0.10}^+0.14+0.08±0.21×10⁻³ and BD⁺→K¯₁1270⁰e⁺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 the K₁(1270) → Kππ decays.