Observation of the semileptonic decays $D^0→ K_S^0π^-π^0 e^+ ν_e$ and $D^+→ K_S^0π^+π^- e^+ ν_e$

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→ KS⁰π⁻π⁰ e⁺ νₑ and D⁺→ KS⁰π⁺π⁻ e⁺ νₑ is reported. With a dominant hadronic contribution from K₁(1270), the branching fractions are measured to be B(D⁰→ K₁(1270)⁻(→ K⁰Sπ⁻π⁰)e⁺νₑ)=(1.69+0.53-0.46±0.15)×10⁻⁴ and B(D⁺→ K̄₁(1270)⁰(→ K⁰Sπ⁺π⁻)e⁺νₑ)=(1.47+0.45-0.40±0.20)×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 B(D⁰→ K₁(1270)⁻e⁺νₑ)=(1.05+0.33-0.28±0.12±0.12)×10⁻³ and B(D⁺→ K̄₁(1270)⁰e⁺νₑ)=(1.29+0.40-0.35±0.18±0.15)×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.