Amplitude analysis of the charmed baryon decay Lambda_c+ to p K_S^0 pi0

Using e⁺e⁻ annihilation data corresponding to an integrated luminosity of 4.5 fb⁻¹ collected with the BESIII detector at center-of-mass energies between 4.600 and 4.699 GeV, the first amplitude analysis of the charmed baryon decay Λc⁺ → p KS⁰ π⁰ is performed. The processes Λc⁺ → p K̄*(892)⁰, Λc⁺ → Δ(1600)⁺ KS⁰, and Λc⁺ → N(1710)⁺ KS⁰ are identified with statistical significances of $12.8σ$, $14.5σ$, and $6.2σ$, respectively. The mass and width of Δ(1600)⁺ are measured to be (1520.4 ± 8.8 ± 37.7)~MeV and (199.4 ± 26.4 ± 39.9)~MeV, respectively. The mass and width of N(1710)⁺ are measured to be (1719.7 ± 9.4 ± 9.1)~MeV and (72.0 ± 18.0 ± 15.0)~MeV, respectively. The branching fractions of these processes are determined to be B[Λc⁺ → Δ(1600)⁺ (→ p π⁰) KS⁰] = (8.10 ± 0.80 ± 5.57) × 10⁻³, B[Λc⁺ → N(1710)⁺ (→ p π⁰) KS⁰] = (1.58 ± 0.48 ± 0.77) × 10⁻³, and B[Λc⁺ → p K̄*(892)⁰ (→ KS⁰ π⁰)] = (2.63 ± 0.47 ± 0.29) × 10⁻³, where the first uncertainties are statistical and the second systematic.