Probing the nature of D₁ K and D₂ K molecules through Dₛ(*)π π and Dₛ₀₍ₛ₁₎π decays

We study the two- and three-body decays of the $$I=0$$ I = 0 D₁K D 1 K and D₂K D 2 K molecular states Tcs̄1^* T c s ¯ 1 ∗ and Tcs̄2^* T c s ¯ 2 ∗ into Dₛ(*) D s ( ∗ ) mesons and pions. Triangle singularities produce narrow peaks in the Dₛ^*π D s ∗ π and Dₛπ D s π invariant mass spectra near the D^*K D ∗ K and DK thresholds. The isospin-violating two-body decays Tcs̄1^*→ Dₛ₁(2460)π ⁰ T c s ¯ 1 ∗ → D s 1 ( 2460 ) π 0 , Tcs̄2^*→ Dₛ₁(2460)π ⁰ T c