Coupled-Channel Dynamics of Tcs̄ in Dₛ₁(2460/2536)→ Dₛππ

The Tcs̄ state observed in the decay Dₛ₁(2460)⁺ → Dₛ⁺π⁺π⁻ provides direct evidence for an isovector open-charm tetraquark state with strangeness. We develop a unified theoretical framework that consistently incorporates triangle loops and $DK$-Dₛπ rescattering. Especially, $DK$-Dₛπ coupled-channel interactions through off-diagonal potential terms provide a novel perspective on the origin of the Tcs̄ pole. Based on the systematic description of the Dₛ₁ mass spectrum, the two-peak structure in Dₛ₁(2460) decay is perfectly reproduced, and explained by the interference of the f₀ resonance and rescattering diagrams. In contrast, only one-peak structure is predicted in Dₛ₁(2536) decay, since it is dominated by rescattering only. This difference originates from the S- and D-wave dominance for Dₛ₁(2460) and Dₛ₁(2536) coupling with D^*K channel, respectively, which reflects the internal structures of the two Dₛ₁ states. This unified approach demonstrates how decay and production mechanisms encode different aspects of dynamics, offering an opportunity to disentangle the nature of exotic hadrons.