Coupled-Channel Dynamics of $T_{c\bar{s}}$ in $D_{s1}(2460\mathrm{/}2536)\to D_s\pi \pi$

The $T_{c\bar{s}}$ state observed in the decay $D_{s1}(2460{)}^{+}\to D_s^{+}{\pi }^{+}{\pi }^{-}$ provides direct evidence for an isovector open-charm tetraquark state with strangeness. We develop a unified theoretical framework that consistently incorporates triangle loops and $DK$-$D_s\pi$ rescattering. Especially, $DK$-$D_s\pi$ coupled-channel interactions through off-diagonal potential terms provide a novel perspective on the origin of the $T_{c\bar{s}}$ pole. Based on the systematic description of the $D_{s1}$ mass spectrum, the two-peak structure in $D_{s1}(2460)$ decay is perfectly reproduced, and explained by the interference of the $f_0$ resonance and rescattering diagrams. In contrast, only one-peak structure is predicted in $D_{s1}(2536)$ decay, since it is dominated by rescattering only. This difference originates from the $S$- and $D$-wave dominance for $D_{s1}(2460)$ and $D_{s1}(2536)$ coupling with $D^{\ast }K$ channel, respectively, which reflects the internal structures of the two $D_{s1}$ 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.