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

TL;DR

Addresses the isovector open-charm tetraquark candidate $T_{c\bar{s}}$ in the decay $D_{s1}(2460)^+\to D_s^+\pi^+\pi^-$ and develops a unified framework that includes triangle loops and $DK$-$D_s\pi$ rescattering. The off-diagonal potential $V_{DK\to D_s\pi}$ drives the resonance, with diagonal interactions vanishing in the $I=1$ channel; the $D_{s1}$ spectrum fixes the $D_{s1}D^*K$ vertices, enabling a simultaneous description of $D_{s1}(2460)$ and $D_{s1}(2536)$ decays. The analysis reproduces the two-peak structure in $D_{s1}(2460)^+$ decay via interference between triangle diagrams and rescattering, while the $D_{s1}(2536)^+$ decay is dominated by rescattering, yielding a broad single peak; a pole on the second Riemann sheet is extracted. The framework explains the role of $S$- and $D$-wave couplings at the $D_{s1}D^*K$ vertex and the impact of different form-factor cutoffs on the effective potential. It yields predictions for $D_{s1}(2536)^+\to D_s^+\pi^+\pi^-$ lineshapes and provides a holistic method to connect spectroscopy and decay, with implications for LHCb, Belle II, and the Electron-Ion Collider.

Abstract

The $T_{c\bar{s}}$ state observed in the decay $D_{s1}(2460)^+ \to D_s^+π^+π^-$ provides direct evidence for an isovector open-charm tetraquark state with strangeness. We develop a unified theoretical framework that consistently incorporates triangle loops and $DK$-$D_sπ$ rescattering. Especially, $DK$-$D_sπ$ 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 $D^*K$ 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.

Figures (5)

• Figure 1: The illustrative Feynman diagrams for $D_{s1}(2460)$ and $D_{s1}(2536)$ decays into $D_s^+\pi^+\pi^-$.
• Figure 2: The fitted lineshapes of the $T_{c\bar{s}}$ in the $D^+_s\pi^+$ and $\pi^+\pi^-$ invariant mass spectrum. The labels (a), (b), and (c) correspond to the contributions from the individual Feynman diagrams. The "++" and "+-" notations refer to the $D_s^+\pi^+$ and $D_s^+\pi^-$ final states in the $T$-matrix calculation, respectively. Here we use the efficiency-corrected data provided by the LHCb collaboration LHCb:2024iuo.
• Figure 3: The Dalitz plot of the $D_{s1}(2460)^+\to D_s^+\pi^+\pi^-$ process from our fit (left), compared with the detected LHCb result (right).
• Figure 4: The predicted lineshape of the $D_{s1}(2536)^+\to D_s^+\pi^+\pi^-$.
• Figure 5: The predicted dalitz plot of the $D_{s1}(2536)^+\to D_s^+\pi^+\pi^-$ process.