Deep learning topological inference-guided $T_{cc}^{+}$ pole parameter extraction

We perform a data-driven study of the doubly charmed tetraquark candidate $T_{cc}^+$. An ensemble of deep neural network classifiers, trained on synthetic amplitudes with controlled analytic structures, identifies a dominant pole topology characterized by an isolated pole on the $[bt]$ Riemann sheet which is robust against left-hand cut effects. A subsequent pole parameter extraction was performed via the uniformized $\mathcal{S}$-matrix and a complementary $\mathcal{K}$-matrix parameterization, which respectively provides a model-independent baseline and dynamical insight on the pole position and trajectory of the resonant state. Using this two-pronged approach, we submit that the $T_{cc}^{+}$ is a shallow $D^0D^{*+}$ bound state in the second Riemann sheet of the complex plane.

💡 Research Summary

The authors present a novel, data‑driven analysis of the doubly‑charmed tetraquark candidate T_cc^+, combining modern deep‑learning techniques with rigorous coupled‑channel scattering theory. The study begins by outlining the experimental observation of a narrow enhancement just below the D^0 D^{*+} threshold in the D^0 D^0 π^+ invariant‑mass spectrum, and reviews the competing theoretical interpretations (compact tetraquark, loosely bound molecule, virtual state, or kinematic effects). Recognizing that the proximity of multiple thresholds demands a coupled‑channel treatment, the authors construct a two‑channel S‑matrix formalism that respects analyticity, unitarity, and hermiticity.

To handle the multi‑sheeted Riemann surface generated by the two thresholds, they adopt a conformal uniformization variable ω, following Kato’s method, which maps the four‑sheeted s‑plane onto a single ω‑plane. In this representation the S‑matrix elements acquire a compact form expressed through a Jost‑like function Q(ω). Physical poles (ω_pole) and regulator poles (ω_reg) are introduced as free complex parameters, allowing the generation of amplitudes with arbitrary pole topologies across the four sheets. Left‑hand cuts (LHC), arising from t‑channel meson exchange, are incorporated phenomenologically by multiplying each diagonal S‑matrix element by a pure‑phase factor exp