2023/09/18 by Jun-Zhang Wang, Wang, Jun-Zhang, Zi-Yang Lin +3 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Nuclear Theory (nucl-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2309.09861
openalex publication_date 2023/09/18 · openalex created_date 2023/09/20 · openalex updated_date 2026/07/28
The three-body threshold effect, the distinctive and intriguing non-perturbative dynamics in the low-energy hadron-hadron scattering, has acquired compelling significance in the wake of the recent observation of the double-charm tetraquark Tcc+. This dynamics is characterized by the emergence of singular points and branch cuts within the interaction potential, occurring when the on-shell condition of the mediated particle is satisfied. The presence of these potential singularities indicates that the system is no longer Hermitian and also poses intractable challenges in obtaining exact solutions for dynamical scattering amplitudes. In this work, we develop a complex scaled Lippmann-Schwinger equation as an operation of analytical continuation of the T matrix to resolve this problem. Through a practical application to the DD^* → DD^* process, we reveal complicated cut structures of the three-body threshold dynamics in the complex plane, primarily stemming from the one-pion exchange. Notably, our methodology succeeds in reproducing the Tcc+ structure, in alignment with the quasi-bound pole derived from the complex scaling method within the Schrödinger equation framework. More remarkably, after solving the on-shell T matrix on the positive real axis of momentum plane, we find an extra new structure in the DD^* mass spectrum, which arises from a right-hand cut at a physical pion mass and should be observable in Lattice QCD simulations and future high-energy experiments.