Constraining the DDD* three-body bound state via the Zc(3900) pole

Abstract

In this study, we propose using the Zc(3900) pole position to constrain the existence of the DDD* three-body bound state within the one-boson-exchange (OBE) model. The existence of the DDD* bound state remains uncertain due to significant variations in the OBE interaction, particularly in the strength of scalar-meson-exchange interactions, which can differ by a factor about 20 between two commonly used OBE models. This discrepancy renders the DDD* system highly model-dependent. To address this issue, we constrain the scalar-meson-exchange interaction using the Zc(3900) pole position, where the pseudoscalar-meson coupling is well-determined, and the ρ- and ω-exchange interactions nearly cancel each other out, leaving the coupling constant of the σ-exchange as the only unknown parameter. Our results indicate that the isospin-12 DDD* bound states exist when Zc(3900) is a virtual state of DD¯*/D¯D* located within approximately −15 MeV of the threshold. However, the three-body bound state is gone when the Zc(3900) virtual state pole is more than 20 MeV away from the threshold. Each experimental progress, either on the DDD* state or the Zc(3900), can shed light on the nature of the other state. Another significant outcome is a refined set of OBE model parameters calibrated using the pole positions of X(3872), Tcc(3875), and Zc(3900), rigorously addressing the cutoff dependence. These parameters provide a valuable resource for more accurate calculations of systems involving few-body D, D*, and their antiparticles. Additionally, we find no evidence of the DDD* three-body resonances after extensive search using a combination of the Gaussian expansion method and the complex scaling method. Published by the American Physical Society 2025