From Three-Body Resonances to Bound States in a Continuum: Pole Trajectories

We investigate the formation of three-body bound states in the continuum from resonances by tracing their pole trajectories in the complex energy plane under variation of system parameters. Using a one-dimensional model of two identical bosons and a distinguishable particle interacting via Gaussian potentials, we systematically vary the interaction strength, interaction range, and mass ratio. Our results confirm the single-resonance parametric nature of such three-body bound states in a continuum and extend this characterization to a broader parameter space. While all parameter variations lead to formation of such states, the mass ratio exhibits a richer structure with multiple locations arranged in regular oscillatory trajectories. All three parameters show width minima at a common value of the relative momentum between outgoing subsystems, suggesting some robustness in the formation mechanism.