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From three-body resonances to bound states in a continuum: pole trajectories

We investigate the formation of three-body bound states in the continuum by tracing 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 parametric nature of few-body bound states in a continuum (BIC) and extend this characterization to a broader set of system parameters. Specifically, we find that variations of both interaction parameters and the mass ratio can lead to the formation of at least one three-body BIC. However, the exact shape of trajectories differs, and for the mass ratio variation we find a more regular pattern with multiple BIC locations. These results suggest that the mechanism of few-body BIC formation is more sensitive to the kinematic structure of the problem than to the specific details of the two-body interaction.