Supercircle description of universal three-body states in two dimensions

Bound states of asymmetric three-body systems confined to two dimensions are currently unknown. In the universal regime, two energy ratios and two mass ratios provide complete knowledge of the three-body energy measured in units of one two-body energy. We compute the three-body energy for general systems using numerical momentum-space techniques. The lowest number of stable bound states is produced when one mass is larger than two similar masses. We focus on selected asymmetric systems of interest in cold atom physics. The scaled three-body energy and the two scaled two-body energies are related through an equation for a supercircle whose radius increases almost linearly with three-body energy. The exponents exhibit an increasing behavior with three-body energy. The mass dependence is highly nontrivial. Based on our numerical findings, we give a simple relation that predicts the universal three-body energy. © 2012 American Physical Society.