Evolution of Efimov States

TL;DR

This paper investigates the evolution of Efimov states in relativistic three-body systems, revealing their complex trajectories and universal scaling behavior as they transition between virtual states, bound states, and resonances.

Contribution

It introduces a relativistic scattering theory approach to trace Efimov states' trajectories and addresses the missing states problem with new insights.

Findings

Efimov states follow cyclic trajectories in the complex energy plane.

Universal scaling of energies and couplings observed near unitarity.

Proposal of a partial resolution to the missing states problem.

Abstract

The Efimov phenomenon manifests itself as an emergent discrete scaling symmetry in the quantum three-body problem. In the unitarity limit, it leads to an infinite tower of three-body bound states with energies forming a geometric sequence. In this work, we study the evolution of these so-called Efimov states using relativistic scattering theory. We identify them as poles of the three-particle $S$ matrix and trace their trajectories in the complex energy plane as they evolve from virtual states through bound states to resonances. We dial the scattering parameters toward the unitarity limit and observe the emergence of the universal scaling of energies and couplings -- a behavior known from the non-relativistic case. Interestingly, we find that Efimov resonances follow unusual, cyclic trajectories accumulating at the three-body threshold and then disappear at some values of the two-body scattering length. We propose a partial resolution to this "missing states" problem.