Universality of three-body systems in 2D: parametrization of the bound states energies

TL;DR

This paper investigates the universal properties of 2D three-body systems with mass imbalance, providing a parametrization of their bound state energies using supercircle functions, revealing complex dependencies on masses and two-body energies.

Contribution

It introduces a novel parametrization of three-body bound state energies in 2D systems with mass imbalance using supercircle functions, enhancing understanding of their universal properties.

Findings

Dependence of three-particle binding energy on masses and two-body energies is highly non-trivial.

Bound state energies are parametrized using supercircle functions.

The approach applies to both ground and excited states of three distinguishable particles.

Abstract

Universal properties of mass-imbalanced three-body systems in 2D are studied using zero-range interactions in momentum space. The dependence of the three-particle binding energy on the parameters (masses and two-body energies) is highly non-trivial even in the simplest case of two identical particles and a distinct one. This dependence is parametrized for ground and excited states in terms of {\itshape supercircles} functions in the most general case of three distinguishable particles.