Universality and Leading Corrections in Few-Body Systems

TL;DR

This paper discusses how effective field theory can be used to analyze universal behaviors and leading corrections in few-body systems with large scattering lengths, focusing on three-body bound states and their spectrum.

Contribution

It introduces a method to incorporate finite-range effects into EFT analysis of universal few-body phenomena, extending previous zero-range models.

Findings

EFT effectively describes universal behavior in large scattering length systems.

Finite-range corrections modify the three-body bound state spectrum.

Discrete scale invariance persists with finite-range effects included.

Abstract

A large two-body scattering length leads to universal behavior in few-body systems. In particular, the three-body system displays interesting features such as exact discrete scale invariance in the bound state spectrum in the limit of infinite scattering length. Here, I will discuss how an effective field theory (EFT) can be used to study these features and how the finite range of the underlying interaction impacts the bound state spectrum at first order in the EFT expansion.