An Effective Theory for the Four-Body System

TL;DR

This paper develops an effective theory for non-relativistic four-body systems with large scattering lengths, explaining the correlation between three- and four-body binding energies through the absence of a four-body force at leading order.

Contribution

It introduces an effective contact interaction theory for four-body systems and explains the observed energy correlations without needing a four-body force.

Findings

Calculated binding energies of 4He tetramer and alpha-particle.

Established the linear correlation between three- and four-body energies.

Showed the absence of a four-body force at leading order explains observed correlations.

Abstract

We consider the non-relativistic four-body system with large scattering length and short-range interactions within an effective theory with contact interactions only. We compute the binding energies of the 4He tetramer and of alpha-particle. The well-known linear correlation between the three-body binding energies and the four-body binding energies of these physical systems can be understood as a consequence of the absence of a four-body force at leading order.