# Three-particle quantization condition in a finite volume: 1. The role of the three-particle force

## TL;DR

This paper uses effective field theory to analyze the energy shifts of three-particle bound states, highlighting the impact of three-particle forces and extending the analysis beyond the unitary limit.

## Contribution

It introduces a formalism incorporating three-particle forces into the energy shift calculations, allowing for a transition from weakly bound states to two-particle bound states.

## Key findings

- Three-particle force significantly affects energy shifts.
- Smooth transition from three-particle to two-particle bound states.
- Extended analysis beyond the unitary limit.

## Abstract

Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory formalism allows us to investigate the role of the three-particle force, which has not been taken into account in the earlier treatment of the problem. Moreover, we are able to relax the requirement of the unitary limit of infinite scattering length and demonstrate a smooth transition from the weakly bound three-particle state to a two-particle bound state of a particle and a deeply bound dimer.