Applying the relativistic quantization condition to a three-particle bound state in a periodic box

TL;DR

This paper applies a relativistic three-particle quantization condition to analyze the finite-volume energy shift of a three-particle bound state, confirming previous non-relativistic results and extending them to moving frames.

Contribution

It introduces a relativistic framework for three-particle bound states in finite volume and generalizes existing results to moving frames.

Findings

Reproduces known non-relativistic finite-volume energy shifts

Extends the analysis to systems in moving frames

Validates the relativistic quantization condition for three-particle states

Abstract

Using our recently developed relativistic three-particle quantization condition, we study the finite-volume energy shift of a spin-zero three-particle bound state. We reproduce the result obtained using non-relativistic quantum mechanics by Meissner, Rios and Rusetsky, and generalize the result to a moving frame.