Relativistic-invariant formulation of the NREFT three-particle quantization condition

TL;DR

This paper develops a relativistic-invariant three-particle quantization condition on the lattice using a generalized NREFT approach, explicitly addressing higher partial waves and demonstrating invariance through synthetic data.

Contribution

It introduces a relativistic-invariant formulation of the three-particle quantization condition using NREFT, including higher partial waves and symmetry considerations.

Findings

Relativistic invariance of the three-body spectrum demonstrated

Explicit inclusion of higher partial waves in the quantization condition

Partial diagonalization into irreducible representations achieved

Abstract

A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum.