Three-body resonances in the $\varphi^4$ theory

TL;DR

This paper investigates three-body resonances in a lattice $ ext{φ}^4$ theory, comparing two formal approaches to extract resonance properties, and finds consistent results for the resonance mass and width.

Contribution

It demonstrates the equivalence of two three-particle finite-volume formalisms in analyzing lattice spectra and accurately determines resonance parameters in a scalar field theory.

Findings

Both methods yield consistent energy spectra.

Resonance pole positions agree across approaches.

The formalism accurately extracts resonance mass and width.

Abstract

We study the properties of three-body resonances using a lattice complex scalar $\varphi^4$ theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy-plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.