Particle-dimer approach for the Roper resonance in a finite volume

TL;DR

This paper introduces a novel finite-volume approach using a particle-dimer model to analyze the Roper resonance, integrating two- and three-body dynamics with effective field theory, and compares predictions with lattice QCD data.

Contribution

It presents a new formalism for finite-volume analysis of resonances based on a particle-dimer picture, enhancing the understanding of multi-body effects in lattice QCD.

Findings

Predicted finite-volume energy levels for the Roper resonance.

Compared theoretical predictions with existing lattice QCD results.

Provided guidance on the precision needed for finite-volume spectrum measurements.

Abstract

We propose a new finite-volume approach which implements two- and three-body dynamics in a transparent way based on an Effective Field Theory Lagrangian. The formalism utilizes a particle-dimer picture and formulates the quantization conditions based on the self-energy of the decaying particle. The formalism is studied for the case of the Roper resonance, using input from lattice QCD and phenomenology. Finally, finite-volume energy eigenvalues are predicted and compared to existing results of lattice QCD calculations. This crucially provides initial guidance on the necessary level of precision for the finite-volume spectrum.