Towards the finite-volume spectrum of the Roper resonance

TL;DR

This paper investigates finite-volume energy levels related to the Roper resonance using chiral effective theories and introduces a particle-dimer framework to include three-body dynamics, aiding in extracting the Roper mass from lattice data.

Contribution

It develops a non-relativistic particle-dimer effective field theory to incorporate three-particle interactions for the Roper resonance in finite volume.

Findings

Finite-volume energy levels can determine the Roper mass.

The particle-dimer approach effectively models three-particle scattering.

Comparison shows consistency between chiral Lagrangian and particle-dimer results.

Abstract

The finite-volume energy levels corresponding to the Roper resonance based on a two-flavor chiral effective Lagrangian at leading one-loop order are investigated. It is shown that the Roper mass can be extracted from these levels for not too large lattice volumes. Further, to include three-body $N \pi \pi$ dynamics, a non-relativistic effective field theory for the Roper resonance within a covariant particle-dimer picture is introduced. This particle-dimer approach is a suitable framework to investigate three-particle scattering relevant for the Roper channel. The appearing dimer fields are analyzed, the energy levels of the Roper resonance in a finite volume are calculated and compared to the results from the chiral effective Lagrangian.