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

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.

arXiv comment37 pages, 8 figures, some minor modifications, accepted for publication in JHEP

References in corpus (86)

• Universality in Few-body Systems with Large Scattering Length
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• The $XYZ$ states: experimental and theoretical status and perspectives
• Pentaquark and Tetraquark states
• Heavy-Quark QCD Exotica
• Ab-initio Determination of Light Hadron Masses
• Renormalization of the Three-Body System with Short-Range Interactions
• Baryons as relativistic three-quark bound states
• Extended Partial-Wave Analysis of piN Scattering Data
• The Three-Boson System with Short-Range Interactions
• Quasi-Two-Body Decays of Nonstrange Baryons
• Toward the excited meson spectrum of dynamical QCD
• The light baryon spectrum in a relativistic quark model with instanton-induced quark forces I. The non-strange baryon spectrum and ground-states
• Progress Toward Understanding Baryon Resonances
• A relativistic, model-independent, three-particle quantization condition
• Roy-Steiner-equation analysis of pion-nucleon scattering
• Interaction model for the gap equation
• What is the structure of the Roper resonance?
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• More Effective Field Theory for Nonrelativistic Scattering
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Three particles in a finite volume
• Three-particle scattering amplitudes from a finite volume formalism
• Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
• Three-body Unitarity in the Finite Volume
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• Resonance properties from the finite-volume energy spectrum
• Lattice QCD and Three-particle Decays of Resonances
• QCD with Two Light Dynamical Chirally Improved Quarks: Baryons
• Three-body spectrum in a finite volume: the role of cubic symmetry
• Cusps in K --> 3 pi decays
• Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD
• $I=3$ three-pion scattering amplitude from lattice QCD
• Towards a theory of hadron resonances
• Pion-nucleon scattering in the Roper channel from lattice QCD
• Rho resonance parameters from lattice QCD
• Spectrum of three-body bound states in a finite volume
• Implementing the three-particle quantization condition including higher partial waves
• Generalizing the relativistic quantization condition to include all three-pion isospin channels
• Three pion spectrum in the $I=3$ channel from lattice QCD
• Two-pole structures in QCD: Facts, not fantasy!
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• An solvable three-body model in finite volume
• Three-body Unitarity with Isobars Revisited
• Review of the $\mathbf{\Lambda }$(1405): A curious case of a strange-ness resonance
• Finite-volume energy spectrum of the $K^{-}{K}^{-}{K}^{-}$ system
• Extraction of isoscalar $\pi \pi$ phase-shifts from lattice QCD
• Three-body interactions from the finite-volume QCD spectrum
• Relativistic three-particle quantization condition for nondegenerate scalars
• QCD and the Strange Baryon Spectrum
• Hamiltonian effective field theory study of the ${\mathbf{N}}^{\ast }(1440)$ resonance in lattice QCD
• Light Baryon Spectroscopy
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Scattering of two and three physical pions at maximal isospin from lattice QCD
• Cusps in K --> 3pi decays: a theoretical framework
• Three-particle finite-volume formalism for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• A novel analysis method for excited states in lattice QCD - the nucleon case
• One spatial dimensional finite volume three-body interaction for a short-range potential
• A cross-channel study of pion scattering from lattice QCD
• $DDK$ system in finite volume
• Lattice investigation of the scalar mesons a_0(980) and κ using four-quark operators
• Search for low-lying lattice QCD eigenstates in the Roper regime
• Isospin-0 $\pi \pi$ s-wave scattering length from twisted mass lattice QCD
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Pion scattering in the isospin I=2 channel from elongated lattices
• Finite-volume energy shift of the three-pion ground state
• Multiple-particle interaction in $1+1$ dimensional lattice model
• Three-particle bound states in a finite volume: unequal masses and higher partial waves
• The $\rho$-resonance with physical pion mass from $N_f=2$ lattice QCD
• P-wave nucleon-pion scattering amplitude in the $\Delta (1232)$ channel from lattice QCD
• Multi-${\pi }^{+}$ systems in finite volume
• Decay amplitudes to three hadrons from finite-volume matrix elements
• Nucleon Excited States in N${}_f$=2 lattice QCD
• Determination of Delta resonance parameters from lattice QCD
• Three-body resonances in the ${\phi }^4$ theory
• On the three-particle analog of the Lellouch-Lüscher formula
• Propagation of particles on a torus
• The width of the Roper resonance in baryon chiral perturbation theory
• Study of decuplet baryon resonances from lattice QCD
• Toward $N$ to $N\pi$ matrix elements from lattice QCD
• Spurious poles in a finite volume
• The Beauty of Spin
• The Roper Resonance in a finite volume

Cited by in corpus (2)

• Finite-volume energy shift of the three-nucleon ground state
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD