Hamiltonian effective field theory study of the ${\mathbf{N}}^{\ast }(1440)$ resonance in lattice QCD

Abstract

We examine the phase shifts and inelasticities associated with the $N^{\ast }(1440)$ Roper resonance and connect these infinite-volume observables to the finite-volume spectrum of lattice QCD using Hamiltonian effective field theory. We explore three hypotheses for the structure of the Roper resonance. All three hypotheses are able to describe the scattering data well. In the third hypothesis the Roper resonance couples the low-lying bare basis-state component associated with the ground state nucleon with the virtual meson-baryon contributions. Here the non-trivial superpositions of the meson-baryon scattering states are complemented by bare basis-state components explaining their observation in contemporary lattice QCD calculations. The merit of this scenario lies in its ability to not only describe the observed nucleon energy levels in large-volume lattice QCD simulations but also explain why other low-lying states have been missed in today's lattice QCD results for the nucleon spectrum.

14 pages, 14 figures; version to be published in Phys. Rev. D

References in corpus (11)

• Baryons as relativistic three-quark bound states
• Dynamical coupled-channel model of meson production reactions in the nucleon resonance region
• Lattice QCD Evidence that the Lambda(1405) Resonance is an Antikaon-Nucleon Molecule
• A study of the $P_{11}(1440)$ and $D_{13}(1520)$ resonances from CLAS data on $ep\to e^{\prime }{\pi }^{+}{\pi }^{-}{p}^{\prime }$
• New results on the Roper resonance and the P_{11} partial wave
• Pion-nucleon scattering in the Roper channel from lattice QCD
• Chiral extrapolation of nucleon magnetic form factors
• A novel analysis method for excited states in lattice QCD - the nucleon case
• Lattice baryon spectroscopy with multi-particle interpolators
• The role of $qqqq\bar{q}$ components in the nucleon and the N(1440) resonance
• Roper resonances in chiral quark models

Cited by in corpus (14)

• Three-body Unitarity in the Finite Volume
• Hamiltonian effective field theory in elongated or moving finite volume
• ${\Lambda }_c(2910)$ and ${\Lambda }_c(2940)$ as the conventional baryons dressed with the $D^{\ast }N$ channel
• Particle-dimer approach for the Roper resonance in a finite volume
• Pion Photoproduction off Nucleon with Hamiltonian Effective Field Theory
• Two-body wave functions and compositeness from scattering amplitudes: II. Application to the physical $N^{\ast }$ and ${\Delta }^{\ast }$ resonances
• Pion photoproduction of nucleon excited states with Hamiltonian effective field theory
• Inverse scattering problem with a bare state
• Structure of the ${\Omega }^{-}(2012)$ with Hamiltonian Effective Field Theory
• The Roper Resonance in a finite volume
• Chiral Analysis of the Nucleon Mass and Sigma Commutator
• $\Delta$ baryon spectroscopy in lattice QCD
• Odd-Parity Nucleon Electromagnetic Transitions in Lattice QCD
• Understanding the 1P- and 2S-wave nucleon resonances within the extended Lee-Friedrichs Model