Nucleon resonance structure in the finite volume of lattice QCD

Abstract

An approach for relating the nucleon resonances extracted from $\pi N$ reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of $\pi N$ reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance pole positions can be related to the probability $P_{N^{\ast }}(E)$ of finding the bare state, $N^{\ast }$, in the $\pi N$ scattering states in infinite volume. We further demonstrate that the probability $P_{N^{\ast }}^V(E)$ of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches $P_{N^{\ast }}(E)$ as the volume increases. Our findings suggest that the comparison of $P_{N^{\ast }}(E)$ and $P_{N^{\ast }}^V(E)$ can be used to examine whether the nucleon resonances extracted from the $\pi N$ reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of $P_{N^{\ast }}^V(E)$ directly from lattice QCD. The practical differences between our approach and the approach using the Lüscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.

29 pages, 12 figures

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Cited by in corpus (14)

• Three-body Unitarity in the Finite Volume
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Structure of the Roper Resonance from Lattice QCD Constraints
• The S- and P-wave low-lying baryons in the chiral quark model
• Partial Wave Mixing in Hamiltonian Effective Field Theory
• Hamiltonian effective field theory in elongated or moving finite volume
• More about the light baryon spectrum
• 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
• Inverse scattering problem with a bare state
• Quark model study of the $\pi N\to \pi N$ reactions up to the $N(1440)$ resonance region
• Chiral Analysis of the Nucleon Mass and Sigma Commutator
• Nucleon Excited States from Lattice QCD and Hamiltonian Effective Field Theory
• Towards the continuum coupling in nuclear lattice effective field theory I: A three-particle model