Pion-nucleon scattering in the Roper channel from lattice QCD

Abstract

We present a lattice QCD study of $N\pi$ scattering in the positive-parity nucleon channel, where the puzzling Roper resonance $N^{\ast }(1440)$ resides in experiment. The study is based on the PACS-CS ensemble of gauge configurations with $N_f=2+1$ Wilson-clover dynamical fermions, $m_{\pi }\simeq 156$MeV and $L\simeq 2.9$fm. In addition to a number of $qqq$ interpolating fields, we implement operators for $N\pi$ in $p$-wave and $N\sigma$ in $s$-wave. In the center-of-momentum frame we find three eigenstates below 1.65 GeV. They are dominated by $N(0)$, $N(0)\pi (0)\pi (0)$ (mixed with $N(0)\sigma (0)$) and $N(p)\pi (-p)$ with $p\simeq 2\pi /L$, where momenta are given in parentheses. This is the first simulation where the expected multi-hadron states are found in this channel. The experimental $N\pi$ phase-shift would -- in the approximation of purely elastic $N\pi$ scattering -- imply an additional eigenstate near the Roper mass $m_R\simeq 1.43$GeV for our lattice size. We do not observe any such additional eigenstate, which indicates that $N\pi$ elastic scattering alone does not render a low-lying Roper. Coupling with other channels, most notably with $N\pi \pi$, seems to be important for generating the Roper resonance, reinforcing the notion that this state could be a dynamically generated resonance. Our results are in line with most of previous lattice studies based just on $qqq$ interpolators, that did not find a Roper eigenstate below $1.65$GeV. The study of the coupled-channel scattering including a three-particle decay $N\pi \pi$ remains a challenge.

arXiv comment14 pages, 9 figures, version published in Phys. Rev. D plus additional footnote and reference

References in corpus (37)

• The Spectrum of the Nucleons and the Strange Hyperons and Chiral Dynamics
• 2+1 Flavor Lattice QCD toward the Physical Point
• Excited state baryon spectroscopy from lattice QCD
• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• Multiple-channel generalization of Lellouch-Luscher formula
• Unified description of light- and strange-baryon spectra
• The Pentaquark Candidates in the Dynamical Diquark Picture
• Roy-Steiner-equation analysis of pion-nucleon scattering
• What is the structure of the Roper resonance?
• Scattering phases for meson and baryon resonances on general moving-frame lattices
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Dynamical coupled-channel model of meson production reactions in the nucleon resonance region
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Unitarized Chiral Perturbation Theory in a finite volume: scalar meson sector
• Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
• Coupled channel analysis of the rho meson decay in lattice QCD
• Resonances in coupled πK,ηK scattering from quantum chromodynamics
• An $a_0$ resonance in strongly coupled $\pi \eta$, $K\overline{K}$ scattering from lattice QCD
• QCD with Two Light Dynamical Chirally Improved Quarks: Baryons
• A study of the $P_{11}(1440)$ and $D_{13}(1520)$ resonances from CLAS data on $ep\to e^{\prime }{\pi }^{+}{\pi }^{-}{p}^{\prime }$
• Parameterization dependence of T matrix poles and eigenphases from a fit to piN elastic scattering data
• Scattering in the pion-nucleon negative parity channel in lattice QCD
• Roper Resonance and S_{11}(1535) from Lattice QCD
• Structure and Flow of the Nucleon Eigenstates in Lattice QCD
• A novel analysis method for excited states in lattice QCD - the nucleon case
• Wave Function of the Roper from Lattice QCD
• The role of $qqqq\bar{q}$ components in the nucleon and the N(1440) resonance
• Excited nucleons with chirally improved fermions
• Nucleon Excited State Wave Functions from Lattice QCD
• Nucleon Excited States in N${}_f$=2 lattice QCD
• Isolating the Roper Resonance in Lattice QCD
• N* Spectroscopy from Lattice QCD: The Roper Explained
• Roper resonances in chiral quark models
• A Perspective on Pentaquarks
• N^* electroproduction amplitudes in a model with dynamical confinement
• Review on Hadron Spectroscopy

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