Pion-nucleon scattering in the Roper channel from lattice QCD

Lang, Christian B.; Leskovec, L.; Padmanath, M.; Prelovsek, Sasa

doi:10.1103/PhysRevD.95.014510

Title: 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 $N^*(1440)$ 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. As a result, the study of the coupled-channel scattering including a three-particle decay $$N\pi\pi$$ remains a challenge.

Authors:

Lang, Christian B. ^[1]; Leskovec, L. ^[2]; Padmanath, M. ^[3]; Prelovsek, Sasa ^[4]

Univ. of Graz, Graz (Austria)
Univ. of Arizona, Tucson, AZ (United States)
Univ. of Graz, Graz (Austria); Univ. Regensburg, Regensburg (Germany)
Univ. of Ljubljana, Ljubljana (Slovenia); Jozef Stefan Institute, Ljubljana (Slovenia); Univ. Regensburg, Regensburg (Germany); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Tue Jan 31 00:00:00 EST 2017

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1398393

Alternate Identifier(s):: OSTI ID: 1341928

Report Number(s):: JLAB-THY-16-2330; DOE/OR/23177-3953; arXiv:1610.01422
Journal ID: ISSN 2470-0010; PRVDAQ

Grant/Contract Number:: FWF:I1313-N27; SFB/TRR 55; AC05-06OR23177

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 95; Journal Issue: 1; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Lang, Christian B., Leskovec, L., Padmanath, M., and Prelovsek, Sasa. Pion-nucleon scattering in the Roper channel from lattice QCD.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevD.95.014510.

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                    Lang, Christian B., Leskovec, L., Padmanath, M., & Prelovsek, Sasa. Pion-nucleon scattering in the Roper channel from lattice QCD.  United States.  https://doi.org/10.1103/PhysRevD.95.014510

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                    Lang, Christian B., Leskovec, L., Padmanath, M., and Prelovsek, Sasa. Tue .  
"Pion-nucleon scattering in the Roper channel from lattice QCD".  United States.  https://doi.org/10.1103/PhysRevD.95.014510.  https://www.osti.gov/servlets/purl/1398393.

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@article{osti_1398393,

  title        = {Pion-nucleon scattering in the Roper channel from lattice QCD},

  author       = {Lang, Christian B. and Leskovec, L. and Padmanath, M. and Prelovsek, Sasa},

  abstractNote = {We present a lattice QCD study of $N\pi$ scattering in the positive-parity nucleon channel, where the puzzling Roper resonance $N^*(1440)$ 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. As a result, the study of the coupled-channel scattering including a three-particle decay $N\pi\pi$ remains a challenge.},

  doi          = {10.1103/PhysRevD.95.014510},

  journal      = {Physical Review D},

  number       = 1,

  volume       = 95,

  place        = {United States},

  year         = {Tue Jan 31 00:00:00 EST 2017},

  month        = {Tue Jan 31 00:00:00 EST 2017}

}

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Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B.
Physical Review D, Vol. 95, Issue 3
DOI: 10.1103/physrevd.95.034034

Valence quark contributions for the $γ^{*} N \to N (1440)$ form factors from light-front holography
journal, February 2018

Ramalho, G.; Melnikov, D.
Physical Review D, Vol. 97, Issue 3
DOI: 10.1103/physrevd.97.034037

Variational approach to $N$ -body interactions in finite volume
journal, November 2018

Guo, Peng; Döring, Michael; Szczepaniak, Adam P.
Physical Review D, Vol. 98, Issue 9
DOI: 10.1103/physrevd.98.094502

Three-body unitarity in the finite volume
journal, December 2017

Mai, M.; Döring, M.
The European Physical Journal A, Vol. 53, Issue 12
DOI: 10.1140/epja/i2017-12440-1

The impact of $K^{+}\Lambda$ K + Λ photoproduction on the resonance spectrum
journal, June 2018

Rönchen, D.; Döring, M.; Meißner, U. -G.
The European Physical Journal A, Vol. 54, Issue 6
DOI: 10.1140/epja/i2018-12541-3

Excited-state effects in nucleon structure on the lattice using hybrid interpolators
text, January 2019

Green, Jeremy R.; Engelhardt, Michael; Hasan, Nesreen
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-04199

Structure of the Roper Resonance from Lattice QCD Constraints
text, January 2017

Wu, Jia-jun; Leinweber, Derek B.; Liu, Zhan-wei
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DOI: 10.48550/arxiv.1703.10715

Three-body Unitarity in the Finite Volume
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Three-body unitarity versus finite-volume $π^+π^+π^+$ spectrum from lattice QCD
text, January 2019

Mai, M.; Döring, M.; Culver, C.
arXiv
DOI: 10.48550/arxiv.1909.05749

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Similar Records

Title: Pion-nucleon scattering in the Roper channel from lattice QCD

Abstract

Citation Formats

Wave function of the Roper from lattice QCD journal, August 2013

Are there baryons which contain constituent gluons? journal, July 1983

Multiple-channel generalization of Lellouch-Lüscher formula journal, July 2012

Review of Particle Physics journal, August 2014

Unified description of light- and strange-baryon spectra journal, October 1998

Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD journal, June 2011

Dynamical coupled-channel model of meson production reactions in the nucleon resonance region journal, February 2007

Evidence for a P 11 Pion-Nucleon Resonance at 556 MeV journal, March 1964

N∗ electroproduction amplitudes in a model with dynamical confinement journal, December 2001

Cluster model of baryons journal, July 1983

2 + 1 flavor lattice QCD toward the physical point journal, February 2009

Parameterization dependence of T -matrix poles and eigenphases from a fit to π N elastic scattering data journal, September 2012

The pentaquark candidates in the dynamical diquark picture journal, October 2015

Experimental study of the P 11 ( 1440 ) and D 13 ( 1520 ) resonances from the CLAS data on e p → e ′ π + π − p ′ journal, September 2012

A remnant of chiral symmetry on the lattice journal, May 1982

Novel quark-field creation operator construction for hadronic physics in lattice QCD journal, September 2009

Structure and flow of the nucleon eigenstates in lattice QCD journal, May 2013

Nucleon excited state wave functions from lattice QCD journal, March 2014

QCD with two light dynamical chirally improved quarks: Baryons journal, April 2013

N * Spectroscopy from Lattice QCD: The Roper Explained conference, May 2016

How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation journal, July 1990

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude journal, December 2015

A perspective on pentaquarks journal, February 2004

What is the structure of the Roper resonance? journal, July 2000

Roy–Steiner-equation analysis of pion–nucleon scattering journal, April 2016

Electroproduction of the Roper resonance as a hybrid state journal, July 1992

Excited state baryon spectroscopy from lattice QCD journal, October 2011

Isolating the Roper resonance in lattice QCD journal, August 2009

Scattering in the π N negative parity channel in lattice QCD journal, March 2013

Scattering phases for meson and baryon resonances on general moving-frame lattices journal, November 2012

Coupled channel analysis of the ρ meson decay in lattice QCD journal, September 2011

Isoscalar π π Scattering and the σ Meson Resonance from QCD journal, January 2017

Excited nucleons with chirally improved fermions journal, May 2004

Resonances in Coupled π K − η K Scattering from Quantum Chromodynamics journal, October 2014

Extended coupled channels model for π N scattering and the structure of N * ( 1440 ) and N * ( 1535 ) journal, March 1998

Novel analysis method for excited states in lattice QCD: The nucleon case journal, January 2015

On the generalized eigenvalue method for energies and matrix elements in lattice field theory journal, April 2009

The role of components in the nucleon and the resonance journal, December 2006

Signatures of unstable particles in finite volume journal, October 1991

Baryons in a relativized quark model with chromodynamics journal, November 1986

The spectrum of the nucleons and the strange hyperons and chiral dynamics journal, April 1996

Nucleon excited states in N f = 2 lattice QCD journal, February 2014

An a 0 resonance in strongly coupled π η , K K ¯ scattering from lattice QCD journal, May 2016

Two-particle states on a torus and their relation to the scattering matrix journal, May 1991

Adjoint sources in lattice gauge theory journal, September 1985

Roper resonances in chiral quark models journal, November 2008

Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector journal, November 2011

Erratum: Are there baryons which contain constituent gluons? journal, February 1986

Baryons in a relativized quark model with chromodynamics conference, January 1985

Scattering phases for meson and baryon resonances on general moving-frame lattices text, January 2012

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states journal, June 1986

Novel quark-field creation operator construction for hadronic physics in lattice QCD text, January 2009

Review of Particle Physics text, January 2008

Roy–Steiner-equation analysis of pion–nucleon scattering journal, January 2017

Multiple-channel generalization of Lellouch-Lüscher formula conference, December 2012

Novel quark-field creation operator construction for hadronic physics in lattice QCD text, January 2009

Isoscalar ππ Scattering and the σ Meson Resonance from QCD text, January 2017

Review of Particle Physics text, January 2018

Review of Particle Physics text, January 2012

On the generalized eigenvalue method for energies and matrix elements in lattice field theory text, January 2009

Isolating the Roper Resonance in Lattice QCD text, January 2009

Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD text, January 2011

Coupled channel analysis of the rho meson decay in lattice QCD text, January 2011

Scattering phases for meson and baryon resonances on general moving-frame lattices text, January 2012

Structure and Flow of the Nucleon Eigenstates in Lattice QCD text, January 2013

Nucleon Excited State Wave Functions from Lattice QCD text, January 2013

A novel analysis method for excited states in lattice QCD - the nucleon case text, January 2014

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude text, January 2015

The Pentaquark Candidates in the Dynamical Diquark Picture text, January 2015

Roy-Steiner-equation analysis of pion-nucleon scattering text, January 2015

N* Spectroscopy from Lattice QCD: The Roper Explained text, January 2015

N^* electroproduction amplitudes in a model with dynamical confinement text, January 2001

Roper Resonance and S_{11}(1535) from Lattice QCD text, January 2003

Excited nucleons with chirally improved fermions text, January 2003

The Spectrum of the Nucleons and the Strange Hyperons and Chiral Dynamics text, January 1995

Unified description of light- and strange-baryon spectra text, January 1997

What is the structure of the Roper resonance? text, January 1999

Wave function of the Roper from lattice QCD
journal, August 2013

Are there baryons which contain constituent gluons?
journal, July 1983

Multiple-channel generalization of Lellouch-Lüscher formula
journal, July 2012

Review of Particle Physics
journal, August 2014

Unified description of light- and strange-baryon spectra
journal, October 1998

Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
journal, June 2011

Dynamical coupled-channel model of meson production reactions in the nucleon resonance region
journal, February 2007

Evidence for a $P_{11}$ Pion-Nucleon Resonance at 556 MeV
journal, March 1964

N∗ electroproduction amplitudes in a model with dynamical confinement
journal, December 2001

Cluster model of baryons
journal, July 1983

$2 + 1$ flavor lattice QCD toward the physical point
journal, February 2009

Parameterization dependence of $T$ -matrix poles and eigenphases from a fit to $π N$ elastic scattering data
journal, September 2012

The pentaquark candidates in the dynamical diquark picture
journal, October 2015

Experimental study of the $P_{11} (1440)$ and $D_{13} (1520)$ resonances from the CLAS data on $e p \to e^{'} π^{+} π^{-} p^{'}$
journal, September 2012

A remnant of chiral symmetry on the lattice
journal, May 1982

Novel quark-field creation operator construction for hadronic physics in lattice QCD
journal, September 2009

Structure and flow of the nucleon eigenstates in lattice QCD
journal, May 2013

Nucleon excited state wave functions from lattice QCD
journal, March 2014

QCD with two light dynamical chirally improved quarks: Baryons
journal, April 2013

N * Spectroscopy from Lattice QCD: The Roper Explained
conference, May 2016

How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation
journal, July 1990

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015

A perspective on pentaquarks
journal, February 2004

What is the structure of the Roper resonance?
journal, July 2000

Roy–Steiner-equation analysis of pion–nucleon scattering
journal, April 2016

Electroproduction of the Roper resonance as a hybrid state
journal, July 1992

Excited state baryon spectroscopy from lattice QCD
journal, October 2011

Isolating the Roper resonance in lattice QCD
journal, August 2009

Scattering in the $π N$ negative parity channel in lattice QCD
journal, March 2013

Scattering phases for meson and baryon resonances on general moving-frame lattices
journal, November 2012

Coupled channel analysis of the $ρ$ meson decay in lattice QCD
journal, September 2011

Isoscalar $π π$ Scattering and the $σ$ Meson Resonance from QCD
journal, January 2017

Excited nucleons with chirally improved fermions
journal, May 2004

Resonances in Coupled $π K − η K$ Scattering from Quantum Chromodynamics
journal, October 2014

Extended coupled channels model for $π N$ scattering and the structure of $N^{} (1440)$ and $N^{} (1535)$
journal, March 1998

Novel analysis method for excited states in lattice QCD: The nucleon case
journal, January 2015

On the generalized eigenvalue method for energies and matrix elements in lattice field theory
journal, April 2009

The role of components in the nucleon and the resonance
journal, December 2006

Signatures of unstable particles in finite volume
journal, October 1991

Baryons in a relativized quark model with chromodynamics
journal, November 1986

The spectrum of the nucleons and the strange hyperons and chiral dynamics
journal, April 1996

Nucleon excited states in $N_{f} = 2$ lattice QCD
journal, February 2014

An $a_{0}$ resonance in strongly coupled $π η$ , $K \bar{K}$ scattering from lattice QCD
journal, May 2016

Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991

Adjoint sources in lattice gauge theory
journal, September 1985

Roper resonances in chiral quark models
journal, November 2008

Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector
journal, November 2011

Erratum: Are there baryons which contain constituent gluons?
journal, February 1986

Baryons in a relativized quark model with chromodynamics
conference, January 1985

Scattering phases for meson and baryon resonances on general moving-frame lattices
text, January 2012

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

Novel quark-field creation operator construction for hadronic physics in lattice QCD
text, January 2009

Review of Particle Physics
text, January 2008

Roy–Steiner-equation analysis of pion–nucleon scattering
journal, January 2017

Multiple-channel generalization of Lellouch-Lüscher formula
conference, December 2012

Novel quark-field creation operator construction for hadronic physics in lattice QCD
text, January 2009

Isoscalar ππ Scattering and the σ Meson Resonance from QCD
text, January 2017

Review of Particle Physics
text, January 2018

Review of Particle Physics
text, January 2012

On the generalized eigenvalue method for energies and matrix elements in lattice field theory
text, January 2009

Isolating the Roper Resonance in Lattice QCD
text, January 2009

Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
text, January 2011

Coupled channel analysis of the rho meson decay in lattice QCD
text, January 2011

Scattering phases for meson and baryon resonances on general moving-frame lattices
text, January 2012

Structure and Flow of the Nucleon Eigenstates in Lattice QCD
text, January 2013

Nucleon Excited State Wave Functions from Lattice QCD
text, January 2013

A novel analysis method for excited states in lattice QCD - the nucleon case
text, January 2014

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
text, January 2015

The Pentaquark Candidates in the Dynamical Diquark Picture
text, January 2015

Roy-Steiner-equation analysis of pion-nucleon scattering
text, January 2015

N* Spectroscopy from Lattice QCD: The Roper Explained
text, January 2015

N^* electroproduction amplitudes in a model with dynamical confinement
text, January 2001

Roper Resonance and S_{11}(1535) from Lattice QCD
text, January 2003

Excited nucleons with chirally improved fermions
text, January 2003

The Spectrum of the Nucleons and the Strange Hyperons and Chiral Dynamics
text, January 1995

Unified description of light- and strange-baryon spectra
text, January 1997

What is the structure of the Roper resonance?
text, January 1999

A Lattice QCD Study of Pion–Nucleon Scattering in the Roper Channel
journal, June 2018

The S- and P-Wave Low-Lying Baryons in the Chiral Quark Model
journal, July 2018

Developments of the Jülich–Bonn Dynamical Coupled-Channel Analysis
journal, October 2018