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

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:
 [1] ;  [2] ;  [3] ;  [4]
  1. Univ. of Graz, Graz (Austria)
  2. Univ. of Arizona, Tucson, AZ (United States)
  3. Univ. of Graz, Graz (Austria); Univ. Regensburg, Regensburg (Germany)
  4. 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:
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
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)
Research Org:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
OSTI Identifier:
1398393
Alternate Identifier(s):
OSTI ID: 1341928

Lang, Christian B., Leskovec, L., Padmanath, M., and Prelovsek, Sasa. Pion-nucleon scattering in the Roper channel from lattice QCD. United States: N. p., Web. doi:10.1103/PhysRevD.95.014510.
Lang, Christian B., Leskovec, L., Padmanath, M., & Prelovsek, Sasa. Pion-nucleon scattering in the Roper channel from lattice QCD. United States. doi:10.1103/PhysRevD.95.014510.
Lang, Christian B., Leskovec, L., Padmanath, M., and Prelovsek, Sasa. 2017. "Pion-nucleon scattering in the Roper channel from lattice QCD". United States. doi:10.1103/PhysRevD.95.014510. https://www.osti.gov/servlets/purl/1398393.
@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 = {2017},
month = {1}
}