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

Pion-nucleon scattering in the Roper channel from lattice QCD

Journal Article · Mon Jan 30 23:00:00 EST 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.95.014510· OSTI ID:1398393

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)

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.

View Accepted Manuscript (DOE)

Research Organization:: Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-06OR23177

OSTI ID:: 1398393

Alternate ID(s):: OSTI ID: 1341928

Report Number(s):: JLAB-THY--16-2330; DOE/OR/23177--3953; arXiv:1610.01422

Journal Information:: Physical Review D, Journal Name: Physical Review D Journal Issue: 1 Vol. 95; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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