High Energy Physics - Lattice · arXiv:hep-lat/0209124 v3 · submitted 15 Sep 2002
I=2 Pion Scattering Phase Shift with Wilson Fermions
The paper says
“The phase shift is successfully calculated over the momentum range $0 < p^2 < 0.3 {\rm GeV}^2$.”
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Abstract
We present a lattice QCD calculation of the scattering phase shift for the I=2 S-wave two-pion system using the finite size method proposed by Lüscher. We work in the quenched approximation employing the standard plaquette action at β = 5.9 for gluons and the Wilson fermion action for quarks. The phase shift is extracted from the energy eigenvalues of the two-pion system, which are obtained by a diagonalization of the pion 4-point function evaluated for a set of relative spatial momenta. In order to change momentum of the two-pion system, calculations are carried out on 243 × 60, 323 × 60, and 483 × 60 lattices. The phase shift is successfully calculated over the momentum range $0 < p^2 < 0.3 {\rm GeV}^2$.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.59 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.67 · compares with prior results 0.05 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v3). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We present a lattice QCD calculation of the scattering phase shift for the I=2 $S$-wave two-pion system using the finite size method proposed by L\"uscher. | contribution 1.00 | 0.96 | 0.17 | asserted 1.00 |
| We work in the quenched approximation employing the standard plaquette action at $\beta=5.9$ for gluons and the Wilson fermion action for quarks. | method 0.99 | 0.87 | 0.03 | asserted 0.99 |
| The phase shift is extracted from the energy eigenvalues of the two-pion system, which are obtained by a diagonalization of the pion 4-point function evaluated for a set of relative spatial momenta. | method 1.00 | 0.93 | 0.07 | asserted 1.00 |
| In order to change momentum of the two-pion system, calculations are carried out on $24^3\times 60$, $32^3\times 60$, and $48^3\times 60$ lattices. | method 1.00 | 0.94 | 0.02 | asserted 0.99 |
| The phase shift is successfully calculated over the momentum range $0 < p^2 < 0.3 {\rm GeV}^2$. | result 1.00 | 0.96 | 0.68 | asserted 1.00 |
What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00
What was examined, and what was not
Sources read
- arXiv listing abstract v3
Not examined
- full text
- figures and tables
- references and citing sentences
- relations to other papers
Levels run
- P abstract
Not run
- S sections
- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,409 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 6 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD hep-lat · Jun 2005
- Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD hep-lat · Mar 2004
- Two Nucleons on a Lattice hep-lat · Dec 2003
- Generalized L\"uscher Formula in Multi-channel Baryon-Meson Scattering hep-lat · Sep 2012
- Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD hep-lat · Jun 2007
- Lattice simulations for few- and many-body systems nucl-th · Apr 2008
How the literature uses it
8 arXiv papers cite this in 8 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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We present results of phase shift for I=2 $S$-wave $\pi\pi$ system with the Wilson fermions in the quenched approximation.
Papers citing it · 1 sentence without a confident label
Cites it as background 7 papers
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The first lattice calculations of $ππ$ scattering were performed in quenched QCD [ref] , and the first partially-quenched QCD calculation of $ππ$ scattering (the scattering length and phase-shift) was carried through by the CP-PACS collaboration, who exploited the finite-volume strategy to study $I=2$, s-wave scattering with two flavors ($n_f=2$) of improved Wilson fermions [ref] , with pion masses in the range $m_π≃0.5-1.1 GeV$.
Hadronic Interactions from Lattice QCD · Introduction · 0.98
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Such numerical calculations (usually involving phase shifts and scattering lengths) have been calculated using Wilson lattice actions [ref] along with a several other lattice actions [ref] .
Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory · Introduction · 0.85
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The first lattice calculations of $ππ$ scattering were performed in quenched QCD [ref] , and the first full-QCD calculation of $ππ$ scattering (the scattering length and phase-shift) was carried through by the CP-PACS collaboration, who exploited the finite-volume strategy to study $I=2$, s-wave scattering with two flavors ($n_f=2$) of improved Wilson fermions [ref] , with pion masses in the range $m_π≃0.5-1.1 GeV$.
Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD · Introduction · 0.98
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