High Energy Physics - Lattice · arXiv:hep-lat/0409063 v1 · submitted 14 Sep 2004
I=2 Pion Scattering Length from Two-Pion Wave Function
The paper says
“We also find that the scattering length can be extracted with a smaller statistical error from the wave function than with a time correlation function used in previous studies.”
from the abstract · picked out as the main claim by a classifier
Reviews
Reviews by people
No person has reviewed this paper on Pith yet. A scientist listed on Pith can review it for a fee, and their review is published here whatever it concludes.
The paper
Abstract
We present a report on a calculation of scattering length for I=2 S-wave two-pion system from two-pion wave function. Calculations are made with an RG-improved action for gluons and improved Wilson action for quarks at $a^{-1}=1.207(12) {\rm GeV}$ on 163 × 80, 203 × 80 and 243 × 80 lattices. We investigate the validity of necessary condition for application of Lüscher's formula through the wave function. We find that the condition is satisfied for lattice volumes $L\ge 3.92 {\rm fm}$ for the quark mass range $m_\pi^2 = 0.273-0.736 {\rm GeV}^2$. We also find that the scattering length can be extracted with a smaller statistical error from the wave function than with a time correlation function used in previous studies.
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.
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 0.04 · states limitation 0.70 · human participants 0.01 · controlled comparison 0.18 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.87 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We present a report on a calculation of scattering length for I=2 $S$-wave two-pion system from two-pion wave function. | contribution 1.00 | 0.95 | 0.15 | asserted 0.96 |
| Calculations are made with an RG-improved action for gluons and improved Wilson action for quarks at $a^{-1}=1.207(12) {\rm GeV}$ on $16^3 \times 80$, $20^3 \times 80$ and $24^3 \times 80$ lattices. | method 1.00 | 0.94 | 0.03 | asserted 0.99 |
| We investigate the validity of necessary condition for application of L\"uscher's formula through the wave function. | contribution 0.69 | 0.85 | 0.05 | asserted 0.74 |
| We find that the condition is satisfied for lattice volumes $L\ge 3.92 {\rm fm}$ for the quark mass range $m_\pi^2 = 0.273-0.736 {\rm GeV}^2$. | result 1.00 | 0.97 | 0.22 | asserted 1.00 |
| We also find that the scattering length can be extracted with a smaller statistical error from the wave function than with a time correlation function used in previous studies. | result 0.99 | 0.95 | 0.31 | 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 v1
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, 4,452 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 2 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
- Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD hep-lat · Jun 2007
How the literature uses it
6 arXiv papers cite this in 8 sentences
Papers whose main result relates to this one's
States the same result 1 paper
-
We conclude that the necessary condition is satisfied within the statistical errors for the lattice sizes $L\ge 24$ ($3.92 {\rm fm}$) when the quark mass is in the range that corresponds to $m_\pi^2 = 0.273-0.736 {\rm GeV}^2$.
I=2 Pion Scattering Length from Two-Pion Wave Functions · 0.90
Papers citing it · 2 sentences without a confident label
Uses its method or tool 1 paper
-
The wavefunction given in Eq. ([ref]), $ϕ(|x|;k)∼Z_ππ(|x|;k) ψ_ππ(|x|;k)$ satisfies the Schrodinger equation [ref] [equation] where $U_k(x,y)$ is the Fourier transform of the modified Bethe-Salpeter kernel for the $π^+π^+$ interaction, which is generally nonlocal and energy-dependent [ref] .
Nuclear Physics from Lattice QCD · Scattering Parameters from Wavefunctions. · 0.83
Cites it as background 5 papers
-
There have been independent lattice QCD determinations of the $π^+π^+$ scattering length; with three flavors ($n_f=2+1$) of light quarks using domain-wall valence quarks on asqtad-improved staggered sea quarks [ref] , and with two flavors ($n_f=2$) of light quarks using twisted-mass quarks [ref] and improved Wilson quarks [ref] .
The I=2 pipi S-wave Scattering Phase Shift from Lattice QCD · Introduction · 0.88
-
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
-
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
Challenges and discussion
Know something about this paper? Leave a comment.
Come back by email
A short list of the week's newly reviewed papers. Nothing is sent until you confirm from your inbox, and every email has a link that stops it. No account.
No comments yet.
Sign in to comment