{"arxiv_id":"hep-lat/0506013","incoming":{"papers":34,"sentences":68,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":2,"sentences":9,"quotes":[{"arxiv_id":"1506.00408","title":"Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-2 $\\pi\\pi$ scattering length","url":"/paper/1506.00408","section":"Chiral Extrapolation","sentence":"The NLO $χ$PT expression for $M_πa_0$ written as a function of $(M_π/f_π)$ at a $χ$PT renormalisation scale $μ_R=f_π,phys$ reads [ref] [equation] with $ℓ_ππ$ related to the Gasser-Leutwyler coefficients $ℓ̅_i$ as follows [ref] [equation] Moreover, one can show in Twisted mass $χ$PT that the leading lattice artefacts to $M_πa_0$ are of order $𝒪(a^2M_π^2)$ [ref] .","intent_p":0.83,"contests_p":null},{"arxiv_id":"1303.0517","title":"Lattice QCD study of the s-wave $\\pi\\pi $ scattering lengths in the I=0 and 2 channels","url":"/paper/1303.0517","section":"$I=0$ channel","sentence":"For each lattice ensemble, the energies $a E$ of the $ππ$ system for the $I = 0$ channel are secured from the “effective energy” plots, and chosen by looking for a combination of a “plateau” in the energy as the function of $D_min$, a good confidence level and $D_min$ large enough to suppress the excited states [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1012.0453","title":"On the Quark Mass Dependence of Two Nucleon Observables","url":"/paper/1012.0453","section":"Working in the BKV scheme as an explicit example","sentence":"We can study the size of higher order corrections by including the $m_π$ dependence of $M$, $f$ and $g_A$ (these are next-to-next-to-leading-order corrections) which is extracted from lattice data [ref] to Eqs.( [ref],[ref]).","intent_p":1.0,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":5,"sentences":8,"quotes":[{"arxiv_id":"2008.03035","title":"Scattering of two and three physical pions at maximal isospin from lattice QCD","url":"/paper/2008.03035","section":"Discussion","sentence":"We obtain $M_πa_0 = -0.0481(86)$ (see <Ref> and recall $1/B_0 = M_πa_0$), which also agrees well with all phenomenological determinations [ref] , and other lattice results obtained indirectly by extrapolating to the physical point using ChPT [ref] , see <Ref>.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1303.0517","title":"Lattice QCD study of the s-wave $\\pi\\pi $ scattering lengths in the I=0 and 2 channels","url":"/paper/1303.0517","section":"$I=2$ channel","sentence":"These outcomes are comparable with the aforementioned results of theoretical (or phenomenological) studies [ref] , experimental determinations [ref] and lattice calculations [ref] within statistical errors.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1905.10202","title":"Pion scattering in the isospin I=2 channel from elongated lattices","url":"/paper/1905.10202","section":"Effective range expansion","sentence":"The references for other determinations of the scattering length are, in order: NPLQCD2006 [ref] , NPLQCD2008 [ref] , ETMC2010 [ref] , ETMC2015 [ref] , Yagi2011 [ref] , Fu2013 [ref] , and PACS-CS2013 [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"1904.00191","title":"Meson-meson scattering lengths at maximum isospin from lattice QCD","url":"/paper/1904.00191","section":"$I=2, ππ$","sentence":"In <ref>, we compare our result to those of CP-PACS [ref] , NPLQCD (2006) [ref] , NPLQCD (2008) [ref] , ETM (2013) [ref] , this work denoted as ETM (2015), Yagi et al. [ref] , Fu [ref] and PACS-CS [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1905.04277","title":"Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD","url":"/paper/1905.04277","section":"Results","sentence":"A comparison of our scattering length with previous lattice QCD determinations [ref] , together with the experimental value from [ref] , is shown in the supplemental material .","intent_p":1.0,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"0905.3947","title":"The neutral kaon mixing parameter B_K from unquenched mixed-action lattice QCD","url":"/paper/0905.3947","section":"Chiral and continuum extrapolation of $B_K$","sentence":"There have been several studies showing that NLO $SU(3)$ mixed-action and staggered chiral perturbation theory accurately describe the lattice discretization effects even at the rather large taste-splittings on the coarse MILC lattices [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":11,"sentences":11,"quotes":[{"arxiv_id":"1905.10202","title":"Pion scattering in the isospin I=2 channel from elongated lattices","url":"/paper/1905.10202","section":"Introduction","sentence":"The infinite-volume extrapolation of the $π^+π^+$ system was the first physical application of the original Lüscher formalism, for the scattering length [ref] and extended to higher energies [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"2301.09286","title":"Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD","url":"/paper/2301.09286","section":"Introduction","sentence":"With Lüscher's technique [ref] that relates two-pion energy in a finite box with the corresponding scattering phase shift, there have been many studies of two-pion scattering in lattice QCD at unphysical pion masses [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"1303.0517","title":"Lattice QCD study of the s-wave $\\pi\\pi $ scattering lengths in the I=0 and 2 channels","url":"/paper/1303.0517","section":"Introduction","sentence":"Fully-dynamical computation of the $I=2$ $ππ$ scattering was explored by NPLQCD with the domain-wall valence quarks on a fourth-rooted staggered sea quarks [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"1908.01847","title":"A cross-channel study of pion scattering from lattice QCD","url":"/paper/1908.01847","section":"Introduction","sentence":"In this context, pion-pion scattering has been a prime subject for lattice QCD calculations, in isospin $I=2$ [ref] , $I=1$ [ref] , and $I=0$ [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"0802.2931","title":"Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory","url":"/paper/0802.2931","section":"Introduction","sentence":"Additionally, there are currently only two fully dynamical, 2+1 flavor calculations of I=2 $ππ$ scattering, which use mixed lattice actions [ref] .","intent_p":0.89,"contests_p":null}]}],"unlabelled_sentences":38},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/hep-lat/0506013"}}