{"arxiv_id":"hep-lat/0402025","incoming":{"papers":36,"sentences":51,"groups":[{"kind":"contests","label":"Contests it","papers":1,"sentences":3,"quotes":[{"arxiv_id":"2204.02756","title":"Vector boson scattering from the lattice","url":"/paper/2204.02756","section":"Generalized Zeta-function $𝒵_Jm^d(r,q^2)$","sentence":"[equation] Note, that here the first sum does include $y=0$ not as stated in the published version of [ref] .","intent_p":0.5,"contests_p":0.9}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":3,"sentences":3,"quotes":[{"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":"Method","sentence":"The $δ_0(k)$ can be computed by the Lüscher formula [ref] , [equation] where the dimensionless momentum $q=kL/(2π)$ and the zeta function $𝒵_00(1;q^2)$ is formally expressed by [equation] We generally compute the zeta function by the method discussed in Ref. [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2404.15666","title":"Spectroscopy with the tensor renormalization group method","url":"/paper/2404.15666","section":"INTRODUCTION","sentence":"Furthermore, we will show a scattering phase shift obtained from the two-particle state energy using Lüscher's formula [ref] .","intent_p":0.99,"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":"Phase shifts","sentence":"While the extension to moving frames is straightforward [ref] , we limit our discussion to the case of the rest frame, where one obtains the two-pion $s$-wave scattering phase shift $δ(E_ππ)$ corresponding to a given two-pion energy as follows: [equation] where $E_ππ$ is the energy of the two-pion state in a finite box of size $L^3$, $m_π$ is the pion mass and $Z_00(1,q^2)$ is the Lüscher zeta function, which we compute via an efficient numerical implementation given in Ref. [ref] .","intent_p":0.87,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":4,"sentences":4,"quotes":[{"arxiv_id":"1107.5023","title":"The I=2 pipi S-wave Scattering Phase Shift from Lattice QCD","url":"/paper/1107.5023","section":"Chiral Interpolation of the Phase Shift","sentence":"Fig. [ref] compares the phase shift prediction to the Lattice QCD phase-shift determination by CP-PACS [ref] , and the Roy equation determinations of the phase shift from Refs. [ref] .","intent_p":0.99,"contests_p":null},{"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":"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":"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":"For other lattice studies [ref] , it is actually close to this number.","intent_p":0.93,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":16,"sentences":16,"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":"1107.5023","title":"The I=2 pipi S-wave Scattering Phase Shift from Lattice QCD","url":"/paper/1107.5023","section":"Introduction","sentence":"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] .","intent_p":0.88,"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":"The full lattice study of the $s$-wave $I=2$ $ππ$ scattering length was first carried out by CP-PACS [ref] .","intent_p":0.96,"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}]}],"unlabelled_sentences":25},"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/0402025"}}