Two particle states and the<i>S</i>-matrix elements in multi-channel scattering

He, Song; Feng, Xu; Liu, Chuan

doi:10.1088/1126-6708/2005/07/011

Cited by 227 publications

(239 citation statements)

References 22 publications

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“…In the literature this is known as the Lüscher method [260,266]; originally formulated for the case of a particle at rest, the framework has been generalised to moving frames [267][268][269] and to multi-channel problems, see e.g. [270][271][272][273][274][275] and references therein.…”

Section: Extracting the Hadron Spectrum From Qcdmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

418

530

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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Section: Extracting the Hadron Spectrum From Qcdmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

418

530

View full text Add to dashboard Cite

show abstract

“…In particular, the Lüscher method and its extensions for relating finite-volume spectra to scattering amplitudes are now well established for elastic [5][6][7][8][9][10][11][12][13][14] and coupled-channel [15][16][17][18][19] hadron-hadron scattering. These methods have been demonstrated in a number of applications, notably for the ρ-resonance seen in P -wave ππ scattering [20][21][22][23][24][25][26][27][28][29], and for the σ resonance seen in S-wave ππ scattering [30].…”

Section: Jhep10(2016)011mentioning

confidence: 99%

Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD

Moir

Peardon

Ryan

et al. 2016

J. High Energ. Phys.

172

266

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We present the first lattice QCD study of coupled-channel Dπ, Dη and D sK scattering in isospin-1/2 in three partial waves. Using distillation, we compute matrices of correlation functions with bases of operators capable of resolving both meson and mesonmeson contributions to the spectrum. These correlation matrices are analysed using a variational approach to extract the finite-volume energy eigenstates. Utilising Lüscher's method and its extensions, we constrain scattering amplitudes in S, P and D-wave as a function of energy. By analytically continuing the scattering amplitudes to complex energies, we investigate the S-matrix singularities. Working at m π ≈ 391 MeV, we find a pole corresponding to a J P = 0 + near-threshold bound state with a large coupling to Dπ. We also find a deeply bound J P = 1 − state, and evidence for a J P = 2 + narrow resonance coupled predominantly to Dπ. Elastic Dπ scattering in the isospin-3/2 channel is studied and we find a weakly repulsive interaction in S-wave.

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“…(27) are unprimed and the ellipses denote terms that are higher order in the α, 1/L and 1/M expansions and in the ERE. Eq.…”

Section: B Quantization Condition Including Qedmentioning

confidence: 99%

“…Recently, Lüscher's formalism has been extended to coupled-channels systems (i.e. channels that are coupled in infinite-volume), and to systems comprised of particles with non-zero spin [26][27][28][29][30][31][32][33][34][35][36][37][38]. Further, the FV formalism describing nucleon-nucleon (NN) systems with arbitrary CM momenta, spin, angular momentum, isospin and twisted boundary conditions has been developed, providing the quantization conditions (QCs) for the energy eigenvalues in irreducible representations (irreps) of the FV symmetry groups [39].…”

Section: Introductionmentioning

confidence: 99%

Two-particle elastic scattering in a finite volume including QED

2014

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The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Lüscher. While in infinite volume, QED contributions to low-energy charged particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the A + 1 irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of Lattice QCD+QED calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves.

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Two particle states and theS-matrix elements in multi-channel scattering

Cited by 227 publications

References 22 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD

Two-particle elastic scattering in a finite volume including QED

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