Coupled-channel scattering on a torus

Guo, Peng; Dudek, Jozef J.; Edwards, Robert G.; Szczepaniak, Adam P.

doi:10.1103/physrevd.88.014501

Cited by 169 publications

(184 citation statements)

References 46 publications

(90 reference statements)

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“…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%

“…Having determined the finite-volume spectra, we relate these to infinite-volume scattering amplitudes using the Lüscher method [5,6] and its extensions to moving frames [7,10,13,51] and coupled-channels [16][17][18]52]. In this approach, the dependence of the spectra on finite volume is used as a tool but exponentially-suppressed corrections in the volume are neglected -typically the leading such corrections fall off as e −mπL and, since our volumes have m π L ∼ 4 to 6, we can safely neglect these.…”

Section: Scattering Amplitudes From Finite-volume Spectramentioning

confidence: 99%

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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.

171

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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Section: Jhep10(2016)011mentioning

confidence: 99%

Section: Scattering Amplitudes From Finite-volume Spectramentioning

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.

171

266

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show abstract

“…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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“…Theoretical developments addressing finite-volume effects for three-body systems are pioneered in Refs. [48][49][50][51][52][53][54], although much conceptual work, including three-body unitarity constraints, remains to be done.…”

Section: Discussionmentioning

confidence: 99%

Resonance Extraction from the Finite Volume

Döring¹,

Molina²

2016

Proceedings of the 10th International Workshop on the Physics of Excited Nucleons (NSTAR2015)

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The spectrum of excited hadrons becomes accessible in simulations of Quantum Chromodynamics on the lattice. Extensions of Lüscher's method allow to address multi-channel scattering problems using moving frames or modified boundary conditions to obtain more eigenvalues in finite volume. As these are at different energies, interpolations are needed to relate different eigenvalues and to help determine the amplitude. Expanding the T -or the K-matrix locally provides a controlled scheme by removing the known non-analyticities of thresholds. This can be stabilized by using Chiral Perturbation Theory. Different examples to determine resonance pole parameters and to disentangle resonances from thresholds are discussed, like the scalar meson f 0 (980) and the excited baryons N (1535)1/2 − and Λ(1405)1/2 − .

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Coupled-channel scattering on a torus

Cited by 169 publications

References 46 publications

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

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

Resonance Extraction from the Finite Volume

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