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Multi-particle systems on the lattice and chiral extrapolations: a brief review
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abstract
The extraction of two- and three-body hadronic scattering amplitudes and the properties of the low-lying hadronic resonances from the finite-volume energy levels in lattice QCD represents a rapidly developing field of research. The use of various modifications of the L\"uscher finite-volume method has opened a path to calculate infinite-volume scattering amplitudes on the lattice. Many new results have been obtained recently for different two- and three-body scattering processes, including the extraction of resonance poles and their properties from lattice data. Such studies, however, require robust parametrizations of the infinite-volume scattering amplitudes, which rely on basic properties of $S$-matrix theory and -- preferably -- encompass systems with quark masses at and away from the physical point. Parametrizations of this kind, provided by unitarized Chiral Perturbation Theory, are discussed in this review. Special attention is paid to three-body systems on the lattice, owing to the rapidly growing interest in the field. Here, we briefly survey the formalism, chiral extrapolation, as well as finite-volume analyses of lattice data.
Forward citations
Cited by 5 Pith papers
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Emergence of the $\pi(1300)$ Resonance from Lattice QCD
Lattice QCD plus three-body scattering formalism yields a π(1300)-like pole at (1169±46)−i(62−62+168) MeV, consistent with experiment.
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The $a_1(1420)$ in a Unitary Coupled-Channel Three-Body Approach
Unitary coupled-channel three-body model fitted to COMPASS data reproduces the a1(1420) enhancement via triangle singularity, indicating no genuine resonance pole is required.
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Coupled-channel approach to isotensor $\pi\pi\pi$ scattering from lattice QCD
The I=2 three-pion spectrum from lattice QCD is described by a repulsive rho-pi S-wave interaction, consistent with a leading-order effective Lagrangian.
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Universal parameters of the $\Lambda(1380)$, the $\Lambda(1405)$ and their isospin partners from a combined analysis of Lattice QCD and experimental results
A combined global fit of lattice QCD spectra and experimental Kbar N data within chiral unitary approaches gives pole positions for the Lambda(1380) and Lambda(1405) at physical and lattice quark masses, with systemat...
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Symmetrizing relativistic three-body partial wave amplitudes
The authors derive spectator-symmetric three-body partial wave amplitudes using new recoupling coefficients for arbitrary angular momentum and isospin, and demonstrate them with 3π Dalitz distributions.
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