Open accessJournal Article

# Multi-particle systems on the lattice and chiral extrapolations: a brief review

02 Mar 2021-European Physical Journal-special Topics (Springer Berlin Heidelberg)-Vol. 230, Iss: 6, pp 1623-1643
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 Luscher 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.

Topics: Lattice QCD (63%), , Lattice (module) (56%) ... read more
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Open accessJournal Article
Tyler D. Blanton1, Stephen R. Sharpe1Institutions (1)
30 Aug 2021-Physical Review D
Abstract: We consider three-particle systems consisting of two identical particles and a third that is different, with all being spinless. Examples include ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{K}^{+}$ and ${K}^{+}{K}^{+}{\ensuremath{\pi}}^{+}$. We derive the formalism necessary to extract two- and three-particle infinite-volume scattering amplitudes from the spectrum of such systems in finite volume. We use a relativistic formalism based on an all-orders diagrammatic analysis in generic effective field theory, adopting the methodology used recently to study the case of three nondegenerate particles. We present both a direct derivation, and also a cross-check based on an appropriate limit and projection of the fully nondegenerate formalism. We also work out the threshold expansions for the three-particle K matrix that will be needed in practical applications, both for systems with two identical particles plus a third, and also for the fully nondegenerate theory.

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5 Citations

Open accessPosted Content
Tyler D. Blanton1, Andrew D. Hanlon2, Ben Hörz3, Colin Morningstar4  +2 moreInstitutions (5)
Abstract: We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant $s$-wave interactions, but also those in $d$ waves. In particular, we determine a term in the three-particle K-matrix that contains only two-particle $d$ waves for the first time. We use three $N_f=2+1$ CLS ensembles with pion masses of $200$, $280$, and $340\;$MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.

Topics: , Lattice QCD (59%), Isospin (55%) ... read more

4 Citations

Open accessJournal Article
Tyler D. Blanton1, Andrew D. Hanlon2, Andrew D. Hanlon3, Ben Hörz4  +3 moreInstitutions (6)
Abstract: We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three Nf = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.

Topics: , Lattice QCD (59%), Isospin (56%) ... read more

2 Citations

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Johan Bijnens1, Tomáš Husek1Institutions (1)
28 Sep 2021-Physical Review D
Abstract: Within the framework of the massive $\mathrm{O}(N)$ nonlinear sigma model extended to the next-to-leading order in the chiral counting [for $N=3$ corresponding to the two(-quark)-flavor Chiral Perturbation Theory], we calculate the relativistic six-pion scattering amplitude at low energy up to and including terms $\mathcal{O}({p}^{4})$. Results for the pion mass, decay constant, and four-pion amplitude in the case of $N$ (meson) flavors at $\mathcal{O}({p}^{4})$ are also presented.

Topics: Order (ring theory) (59%), Scattering amplitude (52%),  ... read more

2 Citations

Open accessJournal Article
Maxim Mai1, Andrei Alexandru2, Andrei Alexandru1, Ruairí Brett1  +5 moreInstitutions (5)
Topics: Lattice QCD (65%),

1 Citations

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307 results found

Open accessJournal Article
J. Gasser1, Heinrich Leutwyler2Institutions (2)
01 Nov 1984-Annals of Physics
Abstract: * in terms of a few constants, which may be identified with the coupling constants of a unique effective low energy Lagrangian. The low energy representation of several Green’s functions and form factors and of the na scattering amplitude are then calculated. The values of the low energy coupling constants are extracted from available experimental data. The corrections of order Mj, to the xz scattering lengths and effective ranges turn out to be substantial and the improved low energy theorems agree very well with the measured phase shifts. The observed differences between the data and the uncorrected soft pion theorems may even be used to measure the scalar radius of the pion, which plays a central role in the low energy expansion. 0 1984 Academic Press, Inc.

Topics: Pion decay constant (61%), ,  ... read more

3,062 Citations

Open accessJournal Article
Jürg Gasser1, Heinrich Leutwyler2Institutions (2)
01 Jan 1985-Nuclear Physics
Abstract: In a previous paper, we have shown how to systematically determine the low-energy structure of the Green functions in QCD. The present article extends this framework to expansions in the mass of the strange quark. We construct the generating functional of U(3)×U(3) which allows us to calculate the Green functions up to and including terms of order p4 (at fixed radio m quark p 2 ) in terms of a few coupling constants which chiral symmetry leaves undetermined. We calculate the first non-leading term in the quark mass expansion of the order parameters 〈0| u u|0〉, 〈0| d d|0〉, 〈0| s s|0〉 , and of the masses and decay constants in the pseudoscalar octet. The three coupling constants which are not fixed by experimental low-energy information are estimated by invoking large-Nc arguments.

Topics: , Strange quark (58%), Quark (56%) ... read more

2,709 Citations

Journal Article
Abstract: The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example)

Topics: Scattering amplitude (65%), Elastic scattering (62%), Scattering (58%) ... read more

1,016 Citations

Open accessJournal Article
Abstract: We review the implications of the spontaneous chiral symmetry breaking in QCD for processes involving one, two, or more nucleons.

Topics: , ,  ... read more

872 Citations

Journal Article
06 May 1991-Nuclear Physics
Abstract: The energy spectrum of a system of two particles enclosed in a box with periodic boundary conditions is characteristic for the forces between the particles. For box sizes greater than the interaction range, and for energies below the inelastic threshold, the spectrum is shown to be determined by the scattering phases at these energies. Simple exact formulae are derived which can be used to compute the energy levels given the scattering phases or, conversely, to calculate the scattering phases if the energy spectrum is known.