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Interactions of two and three mesons including higher partial waves from lattice QCD
Tyler D. Blanton,Andrew D. Hanlon,Ben Hörz,Colin Morningstar,Fernando Romero-López,Stephen R. Sharpe +5 more
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In this article, the relativistic finite-volume formalism based on a generic effective field theory was used to determine the parameters of the two-and three-particle K-matrices.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.read more
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Six-pion amplitude
Johan Bijnens,Tomáš Husek +1 more
TL;DR: In this paper, the relativistic six-pion scattering amplitude at low energy up to and including terms $\mathcal{O}({p}^{4})$ was calculated for the case of $N$ (meson) flavors at $N=3$ corresponding to the two-quark-flavor chiral perturbation theory.
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Relativistic-invariant formulation of the three-particle quantization condition.
TL;DR: In this paper, the relativistic invariance of the quantization condition on the lattice of the octahedral group has been demonstrated for the three-body bound state spectrum.
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Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
Maxim Mai,Andrei Alexandru,Ruairí Brett,Chris Culver,Michael Döring,Frank X. Lee,Daniel Sadasivan +6 more
TL;DR: In this paper, the pole position and branching ratios of a three-body resonance were calculated from lattice QCD using one-, two-, and three-meson interpolators and a threebody finite-volume formalism extended to spin and coupled channels.
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Implementing the three-particle quantization condition for $\pi^+\pi^+K^+$ and related systems
TL;DR: In this article, the authors discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition.
References
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Chiral perturbation theory to one loop
J. Gasser,Heinrich Leutwyler +1 more
TL;DR: In this article, the low energy representation of several Green's functions and form factors and of the na scattering amplitude are calculated in terms of a few constants, which may be identified with the coupling constants of a unique effective low energy Lagrangian.
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Volume dependence of the energy spectrum in massive quantum field theories. II. Scattering states
TL;DR: 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 as mentioned in this paper.
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Two-particle states on a torus and their relation to the scattering matrix
TL;DR: In this paper, the energy spectrum of a system of two particles enclosed in a box with periodic boundary conditions is determined by the scattering phases at these energies, and exact exact formulae are derived which can be used to compute the energy levels given the scattering phase.
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How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation
TL;DR: In this paper, a method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the O(3) non-linear σ-model on a simple square lattice.
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Adjoint sources in lattice gauge theory
TL;DR: Variance reduction techniques for the evaluation of Wilson loops in lattice gauge theory are analyzed in this article. But this method is not applicable to adjoint sources, as shown in Section 2.1.
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Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD.
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