Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations

Abstract

We calculate the one-, two- and three-particle energy levels for different lattice volumes in the complex ${\phi }^4$ theory on the lattice. We argue that the exponentially suppressed finite-volume corrections for the two- and three-particle energy shifts can be reduced significantly by using the single particle mass, which includes the finite-size effects. We show numerically that, for a set of bare parameters, corresponding to the weak repulsive interaction, one can reliably extract the two- and three-particle energy shifts. From those, we extract the scattering length, the effective range and the effective three-body coupling. We show that the parameters, extracted from the two- and three-particle energy shifts, are consistent. Moreover, the effective three-body coupling is significantly different from zero.

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References in corpus (51)

• Renormalization of the Three-Body System with Short-Range Interactions
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• The Three-Boson System with Short-Range Interactions
• Weak transition matrix elements from finite-volume correlation functions
• Multiple-channel generalization of Lellouch-Luscher formula
• A relativistic, model-independent, three-particle quantization condition
• Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Finite volume effects for meson masses and decay constants
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Three particles in a finite volume
• Three-particle scattering amplitudes from a finite volume formalism
• A method to measure the antikaon-nucleon scattering length in lattice QCD
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Resonances in coupled πK,ηK scattering from quantum chromodynamics
• Three-body Unitarity in the Finite Volume
• The coupled-channel scattering on a torus
• Scalar mesons in a finite volume
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• The pion mass in finite volume
• An $a_0$ resonance in strongly coupled $\pi \eta$, $K\overline{K}$ scattering from lattice QCD
• Multichannel one-to-two transition amplitudes in a finite volume
• Multi-Pion Systems in Lattice QCD and the Three-Pion Interaction
• Multi-Pion States in Lattice QCD and the Charged-Pion Condensate
• Isoscalar $\pi \pi ,K\overline{K},\eta \eta$ scattering and the $\sigma ,f_0,f_2$ mesons from QCD
• Multichannel 0-to-2 and 1-to-2 transition amplitudes for arbitrary spin particles in a finite volume
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates
• An solvable three-body model in finite volume
• Two Particle States in a Box and the $s$-Matrix in Multi-Channel Scattering
• The $\pi \pi \to \pi {\gamma }^{\star }$ amplitude and the resonant $\rho \to \pi {\gamma }^{\star }$ transition from lattice QCD
• Efimov physics in a finite volume
• The triton in a finite volume
• Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies
• A framework for the calculation of the $\Delta N{\gamma }^{\ast }$ transition form factors on the lattice
• Generalized Lüscher Formula in Multi-channel Baryon-Meson Scattering
• Three particles in a finite volume: The breakdown of spherical symmetry
• Matrix elements of unstable states
• On the modification of the Efimov spectrum in a finite cubic box
• Perturbative results for two and three particle threshold energies in finite volume
• One spatial dimensional finite volume three-body interaction for a short-range potential
• Isospin-0 $\pi \pi$ s-wave scattering length from twisted mass lattice QCD
• Applying the relativistic quantization condition to a three-particle bound state in a periodic box
• Flavor-singlet meson decay constants from $N_f=2+1+1$ twisted mass lattice QCD
• Connecting physical resonant amplitudes and lattice QCD
• The $B\to K^{\ast }$ form factors on the lattice
• Testing the threshold expansion for three-particle energies at fourth order in ${\varphi }^4$ theory
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-1 $KK$ scattering length
• Renormalization of the three-boson system with short-range interactions revisited

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• Implementing the three-particle quantization condition including higher partial waves
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• Three pion spectrum in the $I=3$ channel from lattice QCD
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
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• Finite-volume energy spectrum of the $K^{-}{K}^{-}{K}^{-}$ system
• Scattering amplitudes from finite-volume spectral functions
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• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• Relativistic three-particle quantization condition for nondegenerate scalars
• Alternative derivation of the relativistic three-particle quantization condition
• Equivalence of relativistic three-particle quantization conditions
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Variational approach to $N$-body interactions in finite volume
• Scattering of two and three physical pions at maximal isospin from lattice QCD
• $DDK$ system in finite volume
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Pion scattering in the isospin I=2 channel from elongated lattices
• Finite-volume energy shift of the three-pion ground state
• Multiple-particle interaction in $1+1$ dimensional lattice model
• Relativistic $N$-particle energy shift in finite volume
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance
• Pole position of the $a_1(1260)$ from $\tau$-decay
• Multi-${\pi }^{+}$ systems in finite volume
• Decay amplitudes to three hadrons from finite-volume matrix elements
• Modeling few-body resonances in finite volume
• A lattice model of heavy-light three-body system
• Three-body resonances in the ${\phi }^4$ theory
• Propagation of particles on a torus
• On the three-particle analog of the Lellouch-Lüscher formula
• Visualizing resonances in finite volume
• Threshold expansion formula of $N$-boson in finite volume from variational approach
• Bound states in the B-matrix formalism for the three-body scattering
• Finite-volume energy shift of the three-nucleon ground state
• Spurious poles in a finite volume
• Meson-Nucleon Scattering Amplitudes from Lattice QCD
• Testing a new method for scattering in finite volume in the ${\varphi }^4$ theory