Related papers: Three-body resonances in the $\varphi^4$ theory
We calculate the one-, two- and three-particle energy levels for different lattice volumes in the complex $\varphi^4$ theory on the lattice. We argue that the exponentially suppressed finite-volume corrections for the two- and…
We propose a new finite-volume approach which implements two- and three-body dynamics in a transparent way based on an Effective Field Theory Lagrangian. The formalism utilizes a particle-dimer picture and formulates the quantization…
Strong interactions produce a rich spectrum of resonances that decay into three or more hadrons. Understanding their phenomenology requires a theoretical framework to extract parameters fromexperimental data and Lattice QCD simulations of…
Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity''…
We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Moreover, we consider the extraction of physical observables from the lattice spectrum using the quantization…
We investigate the relativistic scattering of three identical scalar bosons interacting via pair-wise interactions. Extending techniques from the non-relativistic three-body scattering theory, we provide a detailed and general prescription…
We present a study of a $1+1$ dimensional heavy-light three-body system in finite volume. The heavy-light system is simulated by a coupled-channel $\phi^4$ type lattice model, and both ground state and excited states of multiparticle energy…
A new kind of the relativistic three-body equations for the coupled $\pi N$ and $\gamma N$ scattering reactions with the $\pi \pi N$ and $\gamma \pi N$ three particle final states are suggested. These equations are derived in the framework…
We discuss unitarity constraints on the dynamics of a system of three interacting particles. We show how the short-range interaction that describes three-body resonances can be separated from the long-range exchange processes, in particular…
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…
Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well…
The physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above…
One has to study multivariable scattering amplitudes to extract properties of the three-body states from the generalizations of the L\"uscher finite-volume formalism. In particular, a three-body amplitude obtained from a Lattice QCD…
We developed a method to calculate positions and widths of three-body resonances. The method combines the hyperspherical adiabatic approach, slow variable discretization method (Tolstikhin et al., J. Phys. B: At. Mol. Opt. Phys. 29, L389…
Based on Lippmann-Schwinger equation approach, we discuss a three-particle system in finite volume. A set of equations which relate the discrete finite-volume energies to the scattering amplitudes are derived under the approximation of the…
In this work, based on consideration of periodicity and asymptotic forms of wave function, we propose a novel approach to the solution of finite volume three-body problem by mapping a three-body problem into a higher dimensional two-body…
Lattice simulations of light nuclei necessarily take place in finite volumes, thus affecting their infrared properties. These effects can be addressed in a model-independent manner using Effective Field Theories. We study the model case of…
Three-body states are critical to the dynamics of many hadronic resonances. We show that lattice QCD calculations have reached a stage where these states can be accurately resolved. We perform a calculation over a wide range of parameters…
In this note we first introduce the theoretical formalism of the unitarization of the two-body scattering both in the infinite and finite volumes. Then we apply this formalism to the study of the $Z_c(3900)$ resonance in the $J/\psi\,\pi$…
The finite-volume energy levels corresponding to the Roper resonance based on a two-flavor chiral effective Lagrangian at leading one-loop order are investigated. It is shown that the Roper mass can be extracted from these levels for not…