Related papers: Relativistic, model-independent, three-particle qu…
We present a generalization of Luescher's relation between the finite-volume spectrum and scattering amplitudes to the case of three particles. We consider a relativistic scalar field theory in which the couplings are arbitrary aside from a…
Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity $L$. This gives the…
We present a quantization condition for the spectrum of a system composed of three identical bosons in a finite volume with periodic boundary conditions. This condition gives a relation between the finite volume spectrum and infinite volume…
The formalism relating the relativistic three-particle infinite-volume scattering amplitude to the finite-volume spectrum has been developed thus far only for identical or degenerate particles. We provide the generalization to the case of…
Within the non-relativistic potential scattering theory, we derive a generalized version of the L\"uscher formula, which includes three-particle inelastic channels. Faddeev equations in a finite volume are discussed in detail. It is proved…
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''…
In previous work, we have developed a relativistic, model-independent three-particle quantization condition, but only under the assumption that no poles are present in the two-particle K matrices that appear as scattering subprocesses. Here…
In this work, we use an extension of the quantization condition, given in Ref. [1], to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The…
Scattering and transition amplitudes with three-hadron final states play an important role in nuclear and particle physics. However, predicting such quantities using numerical Lattice QCD is very difficult, in part because of the effects of…
In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three scattering amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the…
We present the status of our formalism for extracting three-particle scattering observables from lattice QCD (LQCD). The method relies on relating the discrete finite-volume spectrum of a quantum field theory with its scattering amplitudes.…
The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Luscher. While in infinite volume, QED contributions to low-energy…
We show that a recently derived alternative form of the relativistic three-particle quantization condition for identical particles can be rewritten in terms of the R matrix introduced to give a unitary representation of the infinite-volume…
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 give an update on our derivation of a quantization condition relating the finite-volume spectrum of three particles in a cubic box to infinite-volume scattering quantities. We have discovered and fixed technical problems in the…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
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…
Unitarity identifies all power-law finite-volume effects and is, therefore, the crucial S-matrix principle for a mapping between experimental results and those of Lattice QCD calculations. In this contribution we review how 3-body unitarity…
The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…
We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method…