Related papers: Symmetrizing relativistic three-body partial wave …
We derive the integral equations for partial-wave projected three-body scattering amplitudes, starting from the integral equations for three-body amplitudes developed for lattice QCD analyses. The results, which hold for generic three-body…
As a step toward satisfactory understanding of the quantum dynamics of Dirichlet \break (D-) particles, the amplitude for the basic process describing the scattering of two quantized D-particles is computed in bosonic string theory. The…
We introduce parametrizations of hadronic three-body $B$ and $D$ weak decay amplitudes that can be readily implemented in experimental analyses and are a sound alternative to the simplistic and widely used sum of Breit-Wigner type…
As the study of three-hadron physics from lattice QCD matures, it is necessary to develop proper analysis tools in order to reliably study a variety of phenomena, including resonance spectroscopy and nuclear structure. Reconstructing the…
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 present a general formalism to write the decay amplitude for multibody reactions with explicit separation of the rotational degrees of freedom, which are well controlled by the spin of the decay particle, and dynamic functions on the…
I review recent progress in calculating scattering amplitudes and resonance properties involving three particles using results from lattice QCD. The necessary input is the finite-volume spectrum, and the outputs -- via solutions of integral…
Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on…
Three-body dynamics above threshold is required for the reliable extraction of many amplitudes and resonances from experiment and lattice QCD. The S-matrix principle of unitarity can be used to construct dynamical coupled-channel approaches…
We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an…
We present numerical results showing how our recently proposed relativistic three-particle quantization condition can be used in practice. Using the isotropic (generalized $s$-wave) approximation, and keeping only the leading terms in the…
We discuss the derivation and properties of the general representation of partial wave amplitudes in the context of improving the models currently used in analysis of three particle Dalitz distributions.
These lectures treat scattering theory from a non-perturbative point of view. The course begins with a review of formal aspects in scattering theory, discussing the in/out states and the $S$ matrix that connects them. Unitarity relations,…
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…
We express the amplitudes for charmless three-body B decays in terms of diagrams. In addition, we show how to use Dalitz-plot analyses to obtain decay amplitudes which are symmetric or antisymmetric under the exchange of two of the…
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 partial wave series for the Coulomb scattering amplitude in three dimensions is evaluated in a very simple way to give the closed result.
We present the first determination of $\rho \pi$ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 $\rho \pi$, we calculate…
Partial wave decomposition is one of the main tools within the modern S-matrix studies. We present a method to compute partial waves for $2\to2$ scattering of spinning particles in arbitrary spacetime dimension. We identify partial waves as…
We present a general framework connecting global symmetries to the relativistic $S$-matrix through the lens of quantum information theory. Analyzing the 2-to-2 scattering of particles of any helicity, we systematically characterize…