Related papers: Discretization effects in finite-volume $2\to2$ sc…
We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the…
For resonances decaying in a finite volume, the simple identification of state and eigenvalue is lost. The extraction of the scattering amplitude is a major challenge as we demonstrate by extrapolating the physical S_{11} amplitude of…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
Simulating the kappa(800) on the lattice is a challenging task that starts to become feasible due to the rapid progress in recent-years lattice QCD calculations. As the resonance is broad, special attention to finite-volume effects has to…
A relation is presented between single-hadron long-range matrix elements defined in a finite Euclidean spacetime, and the corresponding infinite-volume Minkowski amplitudes. This relation is valid in the kinematic region where any number of…
I review some of the lattice results on spectroscopy and resonances in the past years. For the conventional hadron spectrum computations, focus has been put on the isospin breaking effects, QED effects, and simulations near the physical…
Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must…
This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed…
In this talk we discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\to\pi\pi$ decays). In particular we show how the relation between finite-volume matrix elements and physical amplitudes,…
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…
We discuss the quantization of the energy levels of two-particle scattering states in a finite volume in the case of Bloch-type boundary conditions. A generalization of the Luescher quantization condition is obtained that can be used in…
This work presents technical details of determining the finite-volume energy spectra for the scattering amplitude of the coupled-channel $\pi\Sigma - \bar{K}N$ from lattice QCD data. The importance of reliably extracting such spectra lies…
Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the…
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…
Discretization effects of lattice QCD are described by Symanzik's effective theory when the lattice spacing, $a$, is small. Asymptotic freedom predicts that the leading asymptotic behavior is $\sim a^n [\bar g^2(a^{-1})]^{\hat\gamma_1} \sim…
In this article I provide an overview of the current state of scattering within lattice QCD, along with ongoing projects that examine weak decays involving scattering states as either final or intermediate states. Significant progress has…
An extended two-hadron operator is developed to extract the spectra of irreducible representations (irreps) in the finite volume. The irreps of the group for the finite volume system are projected using a coordinate-space operator. The…
We put forward a finite theory of quantum scattering of fundamental particles without using auxiliary particles. It suggests that to avoid ultraviolet divergencies and model faster-than-light effects it suffices to appropriately change only…
L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass…
The dynamical formulation of time-independent scattering theory that is developed in [Ann. Phys. (NY) 341, 77-85 (2014)] offers simple formulas for the reflection and transmission amplitudes of finite-range potentials in terms of the…