Related papers: Estimating the two-particle $K$-matrix for multipl…
A new implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the Luescher formalism is described. The method includes higher partial waves and multiple decay channels, and the fitting procedure properly…
We generalize the Lellouch-Luscher formula, relating weak matrix elements in finite and infinite volumes, to the case of multiple strongly-coupled decay channels into two scalar particles. This is a necessary first step on the way to a…
We propose a new method to evaluate the Lellouch-L\"uscher factor which relates the $\Delta I=3/2$ $K\to\pi\pi$ matrix elements computed on a finite lattice to the physical (infinite-volume) decay amplitudes. The method relies on the use of…
We discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\to\pi\pi$ decays). The relation between finite-volume matrix elements and physical amplitudes, recently derived by Lellouch and…
We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle…
We derive a model-independent expression for finite-volume matrix elements. Specifically, we present a relativistic, non-perturbative analysis of the matrix element of an external current between a one-scalar in-state and a two-scalar…
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,…
In order to directly compute physical two-pion K-decay amplitudes using lattice methods we must prepare a two-pion state with non-zero relative momentum. Building upon a proposal of Lellouch and L\"uscher, we describe a finite-volume method…
We propose an alternative approach to L\"uscher's formula for extracting two-body scattering phase shifts from finite volume spectra with no reliance on the partial wave expansion. We use an effective-field-theory-based Hamiltonian method…
We determine scattering phase shifts for S,P,D, and F partial wave channels in two-nucleon systems using lattice QCD methods. We use a generalization of Luscher's finite volume method to determine infinite volume phase shifts from a set of…
It is common practice to truncate the finite-volume formula for $K\to\pi\pi$, and other one-to-two transitions, to only include the lowest partial wave, as in the original derivation by Lellouch and L\"uscher. However, as the precision of…
We derive formalism for determining $\textbf{2} + \mathcal J \to \textbf{2}$ infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume…
In their seminal work, Lellouch and L\"uscher derived a conversion factor relating a finite-volume matrix element, calculable using numerical lattice QCD, with the infinite-volume decay amplitude for $K \to \pi \pi$. The conversion factor…
Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in…
We determine the quantization condition for the energy levels of two interacting particles in a finite box in a ``moving frame'', i.e. one in which the total momentum of pions is non-zero. This condition is valid up to corrections which…
The three-particle $K$-matrix, $\mathcal{K}_{\mathrm{df},3}$, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we…
We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volume $\textbf{0}\rightarrow\textbf{2}$ and $\textbf{1}\rightarrow\textbf{2}$ transition amplitudes. Our result accommodates…
This work presents the first lattice calculation of a two-to-two particle matrix element of a local current. This exploratory calculation is performed using a leading-order pionless effective field theory of two nucleons in a finite 3D…
The rigorous treatment of four-particle intermediate and final states poses a major challenge for lattice calculations of scattering and decay amplitudes, as well as long-distance matrix elements. As a step towards addressing these…
We describe a generalization of the Lellouch-L\"uscher formula to the case of multiple strongly-coupled decay channels. As in the original formula, our final result is a relation between weak matrix elements in finite and infinite volumes.…