Related papers: Efficient solution of the multi-channel L\"uscher …
We make a theoretical study of $\pi\pi$ scattering with quantum numbers $J^{PC}=1^{--}$ in a finite box. To calculate physical observables for infinite volume from lattice QCD, the finite box dependence of the potentials is not usually…
Most discussions of chaotic scattering systems are devoted to two-dimensional systems. It is of considerable interest to extend these studies to the, in general, more realistic case of three dimensions. In this context, it is conceptually…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
Most strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered $X$, $Y$ and $Z$ resonances. In order to study such resonances from first principles using lattice QCD, one…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
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…
In this talk, we present the first chiral extrapolation of a resonant scattering amplitude obtained from lattice QCD. Finite-volume spectra, determined by the Hadron Spectrum Collaboration at $m_\pi = 236$ MeV, for the isotriplet $\pi\pi$…
In this paper, we study the time-independent Schr\"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr\"odinger equation can…
The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The…
The exact two-particle energy eigenstates in a generic asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum…
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…
We present the first ab initio calculation at physical quark masses of scattering amplitudes describing the lightest pseudoscalar mesons interacting via the strong force in the vector channel. Using lattice quantum chromodynamics, we…
A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…
There exist two methods to study two-baryon systems in lattice QCD: the direct method which extracts eigenenergies from the plateaux of the temporal correlator and the HAL QCD method which extracts observables from the non-local potential…
Within a formulation of $\pi\pi$ scattering, we investigate the use of the finite-volume Hamiltonian approach to resolving scattering observables from lattice QCD spectra. We consider spectra in the centre-of-mass and moving frames for both…
In this paper we suggest a new approach for the multichannel Coulomb scattering problem. The Schr\"{o}dinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
An application of the new formulation of the eigenchannel method [R. Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] to quantum scattering of Dirac particles from non-local separable potentials is presented. Eigenchannel vectors,…
We report on our lattice QCD study of coupled $DD_s^* - D^*D_s$ scattering in the $J^P=1^+$ channel and elastic $DD_s$ scattering in the $J^P=0^+$ channel, aimed at investigating the possible existence of $cc\bar{u}\bar{s}$ tetraquarks near…
The multichannel scattering problem for the stationary Schr\"{o}dinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the…