Inversion potentials for meson-nucleon and meson-meson interactions

Abstract

Two-body interactions of elementary particles are useful in particle and nuclear physics to describe qualitatively and quantitatively few-and many-body systems. We are extending for this purpose the quantum inversion approach for systems consisting of nucleons and mesons. From the wide range of experimentally studied two-body systems we concentrate here on πN , ππ, K + N , Kπ and KK. As input we require results of phase shift analyses. Quantum inversion Gelfand-Levitan and Marchenko single and coupled channel algorithms are used for Schrödinger type wave equations in partial wave decomposition. The motivation of this study comes from our two approaches: to generate and investigate potentials directly from data by means of inversion and alternatively use linear and nonlinear boson exchange models. The interesting results of inversion are coordinate space informations about radial ranges, strengths, long distance behaviors, resonance characteristics, threshold effects, scattering lengths and bound state properties.

Phenomenological view on baryon-baryon potentials from lattice QCD simulations

“…Then, the attempt to represent such a possibly highly non-local interaction by a local potential, as done by the HAL QCD Collaboration, could lead to artifacts which manifest themselves in form of a long range and a sizeable strength. Indeed, such a trend has been seen in applications of inverse scattering theory to cases like πN or K K scattering [37].…”

In-medium nucleon-nucleon potentials in configuration space

“…They lead to kernels K (r, r ) of the exact Marchenko [26] and Gel'fand-Levitan [28] integral equations from which the potentials can be constructed. The method has been applied successfully to construct a nucleon-nucleon potential by von Geramb and collaborators (see [29,30] and references therein), as well as neutron-deuteron potentials [31,32]. The Marchenko integral equation, fully equivalent to the Schrödinger equation, reads…”