$\pi \pi$ scattering from a similarity renormalization group perspective

Abstract

A Wilsonian approach based on the Similarity Renormalization Group to $\pi \pi$ scattering is analyzed in the $JI=$00, 11 and 02 channels in momentum space up to a maximal CM energy of $\sqrt{s}=1.4$ GeV. We identify the Hamiltonian by means of the 3D reduction of the Bethe-Salpeter equation in the Kadyschevsky scheme. We propose a new method to integrate the SRG equations based in the Crank-Nicolson algorithm with a single step finite difference so that isospectrality is preserved at any step of the calculations. We discuss issues on the high momentum tails present in the fitted interactions hampering calculations.

Comments: 7 pages, 12 figures. Presented by María Gómez-Rocha at the 15th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon, MENU-2019