$\pi \pi$ 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.

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