Speaker
Description
We present a recent application of the Glazek-Wilson similarity renormalization group for Hamiltonians (SRG).
We consider the $\pi\pi$-scattering problem in the context of the Kadyshevsky equation, a 3D reduction of the Bethe-Salpeter equation that allows for a Hamiltonian formulation. In this scheme, we introduce a momentum grid and provide an isospectral definition of the phase-shift based on a spectral shift of a Chebyshev angle. We introduce a new method to integrate the SRG equations based on 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 unnatural high momentum tails present in the fitted interactions and reaching far beyond the maximal CM energy of $\sqrt{s}=1.4$ GeV and how these tails can be integrated out explicitly by using Block-Diagonal generators of the SRG.
