PoS - Proceedings of Science
Volume 374 - Light Cone 2019 - QCD on the light cone: from hadrons to heavy ions (LC2019) - Contributed
$\pi\pi$ scattering in a renormalized Hamiltonian matrix
M. Gomez Rocha,* E. Ruiz Arriola
*corresponding author
Full text: pdf
Pre-published on: May 06, 2020
Published on: May 26, 2020
A Wilsonian approach to $\pi\pi$ scattering based in the Glazek-Wilson Similarity Renormalization Group (SRG) for Hamiltonians is analyzed in momentum space up to a maximal CM energy of $\sqrt{s}=1.4$ GeV. To this end, we identify the corresponding relativistic Hamiltonian by means of the 3D reduction of the Bethe-Salpeter equation in the Kadyshevsky scheme, introduce a momentum grid and provide an isospectral definition of the phase-shift based on a spectral shift of a Chebyshev angle. We also propose 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.
DOI: https://doi.org/10.22323/1.374.0043
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