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

TL;DR

This paper applies the Similarity Renormalization Group to analyze $$ scattering in momentum space up to 1.4 GeV, introducing a new numerical method that preserves isospectrality and discusses high momentum tail issues.

Contribution

It introduces a novel Crank-Nicolson based method for SRG equations that maintains isospectrality in $$ scattering analysis.

Findings

Effective Hamiltonian identification for $$ channels.

New numerical method preserves isospectrality.

High momentum tail issues in fitted interactions discussed.

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.