Pion-pion interaction in the I=1 channel

TL;DR

This paper introduces a new method to study pion-pion interactions in the I=1 channel by computing Bethe-Salpeter wave functions to extract interaction potentials and phase shifts, using large pion masses.

Contribution

It presents a novel approach to analyze pion-pion interactions through wave functions and potential extraction, applicable at large pion masses.

Findings

Computed Bethe-Salpeter wave functions for ground and excited states.

Attempted to extract interaction kernels and phase shifts.

Used large pion masses where rho decay is not possible.

Abstract

We present preliminary results of a new approach to the study of the pion-pion system in the I=1 channel. The Bethe-Salpeter wave function of the two-pion system is computed on the ground state and the first excited state. From these, we attempt to extract an interaction kernel (potential) which can then be used to extract observables such as the phase shifts. In a first trial, we use rather large pion masses $m_\pi \sim 1.05$ GeV and $m_\pi \sim 0.68$ GeV which do not allow rho decay.