Studies on $\pi^+\pi^-$ phase motion in the $\Psi'\to J/\Psi \pi^+ \pi^-$ process

TL;DR

This paper proposes a method to measure the difference in elastic $\pi ext{ extpm} ext{ extpm}$ scattering phase shifts using the $ ext{ extPsi'} o ext{ extPsi} ext{ extpi}^+ ext{ extpi}^-$ decay process, enabling future experimental insights.

Contribution

It introduces a novel measurement approach for $ ext{ extpi} ext{ extpi}$ phase shift differences via $ ext{ extPsi'}$ decay analysis, supported by theoretical modeling and Monte Carlo simulations.

Findings

Phase shift difference can be extracted from decay data.

Measurement feasible in the 350-550 MeV energy range.

Method applicable to future high-statistics experiments.

Abstract

We propose a measurement on the elastic $\pi\pi$ scattering phase shift difference $\delta^0_0-\delta^2_0$ through $\Psi'\to J/\Psi \pi^+ \pi^-$ process in future high statistics BES-III experiment. The decay amplitude is constructed with seven Lorentz invariant form-factors and is compared with their theoretical estimation. It is found that the phase shift difference can be obtained, based on a Monte Carlo study and it is expected the phase shift in the energy region between 350 MeV to 550 MeV can be measured at future BES-III.