Studies on $pi^+pi^-$ phase motion in the $Psito J/Psi pi^+ pi^-$ process

We propose a measurement on the elastic $pipi$ scattering phase shift difference $delta^0_0-delta^2_0$ through $Psito J/Psi pi^+ pi^-$ 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.