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

Abstract

We propose a measurement on the elastic $\pi \pi$ scattering phase shift difference ${\delta }_0^0-{\delta }_0^2$ through ${\Psi }^{\prime }\to J/\Psi {\pi }^{+}{\pi }^{-}$ 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.

16 pages, 1 figure