Analysis of the s-Wave ππ Interaction from the Reaction π−p→π−π+n

Abstract

Some recent analyses which deduce $s$-wave $\pi \pi$ scattering amplitudes from observed peripheral production of $s$-wave dipions in ${\pi }^{-}p$ reactions are discussed; they assume that the ratio of $s$-wave production to $s$-wave scattering equals the ratio of $p$-wave production to $p$-wave scattering, and take $p$-wave scattering to be given by the Breit-Wigner amplitude describing the $\rho$ meson. As a procedure involving fewer assumptions, it is suggested that one might only assume the phases of these two ratios to be the same, without making assumptions about their relative magnitudes. Applying this procedure to the compilation of experimental data made by Walker et al. provides a strong indication that the $I=0\mathrm{}$ $s$-wave phase shift is $\approx$75-80° at a mass of 750 MeV, and indicates that there is some uncertainty in the relative magnitudes of the two ratios mentioned above.