Left Hand Singularities, Hadron Form Factors and the Properties of the Sigma Meson

Abstract

By applying analyticity and single channel unitarity we derive a new formula which is useful to analyze the role of the left-hand singularities in hadron form factors and in the determination of the resonance parameters. Chiral perturbation theory is used to estimate the left-hand cut effects in $\pi\pi$ scattering processes. We find that in the IJ=11 channel the left-hand cut effect is negligible and in the IJ=20 channel the phase shift is dominated by the left-hand cut effect. In the IJ=00 channel the left-hand cut contribution to the phase shift has the wrong sign comparing with the experimental data and therefore it necessitates the $\sigma$ resonance. The new experimental results from the E865 collaboration is crucial in reducing the uncertainty in the determination of the mass and width of the $\sigma$ resonance within our scheme.