Left-hand singularities, hadron form factors and the properties of the /σ meson

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 ππ scattering processes. We find that in the I, J=1,1 channel the left-hand cut effect is negligible and in the I, J=2,0 channel the phase shift is dominated by the left-hand cut effect. In the I, J=0,0 channel the left-hand cut contribution to the phase shift has the wrong sign comparing with the experimental data and therefore it necessitates the σ 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 σ resonance within our scheme.