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 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 σ resonance. The mass and width of the σ resonance is estimated which is found to be sensitive to the experimental value of the scattering length. PACS numbers: 11.55.Bq, 14.40.Cs, 12.39.Fe