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

By applying analyticity and single-channel unitarity we derive a new formul a which is useful to analyze the role of the left-hand singularities in had ron form factors and in the determination of the resonance parameters. Chir al perturbation theory is used to estimate the left-hand cut effects in pi pi scattering processes. We find that in the I, J = 1, 1 channel the left-h and 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 1, J = 0, 0 channel the l eft-hand cut contribution to the phase shift has the wrong sign comparing w ith the experimental data and therefore it necessitates the cr resonance. T he new experimental results from the E865 collaboration is crucial in reduc ing the uncertainty in the determination of the mass and width of the a res onance within our scheme. (C) 2001 Elsevier Science B.V. All rights reserve d.