The shape of the ρ(ππ → ππ andee → ππ)

The shape of the ϱ-resonance is calculated, in ππ → ππ and in ee → ππ. The l = 1 ππ phase shift δ(s) is calculated up to s ≈ 1 GeV2, using elastic unitarity and a fixed-t dispersion relation; the solution contains two parameters M and Γ, the mass and width of the ϱ. If elastic unitarity is assumed even at high energies this leads to a prediction for the pion form factor Fπ in terms of M and Γ, which when fitted to the Orsay data leads to a somewhat higher value of Γ than does the usual Gounaris-Sakurai formula. However, the introduction of a reasonable amount of high-energy inelasticity results in a third parameter and with this the present Orsay data permits a wide range of values of Γ. Simple parametrizations are given for cotδ(s) and Fπ(s). A brief general discussion is given of the prediction of elastic resonances from unitarity.