Role of crossing and the rho meson in low energy pi pi amplitudes

The crossing conditions on physical region pi pi partial wave amplitudes are used to study the implications of the existence of the rho . The authors show that the mere existence of the rho does not constrain appreciably the s wave scattering lengths and that no correlation from crossing between the rho and the I=0 epsilon resonance can be established without further physical assumptions. (16 refs).