Bounds on the pi /sup 0/ pi /sup 0/ amplitude

A new approach to the problem of constraining the scattering amplitudes by using axiomatically proved properties of unitarity, analyticity and crossing is developed. It is applied to obtain absolute and semi-phenomenological bounds on the pi /sup 0/ pi /sup 0/ amplitude at points lying on the Mandelstam triangle, in particular at the physical threshold (scattering length) and at the symmetric point (which is used to define the coupling constant). The authors have already reported (see Phys. Lett., vol.60B, p.63 (1975)) a less general and powerful approach which improved the previous results in this field. The present version, which constitutes a noticeable generalisation of the method, allows a new improvement of the bounds, both absolute and semi-phenomenological. (11 refs).