Rigorous lower bounds on the imaginary parts of the scattering amplitudes and the positions of their zeros

Rigorous lower bounds are derived from axiomatic field theory, by invoking analyticity and unitarity of the S-matrix. The bounds are expressed in terms of the total cross section and the slope parameter, and are found to be compatible with CERN experimental pp scattering data. It is also shown that the calculated lower-bound values imply non-existence of zeros for -t<or=0.45 (GeV/c)/sup 2/, and an interaction radius of 1 fm. (5 refs).