Unitarity bound of total cross-section and the forward slope of deep inelastic πN scattering amplitude

With the aid of the generalized Lagrange multiplier method the problem of unitarity maximization of the total cross-section σsub(t) of the deep inelastic spin 0-spin 1/2 particle scattering is solved for arbitrary energies in the explicit analytic form. The upper bound on σsub(t) is expressed in terms of the total elastic cross-section σsub(e) and the forward slope bsub(+) of the imaginary part of the helicity non-flip amplitude. The lower bound of bsub(+) in terms of σ(e) and sigma(t) is also found which represents the specification of the well-known MacDowell-Martin bound for the case of meson-nucleon scattering