Geodesic
Unitarity bound on the total cross section and forward slope of the deep inelastic $\pi N$ scattering amplitude
Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 2, pp. 195-204

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The generalized method of Lagrangian multipliers is used to solve in explicit analytic form the problem of unitarity maximization of the total cross section $\sigma_t$ of deep inelastic scattering of particles with spin $0$ on spin $1/2$ particles at all energies. The upper bound $\sigma_t^{\max}$ ax is expressed in terms of the total elastic cross sectione $\sigma_e$ and the forward slope $b_+$ of the imaginary part of the helicity nonflip amplitude. A lower bound is also found for $b_+$ in terms of $\sigma_e$ and $\sigma_t$, this making more precise the well-known bound of MacDowell and Martin for the case of meson-nucleon scattering. 
@article{TMF_1979_39_2_a5,
     author = {I. Yu. Krivsky and Yu. A. Ksaverii},
     title = {Unitarity bound on the total cross section and forward slope of the deep inelastic $\pi N$ scattering amplitude},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {195--204},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_39_2_a5/}
}
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I. Yu. Krivsky; Yu. A. Ksaverii. Unitarity bound on the total cross section and forward slope of the deep inelastic $\pi N$ scattering amplitude. Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 2, pp. 195-204. http://geodesic.mathdoc.fr/item/TMF_1979_39_2_a5/