Geodesic
Contribution from far singularities in the $\cos\theta$ plane to the scattering amplitude and to the distribution function of inclusive processes
Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 3, pp. 291-308 
A. A. Logunov; M. A. Mestvirishvili; G. L. Rcheulishvili; A. P. Samokhin. Contribution from far singularities in the $\cos\theta$ plane to the scattering amplitude and to the distribution function of inclusive processes. Teoretičeskaâ i matematičeskaâ fizika, Tome 43 (1980) no. 3, pp. 291-308. http://geodesic.mathdoc.fr/item/TMF_1980_43_3_a0/
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     title = {Contribution from far singularities in~the $\cos\theta$ plane to~the scattering amplitude and to~the distribution function of~inclusive processes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Using the imitarity condition, polynomial boundedness with respect to energy and analyticity of the amplitude $F(s,z)$ in the $z=\cos\theta$-plane in a certain fixed complex neighbourhood of the physical points $-1, it is shown that if the high-energy asymptotics of the amplitude is such that $|F(s,1)|\geqslant c(\ln s)^{2+\varepsilon}$, then such behaviour of the amplitude is completely determined by the nearest to the point $z=1$ singularity of the amplitude. The similar results are obtained for the spectrum of one-particle inclusive process integrated over the momentum values. It is also shown that if the absorptive part of the elastic scattering amplitude is analytic in a certain bounded region of the $z$-plane with cuts along the real axis and $\sigma_{\mathrm {tot}}(s)>(\ln s)^{-1}$ then the discontinuity of the amplitude on the right-hand side cut is a sign-changing function of $z$.

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