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

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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 $z$. 
@article{TMF_1980_43_3_a0,
     author = {A. A. Logunov and M. A. Mestvirishvili and G. L. Rcheulishvili and A. P. Samokhin},
     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},
     pages = {291--308},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_43_3_a0/}
}
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AU  - M. A. Mestvirishvili
AU  - G. L. Rcheulishvili
AU  - A. P. Samokhin
TI  - Contribution from far singularities in~the $\cos\theta$ plane to~the scattering amplitude and to~the distribution function of~inclusive processes
JO  - Teoretičeskaâ i matematičeskaâ fizika
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%0 Journal Article
%A A. A. Logunov
%A M. A. Mestvirishvili
%A G. L. Rcheulishvili
%A A. P. Samokhin
%T Contribution from far singularities in~the $\cos\theta$ plane to~the scattering amplitude and to~the distribution function of~inclusive processes
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1980
%P 291-308
%V 43
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1980_43_3_a0/
%G ru
%F TMF_1980_43_3_a0
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/