Geodesic
Singularities of the amplitude in the~$\cos\theta$; plane and scattering at high energies
Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 2, pp. 147-164

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Unitarity and analyticity of the elastic scattering amplitude in the $\cos\theta$ plane are used to show that if $d\sigma/dt|_{t=0}\geqslant\text{const}/s^{2-\varepsilon}$ $(\varepsilon>0)$ at high energies then the contribution to the differential cross section of forward elastic scattering from the left-hand "$u$-channel" singularities of the amplitude is negligibly small. 
@article{TMF_1979_39_2_a0,
     author = {A. A. Logunov and M. A. Mestvirishvili and G. L. Rcheulishvili and A. P. Samokhin},
     title = {Singularities of the amplitude in the~$\cos\theta$; plane and scattering at high energies},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {147--164},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_39_2_a0/}
}
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A. A. Logunov; M. A. Mestvirishvili; G. L. Rcheulishvili; A. P. Samokhin. Singularities of the amplitude in the~$\cos\theta$; plane and scattering at high energies. Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 2, pp. 147-164. http://geodesic.mathdoc.fr/item/TMF_1979_39_2_a0/