Singh, Virendra ; Vengurlekar, A. S. (1972) Asymptotic bounds on the absorptive parts of the elastic scattering amplitudes Physical Review D - Particles, Fields, Gravitation and Cosmology, 5 (9). pp. 2310-2315. ISSN 1550-7998
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Official URL: http://prd.aps.org/abstract/PRD/v5/i9/p2310_1
Related URL: http://dx.doi.org/10.1103/PhysRevD.5.2310
We establish exact bounds on the absorptive parts A(s,t) of an elastic scattering amplitude (spinless case) and evaluate them for positive t values lying within the Lehmann-Martin ellipse [the major axis = 2(1+t0/2k2)]. These bounds are used to derive a number of asymptotic results; e.g., (i) the "diffraction-peak width" W is larger than Wmin~4t0/(1+λ)2× (1-1/2σ)(lns)2 (for s→∞); (ii) the leading Regge trajectory for t0 > t > 0 lies below [1+(t/t0)1/2]-λ[1-(t/t0)1/2]; (iii) there are no complex zeros of A(s,t) for |t| < 4t0/(1+λ)2e2(lns)2 (for s→∞) and no real zeros for t0 > t >-Wmin, where λ=lims→∞lnσtot(s)/lns and σ=lims→∞t0σtot(s)/4Π(lns)2.
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