Lower bounds on the slope parameter

• Published in: Nuclear physics. B Vol. 119; no. 3; pp. 453 - 460
• Main Author: Vengurlekar, A.S.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.1977
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(77)90007-4

A rigorous lower bound on the slope parameter γ( s, t) = d ln A( s, t)/d t is derived for 0 < t < t 0 where A( s, t) is the absorptive part of the elastic scattering amplitude and t 0 is related to the right extreme of the Lehmann-Martin ellipse. When A( s, t) has high-energy behavior like s α( t) ln η( t) s…, this lower bound on α( s, t) is used to obtain lower bounds on α′( t) for 0 < t < t 0, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ( s, t) for t < 0 which can be used to find the nearforward region in which γ( s, t) cannot vanish.