Comments on Arnold and Barnett's Shielding-Cut Mechanism. II

Abstract

Over-simplified models of the fixed-pole Porneron have often been discussed by many high energy phenomenologists. 1 ) No one else but Arnold and Barnett 2 ) has ever looked into generation mechanism of the shielding branch-cut, which is essential for the fixed-pole Pomeron to reconcile with t channel unitarity. 3 )' 4 ) However, nothing is known about phenomenological consequences of Arnold and Barnett's shielding branch-cut (ABSC). In this note, the asymptotic behaviour of diffraction scattering is studied by the use of the fixed-pole Pomeron of ABSC. In the case of proton-proton scattering, it is examined whether or not the fixed­ pole Pomeron of ABSC can consistently explain the presently available data 5 ) on total cross section, real to imaginary ratio of the forward amplitude and the slope parameter of diffraction peak. As is well known, the :fixed-pole Pomeron lXp(t) =1 can be consistent with t-channel unitarity if and only if there exist a set of moving branch-points a0 (t) of Oehme type. 3 ) As Jtends to 1, these shielding branch-points l 0 =a0 - 1 (J) should coincide in position and character with the corresponding two-body unitarity cuts in the t channel. 3 ) I£ the Pomeron is decoupled from nonsense states as is usually assumed, 4 )' 6 ) however, the generation mechanism of a0 (t) will be quite different from that of the Mandelstam branch-cuts which allow the fixed poles at nonsense, wrong-signature values of J. On an assumption of a high-lying pole trajectory ax(t) = 1-m" 2 + t, Arnold and Barnett have recently proposed a model which generates explicitly a shielding branch-cut of the required property a0 (4m" 2 ) = 1. Their model yields the Mellin transformed, even-signatured, partial-wave amplitude in the t channel