Eikonalization and unitarity constraints

Abstract

An extensive generalization of the ordinary and quasi-eikonal methods is presented for the pp andpp elastic scattering amplitudes, which takes into account in a phenomenological way all intermediate multiparticle states involving the crossing even and crossing odd combinations of Reggeons. The formalism in this version involves a maximum of three parameters corresponding to the intermediate states which are possible in this configuration. The unitarity restriction is investigated and particular cases are discussed. An interesting result that emerges concerns the Odderon trajectory intercept: we find that unitarity dictates that this quantity must be below or equal unity unless a very peculiar equality exists between the coupling of the particles to the Pomeron and the Odderon.

On dips, structures and eikonalization

“…More recently, counterarguments have been given [3] to suggest that δ O should be negative. This possibility had been anticipated in [1] on purely phenomenological grounds and, subsequently, we have found that such a requirement is, in general, consequence of unitarity [4].…”

“…Omitting all details of calculations, which can be found in [4], the final expression for the three-parameters eikonalized amplitudes are…”

“…Considering a general case, when there are no any special relations between λ i , we have found in [4] that the unitarity inequality…”

“…The rôle of eikonalization has not been fully clarified in spite of having been investigated by many authors [12] but many results have been obtained recently [13,4].…”

“…We briefly revise (in Sec. 3) the Ordinary Eikonalization (OE) and, after (re)discovering its limits, we pro-ceed to discuss a one-parameter generalization called Quasi Eikonalization (QE) [12] and to propose a three-parameter extension which we term Generalized Eikonalization (GE) (see [4]). Although a useful tool to alleviate the violations of s-channel unitarity at some level (as emphasized in [13]), eikonalization does not mean unitarization.…”