Does the diffraction cone shrinkage with energy originate from unitarity?

Abstract

We note that the diffraction cone shrinkage might result from unitarization only, i.e. there is no need to introduce it into an input amplitude ab initio.

Implications of the ρ(s) measurements by TOTEM at the LHC

“…It should be noted that the resulting amplitude f (s, b) is not a factorized function of its variables as well as the amplitude F (s, t). Energy dependence of the slope parameter B(s) is generated by the unitarity and it has an asymptotic dependence B(s) ∼ ln 2 s [11].…”

Direct-Channel Option of the Forward Slope Increase

“…To demonstrate this possibility, we have considered a wide class of the geometrical models [14,15]. These models presuppose a factorized form of the input amplitude.…”

“…which replaces a power-like dependence in the limit of s → ∞. The transformation of these two dependencies is provided by the unitarization procedure [15]. Thus, unitarity plays an essential role at the LHC energies and the observed speeding up of the slope B shrinkage can be qualitatively explained as follows.…”

Centrality in hadron collisions

“…where g(s) ∼ s λ at the large values of s, and the power dependence guarantees asymptotic growth of the total cross-section σ tot ∼ ln 2 s. Such a factorized form corresponds to a common source for the increase with energy of the total crosssections and the slope of the diffraction cone in elastic scattering due to unitarization [16]. The particular form of the function ω(b) ∼ exp(−µb) is consistent with analytical properties of the scattering amplitude.…”

“…A wide class of the geometrical models for hadron interactions (relevant for the centrality discussion in these processes) allows one to assume that U (s, b) has a factorized form (cf. [16] and references therein):…”