Hadron collisions at ultrahigh energies: Black disk or resonant disk modes?

Abstract

The analysis of current ultrahigh energy data for hadronic total cross sections and diffractive scattering cross sections points to a steady growth of the optical density with energy for elastic scattering amplitudes in the impact parameter space, b. At LHC energy the profile function of the pp-scattering amplitude, TðbÞ, reaches the black disk limit at small b. Two scenarios are possible at larger energies, ffiffi ffi s p ≳ 100 TeV. First, the profile function gets frozen in the black disk limit, TðbÞ ≃ 1, while the radius of the black disk R black disk is increasing with ln s, providing σ tot ∼ ln 2 s, σ el ∼ ln 2 s, σ inel ∼ ln 2 s. In another scenario the profile function continues to grow at ffiffi ffi s p ≳ 100 TeV approaching the maximal value, TðbÞ ≃ 2, that means the resonant disk mode. We discuss features of the resonant disk mode when the disk radius, R resonant disk , increases providing the growth of the total and elastic cross sections σ tot ∼ ln 2 s, σ el ∼ ln 2 s, but a more slow increase of inelastic cross section, σ inel ∼ ln s.In the impact parameter space the profile function TðbÞ is determined at high energies as PHYSICAL REVIEW D 90, 074005 (2014) 1550-7998=2014=90(7)=074005 (5) 074005-1

Hollowness in $pp$ Scattering at the LHC

“…Here we discuss the sensitivity of this hollowness feature on modeling of the phase of the elastic scattering amplitude as a function of the momentum transfer. In previous analyses [1,[8][9][10][11][12][13][14][15][16][17][18][19] this effect was not treated with sufficient attention.…”

Hollowness in $pp$ Scattering

“…We term this phenomenon hollowness. This unusual feature has been brought up and interpreted by other authors [7][8][9][10][11][12][13][14][15]. A model realization of the effect was implemented via hot-spots in [16].…”

Generalized upper bound for inelastic diffraction

“…Several phenomenological models are able to reproduce such transition and among them the one based on the rational unitarization of the leading vacuum Regge-pole contribution with the intercept greater than unity [22] and similar models known under the generic name of the unitarized supercritical Pomeron (cf. [30] for a recent discussion and the references). The assumption that the unitarity limit instead of the black-disc limit is to be saturated asymptotically leads to a relatively slower increase of the inelastic cross-section…”