Eikonal fit toppandp¯pscattering and the edge in the scattering amplitude

Abstract

We make a detailed eikonal fit to current data on the total and elastic scattering cross sections, the ratios ρ of the real to the imaginary parts of the forward elastic scattering amplitudes, and the logarithmic slopes B of the differential cross sections dσ/dt at t = 0, for proton-proton and antiproton-proton scattering at center-of-mass energies W from 5 GeV to 57 TeV. The fit allows us to investigate the structure of the eikonal amplitudes in detail, including the impact-parameter structure of the energy-independent edge in the scattering amplitude shown to exist by Block et al.[1]. We show that the edge region has an essentially fixed shape with a peak at approximately the "black disk" radius Rtot = σtot/2π of the scattering amplitude, a constant width t edge ≈ 1 fm, and migrates to larger impact parameters with increasing energy proportionally to Rtot. We comment on possible physical mechanisms which could lead to the edge. We show that the eikonal results for the cross sections and ρ values are described to high accuracy by analytic expressions of the forms used in earlier analyses by Block and Halzen, and extend the result to the elastic-scattering slope parameter B. These expressions provide simple extrapolations of the results to much higher energies where the cross sections approach the black disk limit with σ elas , σ inel → σtot/2 and B → σtot/8π. Finally, we calculate the survival probabilities for large rapidity gaps in the scattering.

Introduction to the physics of the total cross section at LHC

“…On the other hand, we notice a recent work by Block and collaborators [289], which we shall see in Sect. 6.8, where the Black Disk limit is used to make predictions at very, extremely, large energies.…”

“…One notices the obvious fact that ρ(s) changes sign in the energy region where the total cross section changes curvature. The change in curvature is attributed in mini-jet models to the fact that perturbative QCD processes become observable, which is also the region where an edge-like behavior has been noticed by Block et al in the scattering amplitude [289].…”

“…97 a recent analysis by Block, Durand, Ha and Halzen [389], in which the high energy behavior of all three cross sections, σ total , σ inel , σ elastic has been constrained by the Froissart limit, σ total ∼ [ln s] 2 , and the black disk behavior, σ elastic /σ total → 1/2, 8π B/σ total → 1.…”

“…1 of [389], where the curve is a fit to the data, with high energy constraints from the Froissart bound and the black disk limit. Reprinted with permission from [389], Fig. (1), ©(2015) by the American Physical Society…”

Exploring central opacity and asymptotic scenarios in elastic hadron scattering

“…It is typical of eikonalized formalisms, as the traditional models by Chou and Yang [37], Bourrely, Soffer and Wu [38][39][40], the hybrid approach by Block and Halzen [41] and a number of models that have been continuously refined and developed (for example, [18][19][20][21][22][23][26][27][28]). …”