The size seems to matter or where lies the “asymptopia”?

Abstract

We discuss an apparent correlation between the onset of the rising regime for the total crosssections and the slowdown of the rise of the forward slopes with energy. It is shown that even at highest energies achieved with the LHC the proper sizes of the colliding protons comprise the bulk of the the interaction region. This seems to witness that the "asymptopia" -a hypothetical "truly asymptotic" regime -lies at energies no less than O(100 TeV). In the course of reasoning we also discuss the question of the dependence of the effective sizes of hadrons in collision on the type of their interaction. The ProblemLet us look at Fig. 1 presenting the energy evolution of the total cross sections (σ tot ) and forward slopes (B) for proton-proton interactions. The database (DB17+) of experimental results for the set of the scattering parameters G pp ≡ {G i pp } 2 i=1 = {σ tot , B} is used in the present paper 1 . The set for σ tot contains the data from [1] and preliminary TOTEM results at √ s = 2.76 [2] and 13 TeV [3], the data sample for B unites the subset from [4] with recent improvement from [5] and the new result at √ s = 8 TeV [6] as well as with preliminary points at √ s = 0.20 [7], 2.76 [8] and 13 TeV [3].

Energy Dependence of the Ratio of the Elastic-to-Total Cross Sections for Proton—Proton and Antiproton—Proton Collisions

“…Also the quantity (1) can be related with the parameter κ(s) ≡ σ tot (s)/8πB(s) indicating the asymptotic domain for such global scattering parameters like total cross sections, slope etc. [3] as follows…”

Global Characteristics of the Medium Produced in Ultra-High Energy Cosmic Ray Collisions

“…where S ⊥ is the nuclei transverse overlap area, the radius for incoming nucleus is estimated as the radius of sphericallysymmetric object ∀ A > 1 : R = r 0 A 1/3 with r 0 = (1.25 ± 0.05) fm [10] and for p + p collisions R = (0.875 ± 0.006) fm [11]. Here the Stefan-Boltzmann relation is used for derivation of the T (τ ) and n qg is the number degrees of freedom of the quark-gluon matter with N f = 3 active quark flavors within the present work.…”

Several Effects Unexplained by QCD

“…4. The relation of this correlation with the spatial picture of proton interactions is discussed in [21].…”

“…The slope changes its fast (almost linear at lower energies) increase with energy to much slower ( logarithmic) dependence shown in Figure 4. The relation of this correlation with the spatial picture of proton interactions is discussed in [21].…”