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 cross-sections 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 $\mathcal{O}$(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.

30 pages, 7 figures and 3 tables

References in corpus (5)

• Measurement of the proton-air cross-section at $\sqrt{s}=57$ TeV with the Pierre Auger Observatory
• Measurement of the total cross section from elastic scattering in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector
• Measurement of Elastic pp Scattering at $\sqrt{s}$ = 8 TeV in the Coulomb-Nuclear Interference Region - Determination of the $\rho$-Parameter and the Total Cross-Section
• Once More on Coulomb-Nuclear Interference
• Glue drops inside hadrons

Cited by in corpus (15)

• Coulomb-Nuclear Interference: Theory and Practice for pp-Scattering at 13 TeV
• Global characteristics of the medium produced in ultra-high energy cosmic ray collisions
• On the shape of nucleons at high energies
• Resonant mode of elastic scattering of protons at ultra-high energies
• On the transverse size of hadrons at asymptotically high energies
• Magnetic field in nuclear collisions at ultra high energies
• Lévy $\alpha$-stable model for the non-exponential low-$|t|$ proton-proton differential cross section
• On the " Froissaron-Maximal Odderon" Model
• Correlations among elastic and inelastic cross-sections and slope parameter
• The energy dependence of the ratio of elastic to total cross section in $pp$ and $\bar{p}p$ collisions
• Two diffraction cones of elastic scattering and structural symmetry conjecture
• pp elastic scattering at ISR and LHC energies
• Soft Pomeron in light of the LHC correlated data
• On Asymptotic Universality of Strong Interactions at Large Distances
• Optical Theorem, Crossing Property and Derivative Dispersion Relations: Implications on the Asymptotic Behavior of ${\sigma }_{tot}(s)$ and $\rho (s)$