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, $T(b)$, reaches the black disk limit at small $b$. Two scenarios are possible at larger energies, $\sqrt{s}\ga 100$ TeV. First, the profile function gets frozen in the black disk limit, $T(b)\simeq 1$ while the radius of the black disk $R_{blackdisk}$ is increasing with $\sqrt{s}$, providing ${\sigma }_{tot}\sim {\ln }^{2}s$, ${\sigma }_{el}\sim {\ln }^{2}s$, ${\sigma }_{inel}\sim {\ln }^{2}s$. In another scenario the profile function continues to grow at $\sqrt{s}\ga 100$ TeV approaching the maximal value, $T(b)\simeq 2$, that means the resonant disk mode. We discuss features of the resonant disk mode when the disk radius, $R_{resonantdisk}$, increases providing the growth of the total and elastic cross sections ${\sigma }_{tot}\sim {\ln }^{2}s$, ${\sigma }_{el}\sim {\ln }^{2}s$, but a more slow increase of inelastic cross section, ${\sigma }_{inel}\sim \ln s$.

9 pages

References in corpus (5)

• Measurement of the proton-air cross-section at $\sqrt{s}=57$ TeV with the Pierre Auger Observatory
• Reflective scattering from unitarity saturation
• Impact analysis of TOTEM data at the LHC: black disk limit exceeded
• Proton-proton, pion-proton and pion-pion diffractive collisions at ultra-high energies
• Hadron diffractive production at ultrahigh energies

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• Comments on high-energy total cross sections in QCD
• Central elastic scattering
• Resonant mode of elastic scattering of protons at ultra-high energies
• Proton Internal Pressure in $pp$ and $\bar{p}p$ Elastic Scattering
• The Effects of the Tsallis Entropy in the Proton Internal Pressure
• pp elastic scattering at ISR and LHC energies
• The invariance of inelastic overlap function