The proton-proton and proton-antiproton inelasticity profiles in the impact parameter display very interesting and sensitive features which cannot be deduced solely from the current large body of high-energy scattering data. In particular, phenomenological studies exhibit a link between the ratio of the real to imaginary parts of the elastic scattering amplitude at a finite momentum transfer, and the corresponding change of character of the inelastic processes from central to peripheral collisions. We describe how a theoretical model, accommodating the existing data, based on the Regge hypothesis including both the Pomeron and odderon as double poles, and ω and f mesons as single poles in the complex-J plane, generates a hollow in the inelasticity at low impact parameters. The hollowness effect, which generally may be sensitive to model details, does unequivocally take place both for pp and pp collisions within the applied Regge framework, indicating inapplicability of inelasticity-folding geometric approaches.
The unitarily extended Bialas–Bzdak model of elastic proton–proton scattering is applied, without modifications, to describe the differential cross-section of elastic proton–antiproton collisions in the TeV energy range, and to extrapolate these differential cross-sections to LHC energies. In this model-dependent study we find that the differential cross-sections of elastic proton–proton collision data at 2.76 and 7 TeV energies differ significantly from the differential cross-section of elastic proton–antiproton collisions extrapolated to these energies. The elastic proton–proton differential cross-sections, extrapolated to 1.96 TeV energy with the help of this extended Bialas–Bzdak model do not differ significantly from that of elastic proton–antiproton collisions, within the theoretical errors of the extrapolation. Taken together these results provide a model-dependent, but statistically significant evidence for a crossing-odd component of the elastic scattering amplitude at the at least 7.08 sigma level. From the reconstructed Odderon and Pomeron amplitudes, we determine the $$\sqrt{s}$$
s
dependence of the corresponding total and differential cross-sections.
Proton-proton differential and total cross sections provide information on the energy dependence of proton shape and size. We show that the deviation from exponential behavior of the diffraction cone observed near t = −0.1 GeV 2 , (so-called break), both at the ISR and the LHC follows from the t-channel two-pion loop contributions, imposed by unitarity. By using a simple Regge-pole model, we extrapolate the "break" from the ISR energy region to that of the LHC. This allows us to answer two important questions: 1) To what extent is the "break" observed recently at the LHC a "recurrence" of that seen at the ISR (universality)? 2) What is the relative weight of two-pion effect to the vertex coupling (Regge residue) compared to expanding size (pomeron propagator) in producing the "break"? We find that the effect comes both from the Regge residue (protonpomeron coupling) and from the Regge propagator. A detail analyses of their balance, including the correlation between the relevant parameters is presented.
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