Narrow Results

The Bialas–Bzdak model of elastic proton–proton scattering is generalized to the case when the real part of the parton–parton level forward scattering amplitude is nonvanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the intersecting storage rings (ISR) energies, and improves significantly the ability of the model to describe also the recent TOTEM data at LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding energies, is related to the increase of the quark–diquark distance and to the increase of the "fragility" of the protons with increasing energies. In addition, we present and test the validity of two new phenomenological relations: one of them relates the total p+p cross-section to an effective, model-independent proton radius, while the other relates the position of the dip in the differential elastic cross-section to the measured value of the total cross-section.

The Bialas–Bzdak model of elastic proton–proton scattering assumes a purely imaginary forward scattering amplitude, which consequently vanishes at the diffractive minima. We extended the model to arbitrarily large real parts in a way that constraints from unitarity are satisfied. The resulting model is able to describe elastic pp scattering not only at the lower ISR energies but also at in a statistically acceptable manner, both in the diffractive cone and in the region of the first diffractive minimum. The total cross-section as well as the differential cross-section of elastic proton–proton scattering is predicted for the future LHC energies of , 14, 15 TeV and also to 28 TeV. A nontrivial, significantly nonexponential feature of the differential cross-section of elastic proton–proton scattering is analyzed and the excitation function of the nonexponential behavior is predicted. The excitation function of the shadow profiles is discussed and related to saturation at small impact parameters.

In this paper we study the contribution of the incoming hadrons’ polarization to the differential cross section of the hadron scattering at the ultra low energy limit. It is shown that their polarization does not have significant effect on the differential cross section of such scattering. The polarization of the outgoing hadrons is also analyzed.