Elastic scattering at $\sqrt{s} = 6$ GeV up to $ \sqrt{s} = 13$ TeV (proton-proton; proton-antiproton; proton-neutron)

Abstract

In the framework of the Regge-eikonal model of hadron interaction based on the analyticity of the scattering amplitude with taking into account the hadron structure, a simultaneous analysis is carried out of 90 sets of data. These sets include the data were obtained at low energies ($\sqrt{s} > 3.6 $ GeV and high energies at FNAL, ISR, $SP\bar{P}S$, TEVATRON and LHC with 4326 experimental points, including the data of $A_N$. The energy and momentum transfer dependence of separate sets of data is analyzed on the basis of the eikonalized Born amplitude with taking into account two additional anomalous terms. Different origins of the nonlinear behavior of the slope of the scattering amplitude are compared. No contribution of hard-Pomeron in the elastic hadron scattering is found. The importance of Odderon's contribution is presented. In the framework of the HEGS model, using the electromagnetic and gravitomagnetic form factors, the differential cross sections in the CNI region and at large $t$ are described well in a wide energy region simultaneously. It is shown that the cross-even part includes the soft pomeron and the additional term with a large slope have energy dependence $\ln^2(s)$. The cross-odd part includes the maximal odderon term with $\ln^{2}(s)$ and an additional oscillation term with $\ln(s)$. It is shown that the additional terms with large slope are proportional to charge distributions but the maximal odderon term and oscillation term are proportional to matter distributions. Also, a good description of proton-neutron differential scattering with 526 experimental points is obtained on the basis of the amplitudes taken from the analysis of $pp$ and $p\bar{p}$ scattering. A good description of the $A_N$ data was also obtained.