A new parton model for the soft interactions at high energies: the Odderon

In this paper we discuss the Odderon contribution in our model[19] that gives a fairly good description of $\sigma_{\rm tot}$ $\sigma_{\rm el}$and $B_{\rm el}$ for proton-proton scattering. We show that the shadowing corrections are large, and induce considerable dependence on energy for the Odderon contribution, which in perturbative QCD does not depend on energy. This energy dependence is in agreement with the experimental data for $\rho = {\rm Re}/{\rm Im}$, assuming that the Odderon gives a contribution of about 1 mb at W = 7 TeV. This differs greatly with our estimates for a CGC based model. We reproduce the main features of the $t$ -dependence that are measured experimentally: the slope of the elastic cross section at small $t$, the existence of the minima in $t$-dependence which is located at $|t|_{min}$ = 0.52 GeV 2 at W= 7 TeV; and the behaviour of the elastic cross section at $|t| > |t|_{min}$.The real part of the elastic amplitude turns out to be much smaller than the experimental one. Consequently, to achieve a description of the data, it is necessary to add an odderon contribution.