The Pomeron and Odderon in elastic, inelastic and total cross sections at the LHC

Abstract: A simple model for elastic diffractive hadron scattering, reproducing the dip-bump structure is used to analyze PP and $\bar PP$ scattering. The main emphasis is on the delicate and non-trivial dynamics in the dip-bump region, near t=-1 GeV$^2$. The simplicity of the model and the expected smallness of the absorption corrections enables one the control of various contributions to the scattering amplitude, in particular the interplay between the C-even and C-odd components of the amplitude, as well as their relative contribution, changing with s and t. The role of the non-linearity of the Regge trajectories is scrutinized. The ratio of the real to imaginary parts of the forward amplitude, the ratio of elastic to total cross sections and the inelastic cross section are calculated. Predictions for the LHC energy region, where most of the exiting models will be either confirmed or ruled out, are presented.