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The presence of Odderon at high energy has been in question for quite some time. We have confronted the Odderon description to the available data especially for pp and scattering including the most recent measurements by UA4/2, E710, CDF and E811 Collaborations. The Odderon in perturbative and nonperturbative QCD has also been discussed along with some phenomenological approaches. A comparison of the Odderon description with other models has also been made for data including the measurements from cosmic ray, which corresponds to the LHC energy of 14 TeV. Our study especially focuses on the measurements at RHIC and LHC and the presence or otherwise of Odderon.

A simple model for elastic diffractive hadron scattering, reproducing the dip-bump structure is used to analyze pp and scattering. The main emphasis is on the delicate and nontrivial dynamics in the dip-bump region, near t = -1 GeV². 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 nonlinearity 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 existing models will be either confirmed or ruled out, are presented.

We review the elastic and diffractive scatterings of protons (called also the “forward physics”) with emphasis on the LHC data, especially those deviating from the expectations based on extrapolations from earlier measurements at the ISR and Fermilab and thus triggering searches for new ideas, models and theories. We list these new data and provide a brief introduction of available theoretical approaches, mainly those based on analyticity, crossing symmetry and unitarity, particularly the Regge pole model realizing these concepts. Fits to the data are presented and tensions between theoretical predictions and the data that may indicate the way to further progress are in the focus of our paper.

We present the first steps in an effort to incorporate the physics of transverse spin asymmetries into the saturation formalism of high energy QCD. We consider a simple model in which a transversely polarized quark scatters on a proton or nuclear target. Using the light-cone perturbation theory the hadron production cross section can be written as a convolution of the light-cone wave function squared and the interaction with the target. To generate the single transverse spin asymmetry (STSA) either the wave function squared or the interaction with the target has to be T-odd. In this work we use the lowest-order q → q G wave function squared, which is T-even, generating the STSA from the T-odd interaction with the target mediated by an odderon exchange. We study the properties of the obtained STSA, some of which are in qualitative agreement with experiment: STSA increases with increasing projectile x_F and is a non-monotonic function of the transverse momentum k_T. Our mechanism predicts that the quark STSA in polarized proton–nucleus collisions should be much smaller than in polarized proton–proton collisions. We also observe that the STSA for prompt photons due to our mechanism is zero within the accuracy of the approximation.

We provide a statistically significant observation of the elusive Odderon exchange, based on novel and model-independent analysis of the scaling properties of the differential cross sections of elastic pp and $p\overline{p}$ scattering in the TeV energy range. We report the statistical significance of the observed Odderon signal at the level of 6.26 σ.