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We compute amplitude of deeply virtual Compton scattering in the parton model. We found that the amplitude up to the accuracy O(1/Q) depends on new skewed parton distributions (SPD's). These additional contributions make the DVCS amplitude explicitly transverse.

We recall the main features of the Regge approach used to understand soft interactions at LHC and higher energies. Unitarity tames the power growth of the elastic protonproton scattering amplitude with energy, and leads to the migration of the secondary particles produced in high-energy proton-proton collisions to larger transverse momenta. We discuss, in qualitative terms, the role of processes containing large rapidity gaps (LRG), and the probability that the gaps survive population by secondaries produced in additional soft interactions. We explain how the Regge diagram corresponding to a LRG event simultaneously describes events with different (single, double, etc.) particle density in the same rapidity interval. We show that the role of these, enhanced, multi-Pomeron diagrams can be studied by measuring multiplicity fluctuations and long-range rapidity correlations between secondaries produced at the Tevatron and the LHC. Finally, we make a list of the characteristic features of the multi-Pomeron description of soft interactions that may be observed at the high energies accessible at the Tevatron and the LHC.

We justify the practical use of the Shuvaev integral transform approach to calculate the skewed distributions, needed to describe diffractive processes, directly from the conventional diagonal global parton distributions. We address doubts which have been raised about this procedure. We emphasise that the approach, on the one hand, satisfies all theoretical reqirements, and, on the other hand, is consistent with DVCS data at NLO. We construct an easily accessible package for the computation of these skewed distributions.

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The cross sections of heavy quark production in pp collision and for their photo-and electroproduction are calculated in the framework of QCD. The virtual nature of the interacting gluons as well as their transverse motion and different polarizations are taken into account. The obtained cross sections exhibit more rapid growth with the initial energy than the parton model predictions and the p T distributions of produced heavy quarks are more smooth.

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Using the conformal invariance the leading-log evolution of the off-forward structure function is reduced to the forward evolution described by the conventional Dokshitzer-Gribov-Lipatov-Altarelli-Parisi ͑DGLAP͒ equation. The method relies on the fact that the anomalous dimensions of the Gegenbauer moments of the off-forward distribution are independent of the asymmetry, or skewedness, parameter and equal to the DGLAP ones. The integral kernels relating the forward and off-forward functions to the same Mellin and Gegenbauer moments are presented for an arbitrary asymmetry value. ͓S0556-2821͑99͒07321-X͔ PACS number͑s͒: 11.15.BtThe logarithmic evolution of the off-forward structure function is described by the generalization of the DokshitzerGribov-Lipatov-Altarelli-Parisi ͑DGLAP͒ equation for the parton distribution. However the explicit dependence on the longitudinal momentum transfer makes the splitting functions much more complicated since they include different pieces in different kinematics regions ͓1͔.On the other hand, it is well known that there is a set of twist-two operators whose leading-log evolution is exactly diagonal due to conformal symmetry remaining to be valid at the one-loop level ͑see e.g., ͓2,3͔͒. The off-forward matrix elements of these operators are the Gegenbauer polynomials, they turn into the simple powers of Bjorken x in the forward kinematics. The Gegenbauer moments of the nonsinglet offforward function have a simple multiplicative evolution like the forward ones. There is a mixture of quark and gluon channels for the singlet function but only between the moments of the same order, the anomalous dimensions being equal for the forward and off-forward cases. This property allows, in principle, to reduce the nondiagonal leading-log evolution to the diagonal one: if one could replace in some way the powers of x in the solution of the conventional DG-LAP equation by the Gegenbauer polynomials the result returns a solution of the off-forward equation. However the Gegenbauer polynomials do not form a complete set on the full interval, where the structure function is defined, therefore this substitution cannot be done straightforward. It is the aim of the present paper to construct explicitly the transformation relating the off-forward and forward evolution.