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We discuss some problems concerning the application of perturbative QCD to high energy processes. In particular for hard processes, we analyze higher order and higher twist corrections. It is argued that these effects are of great importance for understanding the behaviour of pion electromagnetic form factor at moderately large momentum transfers. For soft processes, we show that summing the contributions of the lowest twist operators leads to a Regge-like amplitude.

Anticipating forthcoming publication by the TOTEM collaboration of low-$\left|t\right|$ elastic scattering data at $\sqrt{s}$ = 13 and 2.76 TeV, hereby we emphasize the correlation between two prominent structures seen upon the otherwise exponential diffraction cone, namely a “break” staying fixed around $t\approx -$0.1 GeV² and a dip moving with energy logarithmically inwards; while at the ISR, the two structures are separated by a distance of about 1 GeV², at the LHC, the dip comes close to the periphery of the “break”, thus affecting its parametrization. An unbiased disentangling and identification of the “break” at the LHC should account for this correlation.

Energy resonance in scattering is usually investigated either directly in the complex energy plane (E-plane) or indirectly in the complex angular momentum plane (ℓ-plane). Another formulation complementing these two approaches was introduced recently. It is an indirect algebraic method that studies resonances in a complex charge plane (Z-plane). This latter approach will be generalized to provide a unified algebraic treatment of resonances in the complex E-, ℓ-, and Z-planes. The complex scaling (rotation) method will be used in the development of this approach. The resolvent operators (Green's functions) are formally defined in these three spaces. Bound states spectrum and resonance energies in the E-plane are mapped onto a discrete set of poles of the respective resolvent operator on the real line of the ℓ- and Z-planes. These poles move along trajectories as the energy is varied. A finite L² basis is used in the numerical implementation of this approach. Stability of poles and trajectories against variation in all computational parameters is demonstrated. Resonance energies for a given potential are calculated and compared with those obtained by other studies.

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.