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My research is aimed at solving and broadening the view on current problems related to soft high-energy diffractive processes in proton-proton collisions. In this kinematic domain, where the energy of collision is much larger than the momentum transfer between the protons, perturbative methods of theory of strong interactions - quantum chromodynamics (QCD), cannot be reliably applied. This non-perturbative regime of hadronic interactions is usually treated by phenomenological models in the language of the Regge theory, which was originally used to describe the strong interactions before the QCD was formulated. There, the object called the Pomeron with even C-parity plays the most important role. In QCD, the Pomeron is predominantly gluonic object (a pair of gluons in a color-singlet). There is now some evidence for the existence of the C-odd counterpart of the Pomeron, namely the Odderon (a colorless odd-gluon state).
Central exclusive diffraction production of hadrons is of particular interest and such reactions have been extensively studied in a number of experiments, starting with CERN ISR, WA102, COMPASS, CDF, and are further explored in experiments at RHIC (STAR) and at the LHC (ALICE, ATLAS-ALFA, CMS-TOTEM, LHCb). I will focus in particular on the central exclusive production (CEP) of mesons within the tensor-Pomeron and vector-Odderon approach and interpret already existing experimental results. One of the goals of the theoretical research was to better understand CEP mechanism underlying non-perturbative dynamics, in particular a variety soft reactions p+p → p+X+p with a hadronic system X = f0, f2, f1, ρ0, ϕ, π+π-, K+K-, p anti-p, ϕϕ, 4π, 4K. Different fusion processes through purely diffractive (Pomeron-Pomeron fusion, Odderon-Pomeron fusion) and photoproduction (photon-Pomeron fusion) mechanisms (both resonant and non-resonant contributions including interference effects between them) must be taken into account for a given process. Central diffractive production in hadronic collisions is dominated at high energies by Pomeron-Pomeron fusion. CEP processes, due to the gluonic nature of the Pomeron, are favorable place to look for production of gluon-bound states (glueballs). The observation of glueballs would be a long-awaited confirmation of this crucial prediction of the QCD theory. I will pay special attention to soft CEP reactions that have not been measured at the LHC so far but offer good possiblities to search for effects of the elusive glueballs and Odderon. Finally, I will discuss the photon induced and soft-photon bremsstrahlung processes, the motivation to study them with particular emphasis on their relevance to future experiments at the LHC.