| Summary: | RESULTS OBTAINED: < 1. BFKL Pomeron and confinement: i) We derive the high energy evolution equation in the Gribov-Zwanziger approach, for the confinement of quarks and glu- ons. We demonstrate that the new equation generates an exponential decrease of the scattering amplitude at large impact parameter, and resolves the main difficulties of CGC high energy e↵ective theory. Such behaviour only occurs, if the gluon propaga- tor in Gribov-Zwanziger approach, does not vanish at small momenta. Solving the non-linear equation for deep inelastic scattering, we show that the suggested equation leads to the Froissart disc with a radius (RF), which increases as RF / Y = ln(1/x), and with a finite width for the distribution over |b − RF|. (Phys. Rev. D 103 (2021) no.1, 014020); and (ii) we propose a solution to the long standing problem present in the CGC/saturation approach: i.e. the power-like fall o↵ of the scattering amplitudes at large b. We propose a new non-linear equation, which takes into ac- count random walks both in transverse momenta of the produced gluons, and in their impact parameter. We demonstrate, that this equation is in accord with previous attempts to include di↵usion in impact parameters in the BFKL evolution equation. We show , that the solution to a new equation results in the exponential decrease of the scattering amplitude at large impact parameter, and in the restoration of the Froissart theorem.(Phys.Rev.D 101(2020)014023). 2. A new mechanism of multiparticle production: We developed a new approach based on our achievements in our previous project ( D. E. Kharzeev and E. M. Levin, “Deep inelastic scattering as a probe of entanglement,” Phys. Rev. D 95 (2017) no.11, 114008) which suggest a robust relation between the principle features of high energy scattering and entanglement properties of the hadronic wave function. In particularly, we compare our prediction with the first dedicated experiment (Phys. Rev. D 104 (2021) no.3, L031503) and demonstrated that out hypothesis finds a support in the DIS ...
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