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The probabilistic interpretation of the standard Regge-Gribov model with triple pomeron interactions is discussed. It is stated that introduction of probabilities within this model is not unique and depends on what is meant under the relevant substructures, The traditional interpretation in terms of partons (quarks and gluons) is shown to be external to the model, imported from the QCD, and actually referring to the single pomeron exchange without interactions. So this interpretation actually forgets the model as such. Alternative probabilities based on the pomerons as basic quantities within the model are discussed. Two different approaches are considered, based either on the pomerons in Fock's expansion of the wave function or on pomeron propagators in Feynman diagrams. These pomeron probabilities and entropy turn out to be very different from the mentioned standard ones in the purelyp obabilistic treatment. The entropy, in particular, either rises with the rapidity and saturates at a certain fixed value or first rises, reaches some maximum and goes down to zero afterwards. Possible observable manifestations of these probabilities and entropy are to be seen in the distributions of the cross-section in powers of the coupling constants to the participants. 23, Comment: 23 pages, 12 figures

The Regge-Gribov model of the pomeron and odderon in the non-trivial transverse space is studied by the renormalization group technique. The single loop approximation is adopted. Five real fixed points are found and the high-energy behaviour of the propagators is correspondingly calculated. As without odderon, the asymptotic is modulated by logarithms of energy in certain rational powers. Movement of coupling constants away from the fixed points is investigated both analytically (close to the fixed points) and numerically (far away). In the former case attraction occurs only in restricted domains of initial coupling constants. More generally in one third of the cases the coupling constants instead grow large indicating the breakdown of the single loop approximation., Comment: 39 pages, 10 figures; submitted to Eur.Phys.Jour. C

Production of pions in high-energy collisions with nuclei in the kinematics prohibited for free nucleons ("cumulative pions") is studied in the fusing color string model.The model describes the so-called direct mechanism for cumulative production. The other, spectator mechanism dominates in production of cumulative protons but is suppressed for pions. In the model cumulative pions are generated by string fusion which raises the maximal energy of produced partons above the level of the free nucleon kinematics. Momentum and multiplicity sum rules are used to determine the spectra in the deep fragmentation region. Predicted spectra of cumulative pions exponentially fall with the scaling variable $x$ in the interval $1

We consider the one-dimensional local reggeon theory describing the leading pomeron with the conformal spin $l=0$ and two subdominant pomerons with $l=\pm 2$. The dependence of the propagators of pomerons and the $hA$ amplitude on rapidity are found numerically by integrating the evolution equation., Comment: 15 pages, 7 figures; submitted to Eur.Phys.Jour. C

The four-pomeron vertex is studied in the perturbative QCD. Its dominating terms of the leading (zeroth and first) orders in the coupling constant and subdominant in the number of colors are constructed. The vertex consists of two terms, one with a derivative in rapidity $\pd_y$ and the other with the BFKL interaction between pomerons. The corresponding part of the action and equations of motion are found. The iterative solution of the latter is possible only for rapidities smaller than 2 and quite large coupling constant $\alpha_s$, of the order or greater than unity, when the quadruple pomeron interaction is relatively small. Also iteration of the part with $\pd_y$ is unstable in the infrared region and compels to introduce an infrared cut. The variational approach with simple trying functions allows to find the minimum of the action at $\alpha_s$ of the order 0.2 and rapidities up to 25. Numerical estimates for O-O collisions show that actually the influence of the quadruple pomeron interaction turns out to be rather small., Comment: 27 pages, 10 figures

We propose the one-dimensional reggeon theory describing local pomerons and odderons. It generalizes the well-known one-dimensional theory of pomerons (the Gribov model) and includes only triple interaction vertices. The proposed theory is studied by numerical methods: the one-particle pomeron and odderon propagators and the pA amplitude are found as functions of rapidity by integrating the evolution equation., Comment: 19 pages, 11 figures; submitted to Eur.Phys.Jour. C

In view of the planning experiments for collisions of light nuclei at RHIC the flow coefficients for O-O, Al-AL and Cu-Cu collisions are studied in the color string percolation model. Our results for $v_2$ are somewhat smaller than predicted by other groups although with the same dependence on centrality. Our obtained $v_3$ lie between predictions of other groups., Comment: 11 pages, 4 figures

The C-odd amplitude for the elastic $pp$ and $p\bar{p}$ scattering due to the exchange of the QCD odderon proposed by J.Bartels, L.N.Lipatov and G.P. Vacca is calculated with the Fukugita-Kwiecinski proton impact factor. The found amplitude is very small and cannot be felt in the differential cross-sections at 2.76 and 1.96 Tev respectively., Comment: 10 pages 5 figures

In the effective action approach the imaginary part of the triple pomeron amplitude is calculated. The found dependence on the longitudinal momentum transfer $\e$ is found to separate as a simple factor $1/|\e|$. This result is used to calculate the high-mass diffraction on a hadron and double scattering cross-section off a composite target}, Comment: 19 pages, 10 figures

In the QCD the small~$x$ evolution of the interacting pomerons and odderons is studied with all angular momenta $l$ taken into account. The resulting system of coupled nonlinear evolution equations is formulated in the momentum space and solved numerically. Excellent convergence in $l$ is observed. Also it is found that states with $l>1$ play an important role and substantially reduce the basic pomeron state at large rapidities, Comment: 16 pages, 13 figures

We discuss the odderon in the QCD and analyze the effects of running coupling introduced in a particular way to preserve the reggeization of the gluon within the leading logarithmic description. This idea is also applied to a family of BKP states with arbitrarily number of gluons in the planar limit. The numerical analysis shows that contrary to the pomeron case where the leading states become discretized, the odderon states still remain a continuous family starting at intercept one. The following rapidity dependence of the amplitude is studied. For the pomeron-odderon system the relation between the descriptions in the reggeized gluon (BFKL) framework and the color dipole/CGC one is investigated., Comment: 41 pages, 8 figures; a chapter for the memorial volume "From the past to the future - the legacy of Lev Lipatov"

In the color string picture with fusion and percolation the elliptic and triangular flows are studied for p-Au and d-Au collisions at 200 GeV. The ordering $v_n(d-Au)>v_n(p-Au)$ observed experimentally for central collisions is reproduced.The calculated elliptic flow $v_2$ at central collisions agrees satisfactorily with thedata. The triangular flow $v_3$ is found to be greater than the experimental values, similar to the resultsobtained in the approach based on the Color Glass Condensate initial conditions with subsequenthydrodynamical evolution., Comment: 7 pages 3 pictures

The effective reggeon field theory in zero transverse dimension ("the toy model") is studied. The transcendental equation for eigenvalues of the Hamiltonian of this theory is derived and solved numerically. The found eigenvalues are used for the calculation of the pomeron propagator., Comment: 18 pages, 6 figures, ancillary data files attached; to be published in Eur.Phys.Jour. C

In the framework of the QCD effective action the vertices of gluon emission in interaction of reggeons are studied in the limit of small longitudinal momenta of the emitted gluon. It is found that the vertices drastically simplify in this limit so that the gluon becomes emitted from a single reggeon coupled to the projectile and target via multireggeon vertices. Contribution from this kinematical region is studied for double and 2x2 elementary collisions inside the composite projectile and target., Comment: 20 pages, 13 figures; to be published in Eur.Phys.Jour. C

High-mass diffractive production of protons on the deuteron target is studied in the next-to-leading order (NLO) of the perturbative QCD in the BFKL approach. The non-trivial part of the NLO contributions coming from the triple interactions of the exchanged reggeons is considered. Analytic formulas are presented and shown to be infrared free and so ready for practical calculation., Comment: 28 pages, 2 figures; to be published in Eur.Phys.Jour. C

In the color string picture with fusion and percolation the dependence of the flow coefficients $v_n$ on the transverse momentum is studied for pp collisions the LHC energy respectively. Monte-Carlo simulations are used to locate simple strings and their fused clusters. The results favorably agree with the CMS data in the region $0.2 \le p_t\le 3.$ GeV/c appropriate for the string scenario., Comment: 10 pages, 6 figures. arXiv admin note: text overlap with arXiv:1407.4590

Within the effective QCD action for the Regge kinematics amplitudes for virtual gluon emission are studied in collision of a projectile with two and three targets. It is demonstrated that all un- Feynman singularities cancel between induced vertices and rescattering contributions. Formulas simplify considerably in a special gauge which is a straightforward generalization of the light-cone gauge for emission of real gluons., Comment: 13 pages, 6 figures; submitted to Eur.Phys.Jour.C

High-mass diffractive production of protons on the deuteron target is studied in the perturbative QCD in the BFKL approach. Leading order rearrangement contribution and the standard triple pomeron (the impulse approximation) are studied. In the perturbative limit $\alpha_s\to 0$ the rearrangement contribution dominates. Numerical estimates at realistic values of $\alpha_s$ and energies strongly depend on assumptions made about the behavior of the pomeron attached to the proton due to unitarization. They indicate that irrespective of these assumptions in the realistic situation the rearrangement and triple pomeron contributions turn out to be of comparable magnitude due to large dimensions of the deuteron., Comment: 19 pages, 12 figures

Hadron-nucleus amplitudes at high energies are studied in the "toy" Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and looses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprizing result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies.

Ward identities for reggeons are studied in the framework of effective action approach to the QCD in Regge kinematics. It is shown that they require introduction of new contributions not present in the reggeon diagrams initially. Application to vertices RR$\to$RP and RR$\to$RRP are considered and diagrams which have to be added to the QCD ones are found., Comment: 19 pages, 7 figures; to be published in Phys. Rev. D

The inclusive cross-section for production of a jet with a given transverse momentum off a heavy nucleus is derived in the BFKL framework with a running coupling on the basis of the bootstrap relation. The cross-section depends on the same three different coupling constants as the total cross-section unlike the cross-section for gluon production derived in the dipole approach., Comment: 13 pages, 6 figures, A new paragraph in the Introduction, a new figure in Sec. 3, results not changed

The vertex is constructed for gluon production in interaction of two reggeons coupled to projectiles and two reggeons coupled to targets. The vertex can be used to build cross-sections for collisions of two pairs of nucleons in AA scattering. Transversality of the constructed vertex is demonstrated as well as its good behaviour at large longitudinal momenta necessary for applications. Poles at zero values of longitudinal momenta are discussed and it is found that they remain in the amplitudes unlike in the case of a single projectile., Comment: 22 pages, 3 figures; submitted to Eur.Phys.Jour. C

A brief introduction of the relationship of string percolation to the Quantum Chromo Dynamics (QCD) phase diagram is presented. The behavior of the Polyakov loop close to the critical temperature is studied in terms of the color fields inside the clusters of overlapping strings, which are produced in high energy hadronic collisions. The non-Abelian nature of the color fields implies an enhancement of the transverse momentum and a suppression of the multiplicities relative to the non overlapping case. The prediction of this framework are compared with experimental results from the SPS, RHIC and LHC for $pp$ and AA collisions. Rapidity distributions, probability distributions of transverse momentum and multiplicities, Bose-Einstein correlations, elliptic flow and ridge structures are used to evaluate these comparison. The thermodynamical quantities, the temperature, and energy density derived from RHIC and LHC data and Color String Percolation Model (CSPM) are used to obtain the shear viscosity to entropy density ratio ($\eta/s$). It was observed that the inverse of ($\eta/s$) represents the trace anomaly $\Delta =(\varepsilon-3P)/T^{4}$. Thus the percolation approach within CSPM can be successfully used to describe the initial stages in high energy heavy ion collisions in the soft region in high energy heavy ion collisions. The thermodynamical quantities, temperature and the equation of state are in agreement with the lattice QCD calculations. Thus the clustering of color sources has a clear physical basis although it cannot be deduced directly from QCD., Comment: 107 pages, 37 figures

In the colour string picture with fusion and percolation it is shown that long range azimuthal-rapidity correlations (ridge) can arise from the superposition of many events with exchange of clusters of different number of strings and not from a single event. Relation of the ridge with the flow harmonics coefficients is derived. By direct Monte-Carlo simulations, in the technique previously used to calculate these coefficients, ridge correlations are calculated for AA, pA and pp collisions. The azimuthal anisotropy follows from the assumed quenching of the emitted particles in the strong colour fields inside string clusters. It is confirmed that in pp collisions the ridge structure only appears in rare events with abnormally high multiplicity. Comarison with the experimental data shows a good agreement. Also a good agreement is found for pPb collisions. For AA collisions a reasonable agreement is found for both near-side and away-side angular correlations although it worsens at intermediate angles.

Application of the effective action approach to amplitudes with loop integration is studied for collisions on two and three centers with possible gluon emission. A rule is formulated for the integration around pole singularities in the induced vertices which brings the results in agreement with the QCD. It is demonstrated that the amplitudes can be restored from the purely transverse picture by introducing the standard Feynman propagators for intermediate gluons and quarks., Comment: 16 pages, 9 figures; submitted to Eur.Phys.Jour. C

Double inclusive cross-sections for gluon production in collision of two nucleons with two nucleons are studied in the BFKL approach. Various contributions include emission from the pomerons attached to the participants, from the BFKL interactions between these pomerons and from the intermediate BKP state. The last contribution may be observable provided the growth with energy of the pomeron contribution is tamed in accordance with unitarity. Possibility of long-range azimuthal correlations due to the BKP state are discussed., Comment: arXiv admin note: substantial text overlap with arXiv:1305.1712

Gluon production on two scattering centers is studied in the formalism of reggeized gluons. Different contributions to the inclusive cross-section are derived with the help of the Lipatov effective action. The AGK relations between these contributions are established. The found inclusive cross-section is compared to the one in the dipole picture and demonstrated to be the same., Comment: 27 pages, 14 figures; to be published in Eur.Phys.Jour. C

Inclusive cross-sections for gluon production in collision of two mucleons with two nucleons are studied in the BFKL approach. Various contributions include emission from the pomerons attached to the participants, from the BFKL interactions in between these pomerons and from the intermediate BKP state. The last contribution may be observable provided the growth with energy of the pomeron contribution is tamed in accordance with unitarity.

The amplitude for the collision of two hadrons with the lowest order pomeron loop is calculated. Numerical calculations show that the loop contribution to the amplitude begins to dominate the single pomeron exchange at rapidities 8-10. Full dependence of the triple-pomeron vertex on intermediate conformal weights is taken into account., Comment: 10 pages, 2 figures

High-energy collisions of two nucleons on two nucleons are studied in the BFKL approach in the leading approximation in $\alpha_sN_c$. Diagrams with redistribution of colour are considered. It is found that intermediate BKP states consisting of 4 reggeized gluons give a contribution which may be leading in deuteron-deuteron scattering and thus experimentally observable., Comment: 22 pages, 14 figures

In the Regge kinematics the amplitude for gluon production off three scattering centers is found in the Lipatov effective action technique. The vertex for gluon emission with the reggeon splitting in three reggeons is calculated and its transversality is demonstrated. It is shown that in the sum of all contributions terms containing principal value singularities are cancelled and substituted by the standard Feynman poles. These results may be used for calculation of the inclusive cross-section for gluon production on two nucleons in the nucleus., Comment: 22 pages, 9 figures; submitted to Eur.Phys.Jour. C

The behaviour of the pomeron propagator in the external nuclear field is studied in the (2+1)-dimensional QCD. It is shown that in the physically interesting case when the field does not vanish at large rapidities the propagator in the field vanishes much faster than in the vacuum, in agreement with the results found in the local Regge-Gribov model. However if the nuclear field vanishes at high rapidities the field does not change the behaviour of the pomeron propagator., Comment: 14 pages, 10 figures

By direct Monte-Carlo simulations it is shown that the anisotropic flows can be successfully described in the colour string picture with fusion and percolation provided anisotropy of particle emission from the fused string is taken into account. Quenching of produced particles in the strong colour field of the string is the basic mechanism for this anisotropy. The concrete realization of this mechanism is borrowed from the QED. Due to dependence of this mechanism on the external field strength the found flows grow with energy, with values for $v_2$ at LHC energies greater by ~15% than at RHIC energies., Comment: New version with a non-static distribution of strings

The process of gluon production in quark-nucleus collisions is studied in the framework of Lipatov's effective action formalism. The relevant simplifications and rules for longitudinal integrations are discussed in detail. The results obtained with the help of these rules correspond to the purely transversal formalism based on effective vertices in the transversal space., Comment: 15 pages, 7 figures; some references added; to be published in Eur.Phys.Jour. C

Application of the effective action formalism is studied for processes in which the reggeons may split. It is shown that the gluon production on two centers is described by the contribution of the Reggeon-to-two-Reggeons-plus-Particle vertex supplemented by certain singular contributions from the double gluon exchange. The rules for longitudinal integrations are established from the comparison to perturbative QCD amplitude. Convenient expressions for application to the inclusive gluon production are derived., Comment: 15 pages, 7 figures; some misprints corrected; submitted to Eur.Phys.Jour. C

It is shown by numerical calculations that the convoluted QCD pomeron propagator in the external field created by a solution of the Balitsky-Kovchegov equation in the nuclear matter vanishes at high rapidities. This may open a possibility to apply the perturbative approach for the calculation of pomeron loops., Comment: 17 pages, 15 figures

It is shown by numerical calculations that the convoluted forward pomeron propagator in the external field created by a solution of the Balitski-Kovchegov equation in the nuclear matter vanishes at high rapidities. This may open a possibility to apply the perturbative approach for the calculation of pomeron loops., Comment: 10 pages, 8 figures

It is shown that the elliptic flow can be successfully described in the color string picture with fusion and percolation provided anisotropy of particle emission from the fused string is taken into account. Two possible sources of this anisotropy are considered, propagation of the string in the transverse plane and quenching of produced particles in the strong color field of the string. Calculations show that the second source gives an overwhelming contribution to the flow at accessible energies., Comment: 23 pages, 11 figures

Contribution of simplest loops for hadron-nucleus scattering cross-sections is studied in the Local Reggeon Field Theory with a supercritical pomeron. It is shown that inside the nucleus the supercritical pomeron transforms into a subcritical one, so that perturbative treatment becomes possible. The pomeron intercept becomes complex, which leads to oscillations in the cross-sections., Comment: 13 pages, 6 figures

Inclusive cross-section for gluon production is calculated by the dispersion technique in the NLO in the perturbative QCD with a large number of colours. The found cross-section coincides with the one derived in the dipole picture. No trace of the BKP states is found., Comment: 30 pages, 17 figures. Appendix with a new observation added. Conclusions changed.

It is shown that in the Glauber scattering of a fast quark in the external field loop corrections to the gluon emission amplitude due to virtual softer gluon after renormalization coincide with a correction due to reggeization of the exchanged gluon in the BFKL picture., Comment: 26 pages, 10 figures

Energy loss of a jet due to multiple collisions in the nuclear target is studied in the framework of the perturbative QCD with an infrared cutoff. An iterational procedure for its calculation is developed, which allows to reliably find up to 16 successive collisions in rescattering. The calculated shift of the scaling variable reaches values of the order 0.1 at medium $x$ and transverse momentum $p$ in the interval 5-10 GeV/c. The shift is found to be independent of the atomic number of the target and energy., Comment: 16 pages, 10 figures

The one-loop diffractive amplitude for emission of two real gluons with widely different rapidities is studied in the Lipatov effective action formalism. It is shown that after integration over longitudinal momenta in the loop the resulting expression coincides with the one obtained by the Lipatov-Bartels formalism in transversal space provided the same prescription is used to exclude divergent contributions as previously proposed for emission of a single real gluon., Comment: 15 pages, 3 figures; published in Eur.Phys.J. C

The nucleus-nucleus Glauber amplitude in the tree approximation is studied for heavy participant nuclei. It is shown that, contrary to previous published results, it is not unitary for realistic values of nucleon-nucleon cross-sections., Comment: 15 pages, 1 figure, 1 table. Submitted to Yad. Fiz

The lowest order pomeron loop is calculated for the leading conformal weight with full dependence of the triple pomeron vertex on intermediate conformal weights. The loop is found to be convergent. Its contribution to the pomeron Green function begins to dominate already at rapidities 10$\div$15. The pomeron pole renormalization is found to be quite small due to a rapid fall of the triple pomeron vertex with rising conformal weights., Comment: 17 pages, 2 figures

The local reggeon field theory is studied perturbatively taking advantage of the PT symmetry in the Hamiltonian formulation. In the lowest non trivial order we show that the pomeron interactions renormalize the slope. In the same order we find a non local pair potential acting between pomerons, which has a singular structure. However the analysis of the scattering operator shows that at small coupling constant bound states do not appear so that the two-particle spectrum is not changed., Comment: 20 pages, latex

Contribution of simplest loops is studied in the Local Reggeon Field Theory with a supercritical pomeron in the nuclear matter. It is shown that the latter transforms the supercritical pomeron into the subcritical. Renormalization of the intercept and difficulties related to the fact that the renormalized intercept is complex are discussed. Numerical results with the conventional parameters are reported., Comment: 20 pages, 7 figures

Single and double inclusive cross-sections in nucleus-nucleus collisions are derived in the perturbative QCD with interacting BFKL pomerons in the quasi-classical approximation., Comment: 15 pages, 2 figures

Proceedings of the 12th International Conference on Elastic and Diffractive Scattering (Blois Workshop) - Forward Physics and QCD, Comment: Proceedings of the 12th International Conference on Elastic and Diffractive Scattering (Blois Workshop) - Forward Physics and QCD, 549 pages replaced to include list of conveners

Nucleus-nucleus scattering is studied in the local Reggeon Field Theory in the quasi-classical approximation with non-eikonal boundary conditions corresponding to the Glauber picture at low energies. Comparison with the commonly used eikonal boundary conditions shows that the new conditions make both the action and nucleus-nucleus total cross-sections lower by $3\div 5$ %. They also substantially change the behaviour of the solutions of the equations of motion at low energies. Using expressions for the double inclusive cross-sections derived earlier in the Reggeon Field Theory \cite{CM} long-range rapidity correlations are calculated for the RHIC and LHC energies., Comment: 14 pages, 10 figures