Quasi-multi-Regge Processes with a Quark Exchange in the t-channel

The QCD amplitudes for particle's production in the quasi-multi-Regge kinematics with a quark exchange in crossing channels are calculated in the Born approximation. In particular they are needed to find next-to-leading corrections to the quark Regge trajectory and to the integral kernel of the Bethe-Salpeter equation for the t-channel partial wave with fermion quantum numbers and a negative signature. The gauge-invariant action for the interaction of the reggeized quarks and gluons with the usual particles is constructed.Comment: LaTeX, 10 page

Modular Invariance and the Odderon

We identify a new symmetry for the equations governing odderon amplitudes, corresponding in the Regge limit of QCD to the exchange of 3 reggeized gluons. The symmetry is a modular invariance with respect to the unique normal subgroup of sl(2,Z) {\,} of index 2. This leads to a natural description of the Hamiltonian and conservation-law operators as acting on the moduli space of elliptic curves with a fixed ``sign'': elliptic curves are identified if they can be transformed into each other by an {\em even} number of Dehn twists.Comment: 9 pages, LaTeX, uses amssym.def for \Bbb 'blackboard math' font

BFKL Pomeron in string models

We consider scattering amplitudes in string models in the Regge limit of high energies and fixed momentum transfers with the use of the unitarity in direct channels. Intermediate states are taken in the multi-Regge kinematics corresponding to the production of resonances with fixed invariant masses and large relative rapidities. In QCD such kinematics leads to the BFKL equation for the Pomeron wave function in the leading logarithmic approximation. We derive a similar equation in the string theory and discuss its properties. The purpose of this investigation is to find a generalization of the BFKL approach to the region of small momentum transfers where non-perturbative corrections to the gluon Regge trajectory and reggeon couplings are essential. The BFKL equation in the string theory contains additional contributions coming from a linear part of the Regge trajectory and from the soft Pomeron singularity appearing already in the tree approximation. In higher dimensions in addition, a non-multi-Regge kinematics corresponding to production of particles with large masses is important. We solve the equation for the Pomeron wave function in the string theory for D=4 and discuss integrability properties of analogous equations for composite states of several reggeised gluons in the multi-colour limit.Comment: 48 pages, 2 figure

Deformed Spectral Representation of the BFKL Kernel and the Bootstrap for Gluon Reggeization

We investigate the space of functions in which the BFKL kernel acts. For the amplitudes which describe the scattering of colorless projectiles it is convenient to define, in transverse coordinates, the Moebius space in which the solutions to the BFKL equation vanish as the coordinates of the two reggeized gluons coincide. However, in order to fulfill the bootstrap relation for the BFKL kernel it is necessary to modify the space of functions. We define and investigate a new space of functions and show explicitly that the bootstrap relation is valid for the corresponding spectral form of the kernel. We calculate the generators of the resulting deformed representation of the sl(2,C) algebra.Comment: 22 pages, 1 figur

Direct Calculations of the Odderon Intercept in the Perturbative QCD

The odderon intercept is calculated directly, from its expression via an average energy of the odderon Hamiltonian, using both trial wave functions in the variational approach and the wave function recently constructed by R.A.Janik and J.Wosiek. The results confirm their reported value for the energy. The odderon intercept is calculated directly, from its expression via an average energy of the odderon Hamiltonian, using both trial wave functions in the variational approach and the wave function recently constructed by R.A.Janik and J.Wosiek.The results confirm their reported value for the energy. Variational calculations give energies some 30% higher. However they also predict the odderon intercept to be quite close to unity. In fact, for realistic values of $\alpha_s$, the intercept calculated variationally is at most 2% lower than the exact one: 0.94 instead of 0.96. It is also found that the solution for $q_3=0$ does not belong to the odderon spectrum. The diffusion parameter is found to be of the order 0.6.Comment: 20 page

High energy QCD as a completely integrable model

We show that the one-dimensional lattice model proposed by Lipatov to describe the high energy scattering of hadrons in multicolor QCD is completely integrable. We identify this model as the XXX Heisenberg chain of noncompact spin $s=0$ and find the conservation laws of the model. A generalized Bethe ansatz is developed for the diagonalization of the hamiltonian and for the calculation of hadron-hadron scattering amplitude.Comment: Latex style, 16 pages, ITP-SB-94-1

The effective action and the triple Pomeron vertex

We study integrations over light-cone momenta in the gauge invariant effective action of high energy QCD. A regularization mechanism which allows for the evaluation of the longitudinal integrations is presented. After a rederivation of the reggeized gluon and the BFKL-equation from the effective action, we study the 1-3 and 2-4 reggeized gluon transition vertex of QCD Reggeon field theory and discuss their connection with the usual triple Pomeron vertex of perturbative QCD.Comment: Talk given at the 3rd International Hadron Structure '09 Conference, Tatranska Strba, Slovakia, 30 Aug - 3 Sep 2009; 4 pages, 16 figure

Conformal Invariance of Unitarity Corrections

We study perturbative unitarity corrections in the generalized leading logarithmic approximation in high energy QCD. It is shown that the corresponding amplitudes with up to six gluons in the t-channel are conformally invariant in impact parameter space. In particular we give a new representation for the two-to-six reggeized gluon vertex in terms of conformally invariant functions. With the help of this representation an interesting regularity in the structure of the two-to-four and the two-to-six transition vertices is found.Comment: 11 page

NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories

We study next-to-leading corrections to the integral kernel of the BFKL equation for high energy cross-sections in QCD and in supersymmetric gauge theories. The eigenvalue of the BFKL kernel is calculated in an analytic form as a function of the anomalous dimension \gamma of the local gauge-invariant operators and their conformal spin n. For the case of an extended N=4 SUSY the kernel is significantly simplified. In particular, the terms non-analytic in n are canceled. We discuss the relation between the DGLAP and BFKL equations in the N=4 model.Comment: Latex, 26 pages, typos corrected, to be published in Nucl.Phys.

Feynman rules for effective Regge action

Starting from the gauge invariant effective action in the quasi-multi-Regge kinematics (QMRK), we obtain the effective reggeized gluon (R) -- particle (P) vertices of the following types: $RPP$, $RRP$, $RRPP$, $RPPP$, $RRPPP$, and $RPPPP$, where the on-mass-shell particles are gluons, or sets of gluons with small invariant masses. The explicit expressions satisfying the Bose-symmetry and gauge invariance conditions are obtained. As a comment to the Feynman rules for derivation of the amplitudes in terms of effective vertices we present a ``vocabulary'' for practitioners.Comment: REVTeX, 21 pages, 10 figure