Reggeon Interactions in Perturbative QCD

We study the pairwise interaction of reggeized gluons and quarks in the Regge limit of perturbative QCD. The interactions are represented as integral kernels in the transverse momentum space and as operators in the impact parameter space. We observe conformal symmetry and holomorphic factorization in all cases.Comment: 13 pages LATEX, 2 figures using package FEYNMAN, N4-9

N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution

We further investigate, in the planar limit of N=4 supersymmetric Yang Mills theories,the high energy Regge behavior of six-point MHV scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two loop corrections to the discontinuities of the amplitudes for the transitions 2 to 4 and 3 to 3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. Any improvement of the BDS formula should reproduce this cut to all orders in the coupling

Exact resolution of the Baxter equation for reggeized gluon interactions

The interaction of reggeized gluons in multi-colour QCD is considered in the Baxter-Sklyanin representation, where the wave function is expressed as a product of Baxter functions Q(lambda) and a pseudo-vacuum state. We find n solutions of the Baxter equation for a composite state of n gluons with poles of rank r in the upper lambda semi-plane and of rank n-1-r in the lower lambda semi-plane (0 leq r leq n-1). These solutions are related by n-2 linear equations with coefficients depending on coth (pi lambda). The poles cancel in the wave function, bilinear combination of holomorphic and anti-holomorphic Baxter functions, guaranteeing its normalizability. The quantization of the intercepts of the corresponding Regge singularities appears as a result of the physical requirements that the holomorphic energies for all solutions of the Baxter equation are the same and the total energies, calculated around two singularities lambda, lambda^* --> + i or -i, coincide. It results in simple properties of the zeroes of the Baxter functions. For illustration we calculate the parameters of the reggeon states constructed from three and four gluons. For the Odderon the ground state has conformal spin |m -m | = 1 and its intercept equals unity. The ground state of four reggeized gluons possesses conformal spin 2 and its intercept turns out to be higher than that for the BFKL Pomeron. We calculate the anomalous dimensions of the corresponding operators for arbitrary alpha_s/omega.Comment: LaTex, 42 pages, 8 .ps figures. Expanded and improved versio

Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation

We investigate the Baxter equation for the Heisenberg spin model corresponding to a generalized BFKL equation describing composite states of n Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used to find an unitary transformation from the impact parameter representation to the representation in which the wave function factorizes as a product of Baxter functions and a pseudo-vacuum state. We show that the solution of the Baxter equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0, 1,...) and that the intercept for the composite Reggeon states is expressed through the behavior of the Baxter function around the pole at lambda = i . The absence of pole singularities in the two complex dimensional lambda-plane for the bilinear combination of holomorphic and anti-holomorphic Baxter functions leads to the quantization of the integrals of motion because the holomorphic energy should be the same for all independent Baxter functions.Comment: LaTex, 48 pages, 1 .ps figure, to appear in Phys. Rev.

Regge Asymptotics of Scattering with Flavour Exchange in QCD

The contribution to the perturbative Regge asymptotics of the exchange of two reggeized fermions with opposite helicity is investigated. The methods of conformal symmetry known for the case of gluon exchange are extended to this case where double-logarithmic contributions dominate the asymptotics. The Regge trajectories at large momentum transfer are calculated.Comment: 18 pages LATEX, 3 figures using package FEYNMAN, N3-9

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

Dimensional Regularisation and Factorisation Schemes in the BFKL Equation at Subleading Leve

We study the anomalous dimensions and coefficient functions generated by the BFKL equation in 4+2 epsilon dimensions, by investigating both running coupling effects, and the inclusion of the full next-to-leading kernel. After generalising the Fourier representation of the solutions to this case, we analyse the beta-dependent renormalisation-group factorisation of anomalous dimension and coefficient contributions to the gluon density. We derive on this basis the normalisation factor of the Q0-scheme with respect to the MSbar-scheme, including beta-dependent corrections to it, and we outline the derivation of the full next-to-leading contributions. We also provide an expression for the resummed gamma_qg in the MSbar-scheme which exhibits its universality and is explicit up to quadratures.Comment: 32 pages, 2 figure

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

The Reggeon →\to 2 Reggeons ++ Particle vertex in the Lipatov effective action formalism

The vertex for gluon emission during the splitting of a reggeized gluon into two is constructed in the framework of Lipatov effective action formalism. Its reduction to a pure transverse form for the diffractive amplitude gives the standard Bartels vertex plus an additional contribution corresponding to the emission from a pointlike splitting vertex. This additional contribution turns out to be given by a longitudinal integral divergent both in the ultraviolet and infrared. A certain specific recipe for this part, including the principal value prescription for the integration, allows to eliminate this unwanted contribution.Comment: 4 figures; misprints corrected; to be published in Eur.Phys.J.

Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution

We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary matrix $R$ which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of $s$ - channel gluons. The eigenstates have a natural interpretation in terms of the $t$ - channel exchanges. Studying the single $s$ - channel gluon sector we find the eigenstates which include the reggeized gluon and five other colored Reggeons. In the two ($s$ - channel) gluon sector we study only singlet color exchanges. We find five charge conjugation even states. The bound state of two reggeized gluons is the standard BFKL Pomeron. The intercepts of the other Pomerons in the large $N$ limit are $1+\omega_P=1+2\omega$ where $1+\omega$ is the intercept of the BFKL Pomeron, but their coupling in perturbation theory is suppressed by at least $1/N^2$ relative to the double BFKL Pomeron exchange. For the $[27,27]$ Pomeron we find $\omega_{[27,27]}=2\omega+O(1/N)>2\omega$. We also find three charge conjugation odd exchanges, one of which is the unit intercept Bartels-Lipatov-Vacca Odderon, while another one has an interecept greater than unity. We explain in what sense our calculation goes beyond the standard BFKL/BKP calculation. We make additional comments and discuss open questions in our approach.Comment: 58 pages, 4 figures, Extended version. To appear in JHE