Calculation of Reggeon Vertices in QCD

The method of calculation of effective vertices of interaction of the Reggeized gluon and quark with particles in QCD in the next-to-leading order is developed. The method is demonstrated in the case of already known vertices of both gluon-gluon and quark-quark transitions in the scattering of gluons and quarks on the Reggeized gluon. It is used for the calculation of the gluon-quark transition in the scattering on the Reggeized quark.Comment: 27 pages, LaTex, 1 figure, uses axodraw.st

The Quark Impact Factors

We calculate in the next-to-leading approximation the non-forward quark impact factors for both singlet and octet color representation in the $t$-channel. The integral representation of the octet impact factor in the general case of arbitrary space-time dimension and massive quark flavors is used to check the so-called "second bootstrap condition" for the gluon Reggeization at the next-to-leading logarithmic approximation in perturbative QCD. We find that it is satisfied for both helicity conserving and non-conserving parts. The integrations are then performed for the explicit calculation of the impact factors in the massless quark case.Comment: 23 pages, LaTeX, 1 EPS figure, uses epsf.sty and axodraw.st

The quark part of the non-forward BFKL kernel and the ``bootstrap'' for the gluon Reggeization

We calculate the quark part of the kernel of the generalized non-forward BFKL equation at non-zero momentum transfer $t$ in the next-to-leading logarithmic approximation. Along with the quark contribution to the gluon Regge trajectory, this part includes pieces coming from the quark-antiquark production and from the quark contribution to the radiative corrections in one-gluon production in the Reggeon-Reggeon collisions. The results obtained can be used for an arbitrary representation of the colour group in the $t-$channel. Using the results for the adjoint representation, we demonstrate explicitly the fulfillment of the ``bootstrap'' condition for the gluon Reggeization in the next-to-leading logarithmic approximation in the part concerning the quark contribution.Comment: 26 pages, LaTeX, uses axodraw.sty; revised final comment; to appear on Phys. Rev.

Electroproduction of two light vector mesons in next-to-leading BFKL: study of systematic effects

The forward electroproduction of two light vector mesons is the first example of a collision process between strongly interacting colorless particles for which the amplitude can be written completely within perturbative QCD in the Regge limit with next-to-leading accuracy. In a previous paper we have given a numerical determination of the amplitude in the case of equal photon virtualities by using a definite representation for the amplitude and a definite optimization method for the perturbative series. Here we estimate the systematic uncertainty of our previous determination, by considering a different representation of the amplitude and different optimization methods of the perturbative series. Moreover, we compare our result for the differential cross section at the minimum momentum transfer with a different approach, based on collinear kernel improvement.Comment: 17 pages, 11 figures; journal version, new figures and discussion adde

The Gluon Impact Factors

We calculate in the next-to-leading approximation the non-forward gluon impact factors for arbitrary color state in the $t$-channel. In the case of the octet state we check the so-called "second bootstrap condition" for the gluon Reggeization in QCD, using the integral representation for the impact factors. The condition is fulfilled in the general case of an arbitrary space-time dimension and massive quark flavors for both helicity conserving and non-conserving parts.Comment: 32 pages, LaTeX, 1 EPS figure, uses epsf.sty and axodraw.st

Quark contribution to the reggeon-reggeon-gluon vertex in QCD

The quark loop contribution to the reggeon-reggeon-gluon vertex is calculated in QCD, where the reggeon is the reggeized gluon. Compared with the vertex in the Born approximation, this contribution exhibits a new spin structure as well as the gluon loop one. A remarkable but not complete cancellation between gluon and quark contributions to this new spin structure takes place for the case of three massless quark flavours.Comment: 19 pages + 2 figures(appended as a postscript file), Late

A proof of the reggeized form of amplitudes with quark exchanges

A complete proof of the quark Reggeization hypothesis in the leading logarithmic approximation for any quark--gluon inelastic process in the multi--Regge kinematics in all orders of $\alpha_s$ is given. First, we show that the multi--Regge form of QCD amplitudes is guarantied if a set of conditions on the Reggeon vertices and the trajectories is fulfilled. Then, we examine these conditions and show that they are satisfied.Comment: 22 pages, 7 figures, use elsart.cl

A proof of fulfillment of the strong bootstrap condition

It is shown that the kernel of the BFKL equation for the octet color state of two Reggeized gluons satisfies the strong bootstrap condition in the next-to-leading order. This condition is much more restrictive than the one obtained from the requirement of Reggeized form for the elastic scattering amplitudes in the next-to-leading approximation. It is necessary, however, for self-consistency of the assumption of Reggeized form of the production amplitudes in multi-Regge kinematics, which are used in the derivation of the BFKL equation. The fulfillment of the strong bootstrap condition for the kernel opens a way to a rigorous proof of the BFKL equation in the next-to-leading approximation.Comment: 20 pages; minor changes in the text in Section 1 (Introduction) and in Section 4 (Discussion); one reference adde

Strong Bootstrap Conditions

We reformulate the so-called ``strong bootstrap'' conditions for the gluon Reggeization in the next-to-leading approximation (NLA), firstly suggested by Braun and Vacca, using a different approach, which is not based on properties of the eigenstates of the NLA octet BFKL kernel. We write the second strong bootstrap condition for the NLA octet impact factors in a form which makes clear their dependence on the process. According to this condition, the NLA octet impact factors must be given by the product of the corresponding Reggeon interaction vertices with a universal coefficient function. This function can be used also in the formulation of the first strong bootstrap condition for the NLA BFKL kernel in the octet state.Comment: 10 page

Connection between complete and Moebius forms of gauge invariant operators

We study the connection between complete representations of gauge invariant operators and their Moebius representations acting in a limited space of functions. The possibility to restore the complete representations from Moebius forms in the coordinate space is proven and a method of restoration is worked out. The operators for transition from the standard BFKL kernel to the quasi-conformal one are found both in Moebius and total representations.Comment: Changed title and a short paragraph in the section "Conclusion"; unchanged results. Version to appear on Nucl. Phys.