Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA

The multi--Regge form of QCD amplitudes with gluon exchanges is proved in the next-to-leading approximation. The proof is based on the bootstrap relations, which are required for the compatibility of this form with the s-channel unitarity. We show that the fulfillment of all these relations ensures the Reggeized form of energy dependent radiative corrections order by order in perturbation theory. Then we prove that all these relations are fulfilled if several bootstrap conditions on the Reggeon vertices and trajectory hold true. Now all these conditions are checked and proved to be satisfied.Comment: 15 page

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

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

Radiative corrections to the quark-gluon-Reggeized quark vertex in QCD

This paper is devoted to the calculation of the quark-gluon-Reggeized quark effective vertex in perturbative QCD in the next-to-leading order. The case of QCD with massive quarks is considered. This vertex has a number of applications, in particular, the result can be used for determination of the next-to-leading correction to the massive Reggeized quark trajectory.Comment: 13 pages, LaTeX, uses axodraw.st

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.

On the Calculation of the NLO Virtual Photon Impact Factor

The definition of the virtual photon impact factor involves the integration of the s-channel discontinuity of the photon-Reggeon scattering amplitude over the right cut. It permits to formulate a new approach for the calculation of the impact factor based on analytical properties of the amplitude in question. In the next-to-leading order it may give a possibility for considerable simplification of the calculation. We have shown that a part of the diagrams contributing to the impact factor can be treated without their real calculation.Comment: 18 pages, latex, axodraw.sty for figures, version to appear in Nucl. Phys.

QCD factorization with heavy quarks

We further analyze the definition and the calculation of the heavy quark impact factor at next-to-leading (NL) $\log s$ level, and we provide its analytical expression in a previously proposed k-factorization scheme. Our results indicate that k-factorization holds at NL level with a properly chosen energy scale, and with the same gluonic Green's function previously found in the massless probe case.Comment: LaTeX2e, 4pp, 2 figures, uses espcrc2.sty. Talk given at International Workshop on Diffraction in High-Energy Physics (Diffraction 2000), Cetraro, Italy, Sept. 2-7, 2000. The complete paper is also available at http://www-ttp.physik.uni-karlsruhe.de/Preprints

The dipole form of the gluon part of the BFKL kernel

The dipole form of the gluon part of the colour singlet BFKL kernel in the next-to-leading order (NLO) is obtained in the coordinate representation by direct transfer from the momentum representation, where the kernel was calculated before. With this paper the transformation of the NLO BFKL kernel to the dipole form, started a few months ago with the quark part of the kernel, is completed.Comment: 26 page

The impact factor for the virtual photon to light vector meson transition

We evaluate in the next-to-leading approximation the forward impact factor for the virtual photon to light vector meson transition in the case of longitudinal polarization. We find that in the hard kinematic domain, both in the leading and in the next-to-leading approximation, the expression for the impact factor factorizes, up to power suppressed corrections, into the convolution of a perturbatively calculable hard-scattering amplitude and a meson twist-2 distribution amplitude.Comment: 31 pages latex; few comments and one reference added; version to appear in Eur. Phys. Journal

Electroproduction of two light vector mesons in the next-to-leading approximation

We calculate the amplitude for the forward electroproduction of two light vector mesons in next-to-leading order BFKL. This amplitude is written as a convolution of two impact factors for the virtual photon to light vector meson transition with the BFKL Green's function. It represents the first next-to-leading order amplitude ever calculated for a collision process between strongly interacting colorless particles.Comment: 18 pages, 6 figure