Scale-invariant O(g4) Lipatov kernels at non-zero momentum transfer

Abstract

We summarize recent work on the evaluation of the scale invariant next-toleading order Lipatov kernel, constructed via transverse momentum diagrams. At zero momentum transfer the square of the leading-order kernel appears together with an additional component, now identified as a new partial-wave amplitude, having a separate, holomorphically factorizable, spectrum. We present a simplified expression for the full kernel at non-zero momentum transfer and give a complete analysis of its infrared properties. We also construct a nonforward extension of the new amplitude which is infra-red finite and satifies Ward identity constraints. We conjecture that this new kernel has the conformal invariance properties corresponding to the holomorphic factorization of the forward spectrum. * Work supported by the U.S. Department of Energy, Division of High Energy Physics, † coriano@phys.ufl.edu + parwani@iopb.ernet.in # arw@hep.anl.gov A BRIEF OVERVIEWThe Regge limit of QCD has recently undergone a considerable revival of interest. The small-x behaviour of the parton distributions observed at HERA, characterized by a strong rise of the gluon density, and the detection of diffractive hard scattering events in DIS, both provide motivation for developing a better understanding of the Regge regime of QCD. Because of the overlap of the small-x and Regge limits, it is natural to expect that the theoretical tools developed in the past in the analysis of Regge theory are useful also at small-x. Properties of the "exchanged reggeon singularities" can be constructed from perturbation theory, by resumming the leading log 1/x and/or logQ 2 behaviour. Resummation is achieved in various possible ways, but it is widely anticipated that the BFKL evolution equation [1], first derived more than 20 years ago, plays a crucial role in describing the physical properties of the leading "Pomeron" singularity.The crucial ingredient in the "construction" of the BFKL Pomeron is the kernel of the evolution equation, its spectrum and its leading eigenvalue. Both forward (q = 0) and non-forward (q = 0) versions of the lowest order (O(g 2 )) kernel are known. Conformal partial waves diagonalize the O(g 2 ) equation at non zero q, since the equation is invariant under special conformal transformations, and in the limit of q → 0 reproduce the well known eigenfunctions, and eigenvalues of the BFKL parton (or forward) kernel. A necessary condition for the conformal invariance of the equation is the property of holomorphic factorization of the eigenvalues of the parton kernel.Most analyses of the BFKL equation involve only the O(g 2 ) kernel and its related properties of conformal invariance. It is, of course, important to see how radiative corrections affect the leading order evolution. It is expected that renormalization effects will introduce a running of the coupling and will spoil conformal invariance. The direct evaluation of next-to-leading-order(NLO) contributions to this equation requires both a calculation of the correction to the Regge traject...