Renormalization Group Improved BFKL Equation

I report on the recent proposal of a generalized small-x equation which, in addition to exact leading and next-to-leading BFKL kernels, incorporates renormalization group constraints in the relevant collinear limits.Comment: Talk presented at DIS99, Zeuthen, April 19-23,199

Diffusion corrections to the hard pomeron

The high-energy behaviour of two-scale hard processes is investigated in the framework of small-x models with running coupling, having the Airy diffusion model as prototype. We show that, in some intermediate high-energy regime, the perturbative hard Pomeron exponent determines the energy dependence, and we prove that diffusion corrections have the form hinted at before in particular cases. We also discuss the breakdown of such regime at very large energies, and the onset of the non-perturbative Pomeron behaviour.Comment: 18 pages, 3 Postscript figure

Tunneling transition to the Pomeron regime

We point out that, in some models of small-x hard processes, the transition to the Pomeron regime occurs through a sudden tunneling effect, rather than a slow diffusion process. We explain the basis for such a feature and we illustrate it for the BFKL equation with running coupling by gluon rapidity versus scale correlation plots.Comment: 17 pages, 5 figures, mpeg animations available from http://www.lpthe.jussieu.fr/~salam/tunneling/ . v2 includes additional reference

Minimal Subtraction vs. Physical Factorisation Schemes in Small-x QCD

We investigate the relationship of ``physical'' parton densities defined by kt-factorisation, to those in the minimal subtraction scheme, by comparing their small-x behaviour. We first summarize recent results on the above scheme change derived from the BFKL equation at NLx level, and we then propose a simple extension to the renormalisation-group improved (RGI) equation. In this way we are able the examine the difference between resummed gluon distributions in the Q_0 and MSbar schemes and also to show MSbar scheme resummed results for P_gg and approximate ones for P_qg. We find that, due to the stability of the RGI approach, small-x resummation effects are not much affected by the scheme-change in the gluon channel, while they are relatively more sensitive for the quark-gluon mixing.Comment: 14 pages, 8 figure

Explicit Calculation Of the Running Coupling BFKL Anomalous Dimension

I calculate the anomalous dimension governing the Q^2 evolution of the gluon (and structure functions) coming from the running coupling BFKL equation. This may be expressed in an exact analytic form, up to a small ultraviolet renormalon contribution, and hence the corresponding splitting function may be determined precisely. Rather surprisingly it is most efficient to expand the gluon distribution in powers of alpha_s(Q^2) rather than use the traditional expansion where all orders of alpha_s\ln(1/x) are kept on an equal footing. The anomalous dimension is very different from that obtained from the fixed coupling equation, and leads to a powerlike behaviour for the splitting function as x ->0 which is far weaker, i.e. about x^(-0.2). The NLO corrections to the anomalous dimension are rather small, unlike the fixed coupling case, and a stable perturbative expansion is obtained.Comment: Tex file, including a modification of Harvmac, 15 pages, 5 figures as .ps file

The BFKL Equation at Next-to-Leading Order and Beyond

On the basis of a renormalization group analysis of the kernel and of the solutions of the BFKL equation with subleading corrections, we propose and calculate a novel expansion of a properly defined effective eigenvalue function. We argue that in this formulation the collinear properties of the kernel are taken into account to all orders, and that the ensuing next-to-leading truncation provides a much more stable estimate of hard Pomeron and of resummed anomalous dimensions.Comment: LaTex, 12 pages, 1 eps figur

k-Factorization and Small-x Anomalous Dimensions

We investigate the consistency requirements of the next-to leading BFKL equation with the renormalization group, with particular emphasis on running coupling effects and NL anomalous dimensions. We show that, despite some model dependence of the bare hard Pomeron, such consistency holds at leading twist level, provided the effective variable $\alpha_s(t) log(1/x)$ is not too large. We give a unified view of resummation formulas for coefficient functions and anomalous dimensions in the Q_0-scheme and we discuss in detail the new one for the $q\bar{q}$ contributions to the gluon channel.Comment: Latex2e, 44 pages including 7 PostScript figure

k-Factorization and Impact Factors at Next-to-leading Level

We further analyse,at next-to-leading log(s) level,the form of k-factorization and the definition of impact factors previously proposed by one of us,and we generalize them to the case of hard colourless probes. We then calculate the finite one-loop corrections to quark and gluon impact factors and we find them universal,and given by the same K factor which occurs in the soft timelike splitting functions