Scheme Dependence at Small x

We discuss the evolution of F_2^p at small x, emphasizing the uncertainties related to expansion, fitting, renormalization and factorization scheme dependence. We find that perturbative extrapolation from the measured region down to smaller x and lower Q^2 may become strongly scheme dependent.Comment: 8 pages, LaTeX with epsfig, 2 uuencoded figure

Singlet parton evolution at small x: a theoretical update

This is an extended and pedagogically oriented version of our recent work, in which we proposed an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach.Comment: 30 pages, 8 figures, latex with sprocl.sty and epsfi

An Improved Splitting Function for Small x Evolution

We summarize our recent result for a splitting function for small x evolution which includes resummed small x logarithms deduced from the leading order BFKL equation with the inclusion of running coupling effects. We compare this improved splitting function with alternative approaches.Comment: 5 pages, 2 figures, presented by G.A.at DIS200

Momentum Conservation at Small x

We discuss how momentum conservation is implemented in perturbative computations based on expansions of anomalous dimensions appropriate at small $x$. We show that for any given choice of $F_2$ coefficient functions there always exists a factorization scheme where the gluon is defined in such a way that momentum is conserved at next to leading order.Comment: 11 pages, plain TeX with harvma

BFKL at NNLO

We present a recent determination of an approximate expression for the O(alpha_s^3) contribution chi_2 to the kernel of the BFKL equation. This includes all collinear and anticollinear singular contributions and is derived using duality relations between the GLAP and BFKL kernels.Comment: 8 pages. Talk presented at 12th International Conference on Elastic and Diffractive Scattering: Forward Physics and QCD, Hamburg, DESY, Germany, 21-25 May 200

All Order Running Coupling BFKL Evolution from GLAP (and vice-versa)

We present a systematic formalism for the derivation of the kernel of the BFKL equation from that of the GLAP equation and conversely to any given order, with full inclusion of the running of the coupling. The running coupling is treated as an operator, reducing the inclusion of running coupling effects and their factorization to a purely algebraic problem. We show how the GLAP anomalous dimensions which resum large logs of x can be derived from the running-coupling BFKL kernel order by order, thereby obtaining a constructive all-order proof of small x factorization. We check this result by explicitly calculating the running coupling contributions to GLAP anomalous dimensions up to next-to-next-to leading order. We finally derive an explicit expression for BFKL kernels which resum large logs of Q^2 up to next-to-leading order from the corresponding GLAP kernels, thus making possible a consistent collinear improvement of the BFKL equation up to the same order