The Running coupling BFKL anomalous dimensions and splitting functions.

I explicitly calculate the anomalous dimensions and splitting functions governing the Q2 evolution of the parton densities and structure functions which result from the running coupling BFKL equation at LO, i.e. I perform a resummation in powers of ln(1/x) and in powers of β0 simultaneously. This is extended as far as possible to NLO. These are expressed in an exact, perturbatively calculable analytic form, up to small power-suppressed contributions which may also be modelled to very good accuracy by analytic expressions. Infrared renormalons, while in principle present in a solution in terms of powers in αs(Q2), are ultimately avoided. The few higher twist contributions which are directly calculable are extremely small. The splitting functions are very different from those obtained from the fixed coupling equation, with weaker power-like growth ∼ x−0.25, which does not set in until extremely small x indeed. The NLO BFKL corrections to the splitting functions are moderate, both for the form of the asymptotic power-like behaviour and more importantly for the range of x relevant for collider physics. Hence, a stable perturbative expansion and predictive power at small x are obtained. March 2001 1 Roya

Uncertainties in parton related quantities.

I discuss the issue of uncertainties in parton distributions and in the physical quantities which are determined in terms of them. While there has been significant progress on the uncertainties associated with errors on experimental data, there are still outstanding questions. Also, I demonstrate that in many circumstances this source of errors may be less important than errors due to underlying assumptions in the fitting procedure and due to the incomplete nature of the theoretical calculations

A Leading-Order, But More Than One-Loop, Calculation of structure functions

I present a full leading-order calculation of F_2(x,Q^2) and F_L(x,Q^2), including contributions not only from leading order in \alpha_s, but also from the leading power of \alpha_s for each order in ln(1/x). The calculation is ordered according to the inputs and evolution of the structure functions, and the perturbative form of the inputs is determined. I compare the results of fits to data to those using conventional LO and NLO order calculations, and the correct inclusion of leading ln(1/x) terms is clearly preferred. A prediction for F_L(x,Q^2) is produced which is smaller at small x than that obtained from the conventional approach.Comment: 5 pages, Latex, 1 figure, uses epsfig.sty and aipproc.sty. Talk presented at the 5th International Workshop on ``Deep Inelastic Scattering and QCD'' (DIS 97), Chicago, USA, April, 1997. A couple of minor tyops correcte

Global fits of parton distributions.

I discuss recent developments in the determination of parton distributions from global fits. I concentrate on the errors associated with these parton distributions and with the physical quantities which are determined in terms of them. I outline the various techniques used to quantify the uncertainties due to errors on experimental data used in the fits, and provide a number of examples of predictions with their uncertainties. However, I demonstrate that this source of errors may, in some circumstances, be less important than errors due to underlying assumptions in the fitting procedure and due to the incomplete nature of the theoretical framework currently employed.Comment: Invited talk at the 14th Topical Conference on Hadron Collider Physics (HCP2002), Sept 30th - Oct 4th 2002, Karlsruhe, Germany. 13 pages, 11 figures, uses svmult.cls and physmubb.st

Comparison of NNLO DIS scheme splitting functions with results from exact gluon kinematics at small x.

We consider the effect of exact gluon kinematics in the virtual photon-gluon impact factor at small x. By comparing with fixed order DIS scheme splitting and coefficient functions, we show that the exact kinematics results match the fixed order results well at each order, which suggests that they allow for an accurate NLL analysis of proton structure functions. We also present, available for the first time, x-space parameterisations of the NNLO DGLAP splitting functions in the DIS scheme, and also the longitudinal coefficients for neutral current scattering

Technical Brief 1: Filter Fabric: A Technique for Short-term Stabilization

Filter fabrics have been available for several years and are used most frequently as an underliner for roadbeds and in other construction related activities. These materials are produced both as woven and nonwoven fabrics and are available in varying weights and porosities. Fabric selection is based on the proposed application and the specifications that the desired material must meet. If filter fabric is selected as the stabilization technology that is to be used, it has the advantage of being available from several manufacturers whose products are competitively priced. These materials, regardless of manufacturer, are relatively inert geosynthetics that are resistant to ultra-violent degeneration