A Variable-Flavour Number Scheme for NNLO

At NNLO it is particularly important to have a Variable-Flavour Number Scheme (VFNS) to deal with heavy quarks because there are major problems with both the zero mass variable-flavour number scheme and the fixed-flavour number scheme. I illustrate these problems and present a general formulation of a Variable-Flavour Number Scheme (VFNS)for heavy quarks that is explicitly implemented up to NNLO in the strong coupling constant alpha_S, and may be used in NNLO global fits for parton distributions. The procedure combines elements of the ACOT(chi) scheme and the Thorne-Roberts scheme. Despite the fact that at NNLO the parton distributions are discontinuous as one changes the number of active quark flavours, all physical quantities are continuous at flavour transitions and the comparison with data is successful.Comment: 17 pages, 5 figures included as .ps files, uses axodraw. One additional explanatory sentence after eq. (25). Correction of typos and updated references. To be published in Phys. Rev.

A Variable Flavour Number Scheme at NNLO

I present a formulation of a Variable Flavour Number Scheme for heavy quarks that is implemented up to NNLO in the strong coupling constant and may be used in NNLO global fits for parton distributions.Comment: 4 pages, 6 figures included as .ps files. To appear in proceedings of DIS05, XIII International Workshop on Deep Inelastic Scatterin

Gravitational Waves

This article reviews current efforts and plans for gravitational-wave detection, the gravitational-wave sources that might be detected, and the information that the detectors might extract from the observed waves. Special attention is paid to (i) the LIGO/VIRGO network of earth-based, kilometer-scale laser interferometers, which is now under construction and will operate in the high-frequency band ($1$ to $10^4$ Hz), and (ii) a proposed 5-million-kilometer-long Laser Interferometer Space Antenna (LISA), which would fly in heliocentric orbit and operate in the low-frequency band ($10^{-4}$ to $1$ Hz). LISA would extend the LIGO/VIRGO studies of stellar-mass ($M\sim2$ to $300 M_\odot$) black holes into the domain of the massive black holes ($M\sim1000$ to $10^8M_\odot$) that inhabit galactic nuclei and quasars.Comment: Latex; 25 pages, 14 figures. Figures are in eps files that are bundled together in a tarred, compressed, and uuencoded form; figures are inserted into text via a "special" command rather than psfig or epsf. Uses a style file "snow.sty" that is bundled with the figure

A Complete Leading-Order, Renormalization-Scheme-Consistent Calculation of Small--x Structure functions, Including Leading-ln(1/x) Terms

We present calculations of the structure functions F_2(x,Q^2) and F_L(x,Q^2), concentrating on small x. After discussing the standard expansion of the structure functions in powers of \alpha_s(Q^2) we consider a leading-order expansion in ln(1/x) and finally an expansion which is leading order in both ln(1/x) and \alpha_s(Q^2), and which we argue is the only really correct expansion scheme. Ordering the calculation in a renormalization-scheme- consistent manner, there is no factorization scheme dependence, as there should not be in calculations of physical quantities. The calculational method naturally leads to the ``physical anomalous dimensions'' of Catani, but imposes stronger constraints than just the use of these effective anomalous dimensions. In particular, a relationship between the small-x forms of the inputs F_2(x,Q_0^2) and F_L(x,Q_0^2) is predicted. Analysis of a wide range of data for F_2(x,Q^2) is performed, and a very good global fit obtained, particularly for data at small x. The fit allows a prediction for F_L(x,Q^2) to be produced, which is smaller than those produced by the usual NLO-in-\alpha_s(Q^2) fits to F_2(x,Q^2) and different in shape.Comment: 106 pages, 4 figures as ps files, includes a variation of harmac. Corrections to some typos in references, and form of some references changed, in particular hep-ph(ex) numbers included for papers not yet published. No changes to body of tex

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