The Four-Jet Rate in e+e- Annihilation

We present an analytic expression for the four-jet rate in e+e- annihilation, calculated using the coherent branching formalism in the Durham scheme. Our result resums all the leading and next-to-leading kinematic logarithms to all orders in the QCD strong coupling constant.Comment: 7 pages; Final result for R4 and D7 corrected and a couple of typos fixe

BFKL predictions at small x from k_T and collinear factorization viewpoints

Hard scattering processes involving hadrons at small $x$ are described by a $k_T$-factorization formula driven by a BFKL gluon. We explore the equivalence of this description to a collinear-factorization approach in which the anomalous dimensions $\gamma_{gg}$ and $\gamma_{qg}/\alpha_S$ are expressed as power series in $\alpha_S \log (1/x)$, or to be precise $\alpha_S/\omega$ where $\omega$ is the moment index. In particular we confront the collinear-factorization expansion with that extracted from the BFKL approach with running coupling included.Comment: 11 LaTeX pages, 1 figure (uuencoded

Approximate NNLO Threshold Resummation in Heavy Flavour Decays

We present an approximate NNLO evaluation of the QCD form factor resumming large logarithmic perturbative contributions in semi-inclusive heavy flavour decays.Comment: 16 pages, 3 figures, Latex; minor changes; 2 figures adde

THE GLUON DISTRIBUTION AT SMALL x OBTAINED FROM A UNIFIED EVOLUTION EQUATION.

We solve a unified integral equation to obtain the $x, Q_T$ and $Q$ dependence of the gluon distribution of a proton in the small $x$ regime; where $x$ and $Q_T$ are the longitudinal momentum fraction and the transverse momentum of the gluon probed at a scale $Q$. The equation generates a gluon with a steep $x^{- \lambda}$ behaviour, with $\lambda \sim 0.5$, and a $Q_T$ distribution which broadens as $x$ decreases. We compare our solutions with, on the one hand, those that we obtain using the double-leading-logarithm approximation to Altarelli-Parisi evolution and, on the other hand, to those that we determine from the BFKL equation.Comment: LaTeX file with 10 postscript figures (uuencoded

Threshold Effects in Slepton-Pair Production at the LHC

We present a study of threshold resummation effects for slepton pair production at the Large Hadron Collider (LHC). After confirming the known NLO QCD corrections and generalizing the NLO SUSY-QCD corrections to the case of mixing squarks in the virtual loop contributions, we employ the Mellin N-space resummation formalism to compute logarithmically enhanced soft-gluon terms to all perturbative orders.Comment: 3 pages, 1 figure, presented at HEP 2007 (Manchester, July 2007

The description of F2 at small x incorporating angular ordering

We study the perturbative QCD description of the HERA measurements of $F_2 (x, Q^2)$ using a gluon distribution that is obtained from an evolution incorporating angular ordering of the gluon emissions, and which embodies both GLAP and BFKL dynamics. We compare the predictions with recent HERA data for $F_2$. We present estimates of the charm component $F_2^c (x, Q^2)$ and of $F_L (x, Q^2)$.Comment: 8 LaTeX pages + 4 uuencoded figure

Infrared singularities of scattering amplitudes in perturbative QCD

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.Comment: 4 pages; v2: typo in eq. (12) fixed, references updated; v3: additional term in (12

Quark-Gluon Jet Differences at LEP

A new method to identify the gluon jet in 3-jet ``{\bf Y}'' decays of $Z^0$ is presented. The method is based on differences in particle multiplicity between quark jets and gluon jets, and is more effective than tagging by leptonic decay. An experimental test of the method and its application to a study of the ``string effect'' are proposed. Various jet-finding schemes for 3-jet events are compared.Comment: 11 pages, LaTeX, 4 PostScript figures availble from the author ([email protected]), MSUTH-92-0

Sudakov Resummations at Higher Orders

We summarize our recent results on the resummation of hard-scattering coefficient functions and on-shell form factors in massless perturbative QCD. The threshold resummation has been extended to the fourth logarithmic order for deep-inelastic scattering, Drell-Yan lepton pair production and Higgs production via gluon-gluon fusion. The leading six infrared pole terms have been derived to all orders in the strong coupling constant for the photon-quark-quark and the (heavy-top) Higgs-gluon-gluon form factors. These results have many implications, most notably they lead to a new best estimate for the Higgs production cross section at the LHC.Comment: 12 pages, LaTeX, 2 eps-figures. Uses modification appbav.cls (included) of the appolb.cls style. Presented by S.M. and A.V. at the conferences `Matter to the Deepest', Ustron (Poland), September '05, and RADCOR 2005, Shonan Village (Japan), October '05. To appear, in the latter case in shortened form, in the proceeding

A next-to-next-to-leading order calculation of soft-virtual cross sections

We compute the next-to-next-to-leading order (NNLO) soft and virtual QCD corrections for the partonic cross section of colourless-final state processes in hadronic collisions. The results are valid to all orders in the dimensional regularization parameter \ep. The dependence of the results on a particular process is given through finite contributions to the one and two-loop amplitudes. To evaluate the accuracy of the soft-virtual approximation we compare it with the full NNLO result for Drell-Yan and Higgs boson production via gluon fusion. We also provide a universal expression for the hard coefficient needed to perform threshold resummation up to next-to-next-to-leading logarithmic (NNLL) accuracy.Comment: 25 pages, 4 figure