I present some comments on the relationship between the small- x behaviour of the parton (quark and gluon) densities and the scaling violation of the proton structure function F2 (x,Q 2 ). Resume Je presente un commentaire sur les relations entre le comportement a petit-z des densites de partons (quark et gluon) et la violation d'echelle de la fonction de la fonction de structure du proton F 2 (x,Q 2 ).

We calculate the second-order QCD corrections to the forward-backward asymmetry in e(+)e(-) annihilation. Using the quark axis definition, we do not agree with either existing calculation, but the difference relative to one of them is small and understood. In particular, we point out that the forward-backward asymmetry of massive quarks is enhanced by logarithms of the quark mass. This implies that the forward-backward asymmetry of massless quarks is not computable in QCD perturbation theory and affected by non-power-suppressed corrections coming from the non-perturbative fragmentation functions. We also calculate the second-order corrections using the experimentally-preferred thrust axis definition for the first time.

We give perturbative predictions for the distribution of the $C$-Parameter event shape variable in $e^+e^-$ annihilation, including resummation of large logarithms in the two-jet (small-$C$) region, matched to next-to-leading order results. We also estimate the leading non-perturbative power correction and make a preliminary comparison with experimental data.

The following topics in perturbative QCD are reviewed: recent theoretical progress in higher-order calculations; soft-gluon resummation for hard-scattering processes at large $E_T$ and high $x$; low-$x$ behaviour of structure functions and recent theoretical results on BFKL dynamics; infrared renormalons and power corrections to perturbative predictions; updated summary of $\as$ measurements.

The perturbative QCD approach to quarkonium decay into a photon and hadrons is reconsidered. It is shown that a consistent treatment within perturbative QCD calls for the introduction of a fragmentation contribution which has been neglected so far. The ensuing phenomenological implications are discussed, and, in particular, the possibility of measuring the gluon fragmentation function of the photon is addressed.

Using the recently formulated k⊥-clustering algorithm for lepton-hadron collisions, we compute the average number of hadronic jets produced in deep inelastic scattering, as a function of the momentum transfer Q2, the Bjorken variable x and the jet resolution parameter ƒcut. For samll values of ƒcut we are able to resum leading and next-to-leading logarithms of ƒcut to all orders in QCD perturbation theory. The result is simply related to the average jet multiplicity in e+e− annihilation, with a structure-function-dependent correction. For larger values of ƒcut we match the resummed predictions to first-order numerical results.

High-energy factorization in QCD is investigated beyond leading order and its relationship to the factorization theorem of mass singularities is established to any collinear accuracy. Flavour non-singlet observables are shown to be regular at small x order by order in perturbation theory. In the singlet sector, we derive the relevant master equations for the space-like evolution of gluons and quarks. Their solution enables us to sum next-to-leading corrections to the small-x behaviour of quark anomalous dimensions and deep inelastic scattering coefficient functions. We present results in both MSbar and DIS factorization schemes.

We propose a version of the QCD-motivated “k⊥” jet-clustering algorithm for hadron-hadron collisions which is invariant under boosts along the beam directions. This leads to improved factorization properties and closer correspondence to experimental practice at hadron colliders. We examine alternative definitions of the resolution variables and cluster recombination scheme, and show that the algorithm can be implemented efficiently on a computer to provide a full clustering history of each event. Using simulated data at √S = 1.8 TeV, we study the effects of calorimeter segmentation, hadronization and the soft underlying event, and compare the results with those obtained using a conventional cone-type algorithm.

The relationship between high-energy factorization and the factorization theorem of mass singularities is fully established by performing a complete resummed calculation in dimensional regularization. This result is achieved by deriving and solving a new evolution equation for the gluon-gluon forward scattering amplitude at high energy in n space-time dimensions. This equation reduces to the Balitskii-Fadin-Kuraev-Lipatov equation in the limiting case of four dimensions.

We describe a method for the resummation of leading and next-to-leading large logarithms to all orders in QCD perturbation theory, applicable to e+e− event shape distributions that have the property of exponentiation near the two-jet region. After a general discussion of the conditions for exponentiation and the evaluation of matrix elements and phase space to next-to-leading logarithmic accuracy, we give details of the application of the method to the thrust and heavy jet mass distributions. We show how the resummed expressions can be matched with known second-order results to obtain improved predictions throughout the whole of phase space, and how to suppress spurious higher-order terms generated by resummation outside the physical region. We also give the necessary ingredients for the improvement of third-order predictions by resummation when they become available.

A gauge invariant description of the chromoelectromagnetic field and colour current demands the use of nonlocal operators. We show that such operators can be constructed in a essentially unique way by enforcing full Poincare covariance, and that they are related through Maxwell, rather than Yang-Mills, equations. Their nonlocality entails the fact that causal and time-ordered propagators are no more the same object and, consequently, the relations between causal and retarded propagators, which in the case of local fields are derived by means of Lehman representation, break down. The linear response theory approach to the propagation of long wavelength oscillations in hot gluon plasma is then reconsidered in the light of the above circumstance. We obtain manifestly gauge invariant plasmon frequency and decay width by computing the retarded current-current commutator from its very definition in the real time formalism. In addition to finding the commonly accepted 1-loop value for the plasma frequency and a positive 1-loop value for the Landau damping, we are able to give a non-perturbative proof of the positivity of the decay width, regardless of the high temperature expansion. We finally discuss the coexistence of a positive plasmon width and ultraviolet asymptotic freedom.

Using the recently introduced “k⊥” jet clustering algorithm, we are able to compute the average number of hadronic jets produced in e+e− annihilation, as a function of both the centre-of-mass energy and the jet resolution parameter ycut. For large values of ycut, we give complete numerical results to order αS2, using the results of Bethke et al. on multi-jet fractions to this order. For small values, we give the results of resumming leading and next-to-leading logarithms of ycut to all orders in QCD perturbation theory. Our predictions should be useful both for determining αS and for studying the transition from the perturbative to the hadronization regime at very small ycut.

Predictions are presented for the distributions of two new e+e− event shape measures which involve the summed scalar transverse momentum relative to the thrust axis. The calculations include resummation of leading and next-to-leading logarithms to all orders in QCD perturbation theory, together with non-logarithmic terms up to second order. In the two-jet region the new event measures are complementary to the jet-mass-related quantities that were resummed earlier, and so they could be helpful in further refining the determination of the strong coupling constant from e+e− event shapes.

We propose a new QCD-motivated jet counting algorithm for deep inelastic lepton-hadron scattering. It combines the k(perpendicular-to)-algorithm, proposed earlier for e+e- annihilation, with a pre-clustering procedure that ensures the universal factorization of initial-state collinear singularities.

A form of high energy factorization has been recently proposed in order to find the small-¢x behaviour of heavy mass production in QCD. Here we review the method and discuss its application to heavy flavour photo- and lepto-production at asymptotic and Hera energies.

A QCD theoretical analysis of jet cross sections is presented. We discuss in detail the JADE (invariant mass-type) and k ⊥-algorithms for multijet cross sections in e + e --annihilation, with emphasis on hadronization effects and large perturbative corrections at small values of the jet resolution parameter Y cut. For the k ⊥-algorithm we present results of calculations which include resummation of leading and next-to-leading logarithms of Y cut to all orders in QCD perturbation theory. We also discuss the recently-proposed Geneva algorithm and show that it suffers from some of the same difficulties as the JADE algorithm.