Abstract: We study in QCD the physics of deeply virtual Compton scattering (DVCS){emdash}the virtual Compton process in the large s and small t kinematic region. We show that DVCS can probe a new type of {ital off-forward} parton distributions. We derive an Altarelli-Parisi-type of evolution equations for these distributions. We also derive their sum rules in terms of nucleon form factors of the twist-two quark and gluon operators. In particular, we find that the second sum rule is related to fractions of the nucleon spin carried separately by quarks and gluons. We estimate the cross section for DVCS and compare it with the accompanying Bethe-Heitler process at CEBAF and HERMES kinematics. {copyright} {ital 1997} {ital The American Physical Society}

Abstract: Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements of quark and gluon light-cone operators. They describe two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F{_}/zeta (X;t), discuss their spectral properties, evolution equations which they satisfy, basic uses and general aspects of factorization for hard exclusive processes.

Abstract: We formulate and prove a QCD factorization theorem for hard exclusive electroproduction of mesons in QCD. The proof is valid for the leading power in Q and all logarithms. This generalizes previous work on vector meson production in the diffractive region of small x. The amplitude is expressed in terms of off-diagonal generalizations of the usual parton densities. The full theorem applies to all kinds of meson and not just to vector mesons. The parton densities used include not only the ordinary parton density, but also ! ,

Abstract: Higgs boson production at the LHC within the Standard Model and its minimal supersymmetric extension is reviewed. The predictions for decay rates and production cross sections are updated by choosing the present value of the top quark mass and recent parton density sets. Moreover, all relevant higher order corrections, some of which have been obtained only recently, are included in a consistent way.

Abstract: We present the first explicit formulae for the complete set of one-loop helicity amplitudes necessary for computing next-to-leading order corrections for e^+ e^- annihilation into four jets, for W, Z or Drell-Yan production in association with two jets at hadron colliders, and for three-jet production in deeply inelastic scattering experiments. We include a simpler form of the previously published amplitudes for e^+ e^- to four quarks. We obtain the amplitudes using their analytic properties to constrain their form. Systematically eliminating spurious poles from the amplitudes leads to relatively compact results.

Abstract: A Monte Carlo program solving Boltzmann equation for partons via cascade method is presented. At presented, only gluon-gluon elastic scattering is included. The scattering cross section is regulated by a medium generated screening mass. Three different geometric modes (3 dimension expansion, 1-d expansion, and scattering inside a box) are provided for theoretical study of the parton transport and the applicability of the cascade method. Space cell division is available to save the number of computer operations. This improves the speed of the calculation by a large factor and makes the code best optimized for simulation of parton cascade in ultrarelativistic heavy ion collisions.

Abstract: In this review we discuss the analytical perturbative approach, based on perturbative QCD and local parton hadron duality (LPHD), and its application to multiparticle production in jets in the semisoft region. Analytical formulae are presented for various observables within the accuracy of the modified leading logarithmic approximation (MLLA), i.e. with terms of relative order taken into account systematically, and in some cases with even higher accuracy. These predictions are confronted with existing experimental data. Many details of the perturbative approach to multiple hadroproduction have been consolidated in recent years, and the overall picture is remarkably healthy. The prospects of future studies of the semisoft jet physics are also discussed.

Abstract: An extensive theoretical analysis of off-forward parton distributions (OFPDs) is presented. The OFPDs and the form factors of the quark energy-momentum tensor are estimated at a low energy scale using a bag model. Relations among the second moments of OFPDs, the form factors, and the fraction of the nucleon spin carried by quarks are discussed. {copyright} {ital 1997} {ital The American Physical Society}

Abstract: We present approximations to tree level multiparton scattering amplitudes which are appropriate when two partons are unresolved. These approximations are required for the analytic isolation of infrared singularities of n+2 parton scattering processes contributing to the next-to-next-to-leading order corrections to n jet cross sections. In each case the colour ordered matrix elements factorise and yield a function containing the singular factors multiplying the n parton amplitudes. When the unresolved particles are not colour connected, the approximations are simple products of the familar eikonal and Altarelli-Parisi splitting functions used to describe single unresolved emission. However, when the unresolved particles are colour connected the factorisation is more complicated and we introduce new and general functions to describe the triple collinear and soft/collinear limits in addition to the known double soft gluon limits of Berends and Giele. As expected the triple collinear splitting functions obey an N=1 SUSY identity. To illustrate the use of these double unresolved approximations, we have examined the singular limits of the tree level matrix elements for e+e- to 5 partons when only three partons are resolved. When integrated over the unresolved regions of phase space, these expressions will be of use in evaluating the O(alpha_s^3) corrections to the three jet rate in electron positron annihilation.

Abstract: In this review we discuss the analytical perturbative approach, based on perturbative QCD and Local Parton Hadron Duality (LPHD), and its application to multiparticle production in jets in the semisoft region. Analytical formulae are presented for various observables within the accuracy of the Modified Leading Logarithmic Approximation (MLLA), i.e. with terms of relative order $\sqrt{\alpha_s}$ taken into account systematically, and in some cases with even higher accuracy. These predictions are confronted with existing experimental data. Many details of the perturbative approach to multiple hadroproduction have been consolidated in recent years, and the overall picture is remarkably healthy. The prospects of future studies of the semisoft jet physics are also discussed.

Abstract: Parton distribution functions give the probability to find partons (quarks and gluons) in a hadron as a function of the fraction η of the proton's momentum carried by the parton. They are conventionally defined in terms of matrix elements of certain operators. They are determined from experimental results on short distance scattering of the partons. Integrals of these functions weighted with ηn are calculable using lattice QCD. Some simple models for their behavior have implications that could also be tested in lattice QCD.

Abstract: The current status of measurements of the nucleon structure functions and their understanding is reviewed. The fixed target experiments E665, CCFR and NMC and the HERA experiments H1 and ZEUS are discussed in some detail. The extraction of parton momentum distribution functions from global fits is described, with particular attention paid to much improved information on the gluon momentum distribution. The status of alpha_s measurements from deep inelastic data is reviewed. Models and non-perturbative approaches for the parton input distributions are outlined. The impact on the phenomenology of QCD of the data at very low values of the Bjorken x variable is discussed in detail. Recent advances in the understanding of the transition from deep inelastic scattering to photoproduction are summarised. Some brief comments are made on the recent HERA measurements of the ep NC and CC cross-sections at very high Q2.

Abstract: We investigate the chemical equilibration of the parton distributions in collisions of two heavy nuclei. We use initial conditions obtained from a self-screened parton cascade calculation and, for comparison, from the HIJING model. We consider a one-dimensional as well as a three-dimensional expansion of the parton plasma and find that the onset of the transverse expansion impedes the chemical equilibration. At energies of 100 GeV/nucleon, the results for one-dimensional and three-dimensional expansions are quite similar except at large values of the transverse radius. At energies of several TeV/nucleon, the plasma initially approaches chemical equilibrium, but then is driven away from it, when the transverse velocity gradients develop. We find that the total parton multiplicity density remains essentially unaffected by the flow, but the individual concentrations of quarks, antiquarks, and gluons are sensitive to the transverse flow. The consequences of the flow are also discernible in the transverse momenta of the partons and in the lepton pair spectra, where the flow causes a violation of the so-called ${M}_{T}$ scaling.

Abstract: We estimate the radiative energy-loss of heavy quarks, produced from the initial fusion of partons, while propagating in a quark-gluon plasma which may be formed in the wake of relativistic heavy ion collisions. We find that the radiative energy-loss for heavy quarks is larger than the collisional energy-loss for all energies. We point out the consequences on possible signals of the quark-gluon plasma.

Abstract: ▪ Abstract The electromagnetic form factors of hadrons at large momentum transfer have been the subject of intense theoretical and experimental scrutiny over the past two decades, yet there is still not a universally accepted framework for their description. This review is a synopsis of their current status. The basic theoretical approaches to form factors at large momentum transfer are developed, emphasizing the valence quark and Feynman (soft) pictures. The discussion includes the relation of these descriptions to the parton model, as well as the roles of factorization, evolution, Sudakov resummation and QCD sum rules. This is followed by a discussion of the experimental status of pion and nucleon elastic form factors and resonance production amplitudes in the light of recent data; the successes and shortcomings of various theoretical proposals are highlighted.

Abstract: VNI is a general-purpose Monte-Carlo event-generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. On the basis of renormalization-group improved parton description and quantum-kinetic theory, it uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme that is governed by the dynamics itself. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time-development of the phase-space densities of partons, pre-hadronic parton clusters, and final-state hadrons, in position-space, momentum-space and color-space. The parton-evolution is described in terms of a space-time generalization of the familiar momentum-space description of multipl (semi) hard interactions in QCD, involving 2 -> 2 parton collisions, 2 -> 1 parton fusion processes, and 1 -> 2 radiation processes. The formation of color-singlet pre-hadronic clusters and their decays into hadrons, on the other hand, is treated by using a spatial criterion motivated by confinement and a non-perturbative model for hadronization. This article gives a brief review of the physics underlying VNI, which is followed by a detailed description of the program itself. The latter program description emphasizes easy-to-use pragmatism and explains how to use the program (including a simple example), annotates input and control parameters, and discusses output data provided by it.

Abstract: We present in detail a calculation of the next-to-leading order QCD corrections to the process $e^+e^-\to 3$ jets with massive quarks. To isolate the soft and collinear divergencies of the four parton matrix elements, we modify the phase space slicing method to account for masses. Our computation allows for the prediction of oriented three jet events involving heavy quarks, both on and off the Z resonance, and of any event shape variable which is dominated by three jet configurations. We show next-to-leading order results for the three jet fraction, the differential two jet rate, and for the thrust distribution at various c.m. energies.

Abstract: We describe the application of renormalization group improved perturbative QCD to inelastic lepton-hadron scattering at high center-of-mass energy but comparatively low photon virtuality. We construct a high energy factorization theorem which complements the mass factorization theorem used for processes with high virtualities. From it we derive a renormalization group equation which resums all large logarithms at high energy, thereby extending to this regime asymptotic freedom and thus the full range of perturbative computational techniques. We discuss the solution of this equation in various limits, and in particular show that the high energy behaviour of physical cross-sections is consistent with phenomenological expectations and unitarity bounds.

Abstract: In proton-nucleus and nucleus-nucleus collisions up to central $S-U$ interactions, the $P_T$-dependence of $J/\psi$ production is determined by initial state parton scattering and pre-resonance nuclear absorption (``normal" $J/\psi$ suppression). The ``anomalous" $J/\psi$ suppression in $Pb-Pb$ collisions must reduce the normal $P_T$ broadening, since it occurs mainly in the central part of the interaction region, where also initial state parton scattering and nuclear absorption are strongest. We thus expect for $ $ in $Pb-Pb$ collisions a turn-over and decrease with increasing $E_T$.

Abstract: The confinement transition from the quark and gluon degrees of freedom appropriate in perturbation theory to the hadrons observed by real world experiments is poorly understood. In this strongly interacting transition regime we presently rely on models, which to varying degrees reflect possible scenarios for the QCD dynamics. Because of the absence of beam and target remnants, and the clean experimental conditions and high event rates, e+e- annihilation to hadrons at the Z0 provides a unique laboratory, both experimentally and theoretically, for the study of parton hadronization. This review discusses current theoretical understanding of the hadronization of partons, with particular emphasis on models of the non-perturbative phase, as implemented in Monte Carlo simulation programs. Experimental results at LEP and SLC are summarised and considered in the light of the models. Suggestions are given for further measurements which could help to produce more progress in understanding hadronization.