A QCD analysis of HERA and fixed target structure function data

The parton momentum densities in the proton are obtained from a NLO QCD analysis of structure functions measured by HERA and fixed target experiments. The uncertainties in these parton densities, the structure functions and related cross sections are estimated from the experimental errors, taking into account all correlations. Standard Model predictions for the charged current Born cross sections at large x and Q2 are calculated and compared with recent data from ZEUS.Comment: 4 pages LaTeX, 5 eps figures, uses npb.sty. Presented at DIS99, Zeuthen, Germany, April 19-23, 199

Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one loop helicity amplitudes of all $2\to 3$ parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all $2\to 4$ parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.Comment: Latex,13 pages, ETH-TH/94-

NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories

We study next-to-leading corrections to the integral kernel of the BFKL equation for high energy cross-sections in QCD and in supersymmetric gauge theories. The eigenvalue of the BFKL kernel is calculated in an analytic form as a function of the anomalous dimension \gamma of the local gauge-invariant operators and their conformal spin n. For the case of an extended N=4 SUSY the kernel is significantly simplified. In particular, the terms non-analytic in n are canceled. We discuss the relation between the DGLAP and BFKL equations in the N=4 model.Comment: Latex, 26 pages, typos corrected, to be published in Nucl.Phys.

Isolated Prompt Photon Production in Hadronic Final States of e+e−e^+e^- Annihilation

We provide complete analytic expressions for the isolated prompt photon production cross section in $e^+e^-$ annihilation reactions through one-loop order in quantum chromodynamics (QCD) perturbation theory. Functional dependences on the isolation cone size $\delta$ and isolation energy parameter $\epsilon$ are derived. The energy dependence as well as the full angular dependence of the cross section on $\theta_\gamma$ are displayed, where $\theta_\gamma$ specifies the direction of the photon with respect to the $e^+e^-$ collision axis. We point out that conventional perturbative QCD factorization breaks down for isolated photon production in $e^+e^-$ annihilation reactions in a specific region of phase space. We discuss the implications of this breakdown for the extraction of fragmentation functions from $e^+e^-$ annihilation data and for computations of prompt photon production in hadron-hadron reactions.Comment: 54 pages RevTeX plus 19 postscript figures submitted together in one compressed fil

Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model

We present results for the three-loop universal anomalous dimension of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills model. These results are obtained by extracting the most complicated contributions from the three loop non-singlet anomalous dimensions in QCD which were calculated recently. Their singularities at j=1 agree with the predictions obtained from the BFKL equation for N=4 SYM in the next-to-leading order. The asymptotics of universal anomalous dimension at large j is in an agreement with the expectations based on an interpolation between weak and strong coupling regimes in the framework of the AdS/CFT correspondence.Comment: LaTeX file, 13 pages, no figures. Some corrections, additional remarks and references. In the last version the analysis of anomalous dimension at j -> 2 was improve

Inclusive Prompt Photon Production in Hadronic Final States of e+e−e^+e^- Annihilation

We provide complete analytic expressions for the inclusive prompt photon production cross section in hadronic final states of $e^+e^-$ annihilation reactions through one-loop order in quantum chromodynamics perturbation theory. Computed explicitly are direct photon production through first order in the electromagnetic strength $\alpha_{em}$ and the quark-to-photon and gluon-to-photon fragmentation contributions through first order in the strong coupling $\alpha_s$. The full angular dependence of the cross sections is displayed, separated into transverse $(1 +\cos ^2\theta _\gamma)$ and longitudinal $(\sin ^2\theta_\gamma)$ components, where $\theta_\gamma$ specifies the direction of the photon with respect to the $e^+e^-$ collision axis. We discuss extraction of fragmentation functions from $e^+e^-$ data.Comment: 40 pages, RevTex, 30 figures in postscript available in a separate fil

DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory

We derive the DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions \gamma of twist-2 operators in the non-physical points j=0,-1,... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. Moreover, in the multi-color limit of the N=4 model the BFKL and DGLAP dynamics in the leading logarithmic approximation is integrable for an arbitrary number of particles. In the next-to-leading approximation the holomorphic separability of the Pomeron hamiltonian is violated, but the corresponding Bethe-Salpeter kernel has the property of a hermitian separability. The main singularities of anomalous dimensions \gamma at j=-r obtained from the BFKL and DGLAP equations in the next-to-leading approximation coincide but our accuracy is not enough to verify an agreement for residues of subleading poles.Comment: 45 pages, latex. In the last version the expression (16) for the t-channel partial wave of the process e+e- --> \mu+\mu- in the double-logarithmic approximation at QED is corrected and its derivation is given in the Appendix

Statistical approach for unpolarized fragmentation functions for the octet baryons

A statistical model for the parton distributions in the nucleon has proven its efficiency in the analysis of deep inelastic scattering data, so we propose to extend this approach to the description of unpolarized fragmentation functions for the octet baryons. The characteristics of the model are determined by using some data on the inclusive production of proton and $\Lambda$ in unpolarized deep inelastic scattering and a next-to-leading analysis of the available experimental data on the production of unpolarized octet baryons in $e^+e^-$ annihilation. Our results show that both parton distributions and fragmentation functions are compatible with the statistical approach, in terms of a few free parameters, whose interpretation will be discussed.Comment: 14 pages, 7 eps figures, to appear in Phys. Rev.

Small-x physics in perturbative QCD

We review the parton model and the Regge approach to the QCD description of the deep-inelastic $ep$ scattering at the small Bjorken variable $x$ and demonstrate their relation with the DGLAP and BFKL evolution equations. It is shown, that in the leading logarithmic approximation the gluon is reggeized and the pomeron is a compound state of two reggeized gluons. The conformal invariance of the BFKL pomeron in the impact parameter space is used to investigate the scattering amplitudes at high energies and fixed momentum transfers. The remarkable properties of the Schr\"odinger equation for compound states of an arbitrary number of reggeized gluons in the multi-colour QCD are reviewed. The gauge-invariant effective action describing the gluon-Reggeon interactions is constructed. The known next-to-leading corrections to the QCD pomeron are discussed.Comment: review to be published in Phys. Re