Regular Series


Vol. 39 (2008), No. 9, pp. 2025 – 2586


Proton Structure, Partons, QCD, DGLAP and Beyond

abstract

We present an introductory discussion of deep-inelastic lepton–proton scattering as a means to probe the substructure of the proton. A résumé of QCD is given, emphasising the running of the coupling constant and the DGLAP evolution equations for the parton densities. The determination of parton distributions is discussed and their importance for predictions of processes at the LHC is emphasised. Going beyond the pure DGLAP regime, we briefly discuss the behaviour of parton densities at low \(x\), and the evidence for non-linear absorptive contributions.


The Total Cross-Section at the LHC

abstract

We do not have the ability to perform precise calculations of long-range strong interaction effects, because the effective QCD coupling is not small and so we cannot use perturbation theory. Nevertheless, I will show that we know a lot, though not nearly enough. As a measure of our lack of knowledge, the best prediction for the total cross-section at LHC energy is: \(\sigma ^{\rm LHC}=125 \pm 25~\textrm {mb}\).


Determination of Parton Distribution Functions, Impact of HERA Data and Consequences for the LHC

abstract

Parton distribution functions are non-perturbative inputs necessary to calculate cross-sections for scattering processes involving hadrons in the initial state. They are obtained by fitting theoretical predictions to various sets of experimental measurements, many of which come from Deep Inelastic Scattering experiments. Among those, the experiments at the HERA electron–proton collider have played a crucial role, from the beginning of the data-taking, with the surprising observation of the strong rise of the structure function \(F_2\) at low Bjorken \(x\) in \(1993\), to its end, with the direct measurement of the structure function \(F_{\rm L}\) in \(2008\). This paper presents an overview of HERA measurements which constrain most the proton structure, and of our current knowledge of parton distribution functions (pdf) in the proton. The impact of the current pdf uncertainties on predictions for cross-sections at the LHC collider is also discussed.


Low-\(x\) Final States at HERA

abstract

In this lecture we present data on hadronic final states from electron–proton reactions at low Bjorken \(x\), taken by the two colliding beam experiments H1 and ZEUS at HERA. The data are discussed in the context of a variety of QCD-based models, which allow for a detailed study of the QCD dynamics in the production of partons and their fragmentation into hadrons. The HERA data fully support the perturbative approach of the DGLAP evolution scheme, although some hints may be visible in certain kinematic regions for the need of alternative formulations, such as BFKL dynamics.


Some Basic Ideas of Perturbative QCD

abstract

These lectures were intended to provide a review and introduction to perturbative quantum chromodynamics for participants, many of whom were junior experimentalists, already familiar with the formalism describing experiments like deep inelastic scattering. These are therefore not a self-contained introduction to the strong interactions at high energy. Rather, they were an attempt to relate certain familiar central concepts in QCD, such as asymptotic freedom and infrared safety, to underlying ideas from quantum mechanics, and to provide the students with perspective on the intellectual underpinnings of the many successes of the theory.


The Lund Model, Multiple Scattering, and Final States

abstract

In this talk I present a short review of string hadronization, parton cascades, multiple scattering, final states, and underlying events.


Basics of BFKL Approach

abstract

I present an introductory discussion of the BFKL approach to the theoretical description of QCD processes at high energy and fixed (not growing with energy) momentum transfers. The role of the gluon reggeization which determines the multi-Regge form of QCD amplitudes with gluon exchanges is emphasized. The region of applicability of the BFKL approach is discussed and the BFKL representation of elastic scattering amplitudes with quantum numbers different from the gluon ones is derived.


The High Energy Limit of QCD: BFKL Cross-Sections

abstract

In this contribution we describe in some detail different aspects of the construction of BFKL cross sections. We focus on several effects which are relevant at next-to-leading order. In particular, we describe QCD coherence in DIS final states, improvements of the collinear region in multi-Regge kinematics, inclusive jet production at next-to-leading order, and azimuthal angle decorrelations of Mueller–Navelet jets at hadron colliders.


BFKL Pomeron in QCD and in \(N=4\) SUSY

abstract

We review existing theoretical approaches for the deep-inelastic lepton–hadron interactions and the high energy hadron–hadron scattering in the Regge kinematics. It is demonstrated, that the gluon in QCD is reggeized and the Pomeron is a composite state of the reggeized gluons. A gauge invariant effective action for the reggeized gluon interactions is constructed. Remarkable properties of the BFKL equation for the Pomeron wave function in QCD and supersymmetric gauge theories in leading and next-to-leading approximations are outlined. It is shown, that due to the AdS/CFT correspondence the BFKL Pomeron is equivalent to the reggeized graviton in the extended \(N=4\) supersymmetric model. Its intercept at large coupling constant is calculated in this model.


Maximal Transcendentality and Integrability

abstract

The Hamiltonian describing possible interactions of the Reggeized gluons in the leading logarithmic approximation (LLA) of the multicolor QCD has the properties of conformal invariance, holomorphic separability and duality. It coincides with the Hamiltonian of the integrable Heisenberg model with the spins being the Möbius group generators. With the use of the Baxter–Sklyanin representation we calculate intercepts of the colorless states constructed from three and four Reggeized gluons and anomalous dimensions of the corresponding high twist operators. The integrability properties of the BFKL equation at a finite temperature are reviewed. Maximal transcendentality is used to construct anomalous dimensions of twist-2 operators up to 4 loops. It is shown that the asymptotic Bethe Ansatz in the 4-loop approximation is not in an agreement with predictions of the BFKL equation in \(N=4\) SUSY.


Running Coupling Effects in Small-\(x\) QCD

abstract

We study effects of the running of the coupling in QCD at small Bjorken-\(x\) and in particular the ones related to gluon saturation. After introducing the steps taken to the derivation of the next to leading order nonlinear evolution equation, we discuss the infrared sensitivity of the Pomeron intercept, the energy dependence of the saturation momentum and the appearance of geometrical scaling, and the dominance of the running coupling effects over the ones introduced by loops of Pomerons.


Diffraction at HERA

abstract

The article gives an introduction into deeply inelastic scattering (DIS) at the electron–proton collider HERA and into diffraction in high-energy particle scattering. Selected results on exclusive vectormesons and on deeply-virtual Compton scattering (DVCS) at HERA are presented. An overview is given on results from inclusive diffractive reactions and from exclusive diffractive reactions with jets or heavy quarks in the final state. Possible descriptions of the results in the framework of Regge phenomenology or by perturbative QCD models are discussed.


Diffraction at the Tevatron and the LHC

abstract

In this paper, we present and discuss the most recent results on inclusive diffraction at the Tevatron collider and give the prospects at the LHC. We also describe the search for exclusive events at the Tevatron. Of special interest is the exclusive production of Higgs boson and heavy objects (\(W\), top, stop pairs) at the LHC which will require precise measurements and analyses of inclusive and exclusive diffraction to constrain further the gluon density in the pomeron. At the end of the paper, we describe the projects to install forward detectors at the LHC to fulfil these measurements. We also describe the diffractive experiments accepted or in project at the LHC: TOTEM, ALFA in ATLAS, and the AFP/FP420 projects.


Vector Meson Production in Diffractive DIS: Color Dipole Phenomenology

abstract

In these lectures, we first review the main steps in the calculation of diffractive vector meson production within the color dipole approach, and then compare the results with experimental data from HERA.


NLO BFKL at Work: The Electroproduction of Two Light Vector Mesons

abstract

The forward electroproduction of two light vector mesons is the first example of a collision process between strongly interacting colorless particles for which the amplitude can be written completely within perturbative QCD in the Regge limit with next-to-leading accuracy. This amplitude can be written as a convolution of two impact factors for the virtual photon to light vector meson transition with the BFKL Green’s function. In this lecture we first describe how the relevant impact factor is calculated, then we perform the convolution with the BFKL Green’s function and illustrate the numerical procedure to obtain a well-behaved amplitude.


Gluon Saturation from DIS to Nucleus–Nucleus Collisions

abstract

In this series of three lectures, I discuss several aspects of high energy scattering among hadrons in Quantum Chromodynamics. The first lecture is devoted to a presentation of gluon saturation and of the Color Glass Condensate (CGC). The second lecture describes the application of this framework to Deep Inelastic Scattering and to proton–nucleus collisions. In the third lecture, we present the application of the CGC to the study of high energy hadronic collisions, with emphasis on nucleus–nucleus collisions. In particular, we provide the outline of a proof of high energy factorization for inclusive gluon production.


The ATLAS and CMS Experiments at the LHC

abstract

The Large Hadron Collider LHC will start operating, at CERN, Geneva, Switzerland in 2008. CMS and ATLAS are the two general purpose detectors that will collect data at the LHC. A brief overview of the ATLAS and CMS detector is given, followed by the status of the construction, installation and commissioning. Next, a quick tour on what could be the first physics measurements and search results for new physics at the LHC will be given.


Introduction to String Theory and Gauge/Gravity Duality for Students in QCD and QGP Phenomenology

abstract

String theory has been initially derived from motivations coming from strong interaction phenomenology, but its application faced deep conceptual and practical difficulties. The strong interactions found their theoretical foundation elsewhere, namely on QCD, the quantum gauge field theory of quarks and gluons. Recently, the Gauge/Gravity correspondence allowed to initiate a reformulation of the connection between strings and gauge field theories, avoiding some of the initial drawbacks and opening the way to new insights on the gauge theory at strong coupling and eventually QCD. Among others, the recent applications of the Gauge/Gravity correspondence to the formation of the QGP, the quark–gluon plasma, in heavy-ion reactions seem to provide a physically interesting insight on phenomenological features of the reactions. In this paper we will give a simplified introduction to those aspects of string theory which, at the origin and in the recent developments, are connected to strong interactions, for those students which are starting to learn QCD and QGP physics from an experimental or phenomenological point of view.


Saturation and Hadronic Cross-Sections at Very High Energies

abstract

We propose a simple model for the total \(pp/p\bar {p}\) cross-section, which is a  generalization of the minijet model with the inclusion of a window in the \(p_{\rm T}\)-spectrum associated to the saturation physics. Our model implies a natural cutoff for the perturbative calculations which modifies the energy behavior of this component, so that it satisfies the Froissart bound. Including the saturated component, we obtain a satisfactory description of the very high energy experimental data.


Measurement of the Longitudinal Proton Structure Function in Diffraction at the H1 Experiment

abstract

The measurement of the inclusive and diffractive longitudinal proton structure function at low-\(x\) and low \(Q^2\) has been considered to be essential to complete the HERA \(ep\) programme and has motivated a run at reduced \(\sqrt {s}\) at the end of HERA. The theoretical interest in longitudinal structure functions is shortly motivated and basic principles of their direct measurements are outlined. A referenced simulation study anticipates the results that are awaited soon.


Diffractive Jet Production at HERA

abstract

The measurement of diffractive structure functions is one of the leading topics of the diffractive programme at the H1 experiment at HERA. In this study, diffraction at HERA is shortly described with special emphasis of the production of diffractive dijets and forward jets in the final state. The aim is to measure the \(t\)-dependence of the diffractive dijet cross section and to analyse a possibility of distinguishing between DGLAP and BFKL evolution equations in the low-\(x\) regime by measuring forward jets.


Jet Measurements at DØ

abstract

The goal of the student’s talk was to present all stages of any jet measurement from data collection to comparison of experimental results with theoretical predictions. All experimental examples were taken from the \(D\rlap {/}0\) experiment at the Fermilab Tevatron Collider.


Looking for the Diffractive Exclusive Signal in the Dijet Mass Fraction Measurement

abstract

New HERA QCD fits are used to extract the exclusive signal from the CDF dijet mass fraction \(R_{JJ}\) diffractive measurement, using several available models of inclusive diffraction. Subsequently, a prediction of dijet mass fraction distribution at the LHC is presented and the appearance of the exclusive signal in such measurement is discussed.


Exclusive Diffractive Higgs Boson Production at the LHC

abstract

The analysis of exclusive Higgs boson production in Atlas based on Atlfast simulation is presented in this paper. Significant background processes including pile-up were also simulated. The feasibility of measurement of exclusive diffractive Higgs production is discussed at the end of this report.


Diffractive \(\chi \) Production at the Tevatron and the LHC

abstract

We give the predictions for the diffractive production cross-sections of \(\chi \) mesons based on the Bialas–Landshoff formalism in the central rapidity region. We use of the DPEMC Monte Carlo simulation with the appropriate kinematics for small-mass diffractive production. We compare generator-level results with a CDF measurement for exclusive \(\chi \) production, and study the background including the contribution of inclusive \(\chi \) production. We show that the results agree with Tevatron data. We also highlight the exclusive \(\chi _{c_0}\) production at LHC energies, and we investigate a possible measurement at the Tevatron using the \(D\rlap {/}0\) forward proton detectors.


Hadrochemistry of Jet Quenching at the LHC

abstract

We point out that jets propagating through the medium created in heavy ion collisions can be modified not only in the longitudinal and transverse multiplicity distributions, but also in the hadrochemical composition. We use the theoretical framework of the MLLA+LPHD formalism, supplemented by medium-modified splitting functions.


Universality of QCD Traveling-Waves with Running Coupling Beyond Leading Logarithmic Accuracy

abstract

We discuss the solutions of QCD evolution equations with saturation in the high energy limit. We present a general argument showing that, in the running coupling case, the Next-to-Leading-Logarithmic (NLL) and higher order terms are irrelevant for the universal asymptotic features of the solutions.


NLO Evolution of Color Dipole

abstract

The small-\(x\) deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. In the next-to-leading order the BK equation gets contributions from quark and gluon loops as well as from the tree gluon diagrams with quadratic and cubic nonlinearities.


Unitarity Corrections from the High Energy QCD Effective Action

abstract

We investigate the derivation of reggeon transition vertices from Lipatov’s gauge invariant effective action for high energy processes in QCD. In particular we address the question of longitudinal integrations in order to reduce the vertices into the required purely transverse form. We explicitly derive the BFKL-kernel and verify vanishing of the 2-to-3 reggeon transition vertex. First results on the derivation of the 2-to-4 reggeon transition vertex are discussed.


Collinear Improvement of the BFKL Kernel in the Electroproduction of Two Light Vector Mesons

abstract

We test the performance of a RG-improved kernel in the determination of the amplitude of a physical process, the electroproduction of two light vector mesons, in the BFKL approach at the next-to-leading approximation (NLA). We find that a smooth behavior of the amplitude with the center-of-mass energy can be achieved, setting the renormalization and energy scales appearing in the subleading terms to values much closer to the kinematical scales of the process than in approaches based on unimproved kernels.


A Test of the BFKL Resummation at ILC

abstract

We consider the exclusive production of \(\rho ^0\) meson pairs in \(\gamma ^*\gamma ^*\) scattering in the Regge limit of QCD as a probe of BFKL resummation effects and we show the feasibility of the measurement of this process at the ILC.


An Unified Description of HERA and RHIC Data

abstract

Perturbative Quantum Chromodynamics (pQCD) predicts that the small-\(x\) gluons in the hadron wavefunction should form a Color Glass Condensate (CGC), which has universal properties, which are the same for nucleon or nuclei. Making use of the results in V.P. Goncalves, M.S. Kugeratski, M.V.T. Machado, F.S. Navarra, Phys. Lett. B643, 273 (2006), we study the behavior of the anomalous dimension in the saturation models as a function of the photon virtuality and of the scaling variable \(r Q_{\rm s}\), since the main difference among the known parameterizations are characterized by this quantity.


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