J. Bartels — Page 3

arXiv2007

HERA and the LHC - A workshop on the implications of HERA for LHC physics: Proceedings - Part B

The HERA electron--proton collider has collected 100 pb$^{-1}$ of data since its start-up in 1992, and recently moved into a high-luminosity operation mode, with upgraded detectors, aiming to increase the total integrated luminosity per experiment to more than 500 pb$^{-1}$. HERA has been a machine of excellence for the study of QCD and the structure of the proton. The Large Hadron Collider (LHC), which will collide protons with a centre-of-mass energy of 14 TeV, will be completed at CERN in 2007. The main mission of the LHC is to discover and study the mechanisms of electroweak symmetry breaking, possibly via the discovery of the Higgs particle, and search for new physics in the TeV energy scale, such as supersymmetry or extra dimensions. Besides these goals, the LHC will also make a substantial number of precision measurements and will offer a new regime to study the strong force via perturbative QCD processes and diffraction. For the full LHC physics programme a good understanding of QCD phenomena and the structure function of the proton is essential. Therefore, in March 2004, a one-year-long workshop started to study the implications of HERA on LHC physics. This included proposing new measurements to be made at HERA, extracting the maximum information from the available data, and developing/improving the theoretical and experimental tools. This report summarizes the results achieved during this workshop.

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arXiv2006

NLO inclusive jet production in $k_T$--factorization

The inclusive production of jets in the central region of rapidity is studied in $k_T$-factorization at next-to-leading order (NLO) in QCD perturbation theory. Calculations are performed in the Regge limit making use of the NLO BFKL results. A jet cone definition is introduced and a proper phase--space separation into multi-Regge and quasi-multi-Regge kinematic regions is carried out. Two situations are discussed: scattering of highly virtual photons, which requires a symmetric energy scale to separate the impact factors from the gluon Green's function, and hadron-hadron collisions, where a non--symmetric scale choice is needed.

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arXiv2006

NLO jet production at central rapidities in $k_T$ factorization

In this contribution we discuss the inclusive production of jets in central regions of rapidity in the context of $k_T$-factorization at next-to-leading order (NLO). We work in the Regge limit of QCD and use the NLO BFKL results. A jet cone definition is proposed together with a phase-space separation into multi-Regge and quasi-multi-Regge kinematics. We discuss scattering of highly virtual photons, with a symmetric energy scale to separate the impact factors from the gluon Green's function, and hadron-hadron collisions, with a non-symmetric scale choice.

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arXiv2006

HERA and the LHC - A workshop on the implications of HERA for LHC physics: Proceedings - Part A

The HERA electron--proton collider has collected 100 pb$^{-1}$ of data since its start-up in 1992, and recently moved into a high-luminosity operation mode, with upgraded detectors, aiming to increase the total integrated luminosity per experiment to more than 500 pb$^{-1}$. HERA has been a machine of excellence for the study of QCD and the structure of the proton. The Large Hadron Collider (LHC), which will collide protons with a centre-of-mass energy of 14 TeV, will be completed at CERN in 2007. The main mission of the LHC is to discover and study the mechanisms of electroweak symmetry breaking, possibly via the discovery of the Higgs particle, and search for new physics in the TeV energy scale, such as supersymmetry or extra dimensions. Besides these goals, the LHC will also make a substantial number of precision measurements and will offer a new regime to study the strong force via perturbative QCD processes and diffraction. For the full LHC physics programme a good understanding of QCD phenomena and the structure function of the proton is essential. Therefore, in March 2004, a one-year-long workshop started to study the implications of HERA on LHC physics. This included proposing new measurements to be made at HERA, extracting the maximum information from the available data, and developing/improving the theoretical and experimental tools. This report summarizes the results achieved during this workshop.

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arXiv2006

Exclusive Higgs boson production at the LHC: hard rescattering corrections

We examine, as a correction to the central exclusive Higgs boson production in $pp$ collisions at the LHC, the rescattering of gluonic ladders off the proton. As usual, at the lowest order the hard part of this process can be described as a fusion of two hard gluonic ladders. We calculate corrections to this hard amplitude which are due to rescattering of these ladders. These corrections, which contain high mass diffractive excitations of the proton, have not yet been taken into account by the usual soft survival probabilities. We find that the correction due to the exchange of a single hard rescattering is negative, large and infrared sensitive. As a first step towards a more reliable description we therefore replace the rescattering exchange by a unitarized amplitude using the BK equation which generates the saturation scale $Q_s(x)$. We also include a soft gap survival probability factor. We discuss the results and outline possible future strategies.

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arXiv2005

Off-Shell Scattering Amplitudes for WW Scattering and the Role of the Photon Pole

We derive analytic expressions for high energy $2 \to 2$ off-shell scattering amplitudes of weak vector bosons. They are obtained from six fermion final states in processes of the type $e^+ e^- \to \barν_e + (WW) + ν_e \to \barν_e + (lν)(lν) + ν_e$. As an application we reconsider the unitarity bounds on the Higgs mass. Particular attention is given to the role of the photon exchange which has not been considered in earlier investigations; we find that the photon weakens the bound of the Higgs mass.

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arXiv2005

AGK Cutting Rules and Multiple Scattering in Hadronic Collisions

We discuss the AGK rules for the exchange of an arbitrary number of reggeized gluons in perturbative QCD in the high energy limit. Results include the cancellation of corrections to single jet and double jet inclusive cross sections, both for hard and soft rescattering contributions.

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arXiv2004

Pomeron Vertices in Perturbative QCD in Diffractive Scattering

We analyse the momentum space triple Pomeron vertex in perturbative QCD. In addition to the standard form of this vertex which is used in the context of total cross-sections at high energies and in the QCD reggeon field theory, there exists an alternative form which has to be used in the study of high-mass diffraction. We review and analyse the relation between these two versions. We discuss some implications for the BK-equation. In the second part of our paper we extend this analysis to the Pomeron-Odderon-Odderon vertex.

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arXiv2004

NLO Corrections to the γ* Impact Factor: First Numerical Results for the Real Corrections to γ*_L

We analytically perform the transverse momentum integrations in the real corrections to the longitudinal γ*_L impact factor. The resulting integrals are Feynman parameter integrals, and we provide a MATHEMATICA file which contains the integrands. The remaining integrals are carried out numerically. We perform a numerical test, and we compute those parts of the impact factor which depend upon the energy scale s_0: they are found to be negative and, with decreasing values of s_0, their absolute value increases.

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arXiv2004

Solution of the Fan Diagram Equation in 2+1 Dimensional QCD

We investigate the Balitsky-Kovchegov (BK) equation for D=3 space-time dimensions, corresponding to one transverse coordinate, and we show that it can be solved analytically. The explicit solutions are found in the linear approximation and for the paricular cases when they do not depend on the impact parameter of the dipole or on its rapidity. It is shown, that in a general case different solutions are related by an infinite parameter group of transformations. The key observation is that the equation has the Kowalewskaya-Painlevé property, which gives the possibility of reducing the non-linear problem to the solution of a linear integral equation.

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arXiv2004

Interactions of Reggeized Gluons in the Möbius Representation

We investigate consequences of the Möbius invariance of the BFKL Hamiltonian and of the triple Pomeron vertex. In particular, we show that the triple Pomeron vertex in QCD, when restricted to the large $N_c$ limit and to the space of Möbius functions, simplifies and reduces to the vertex used in the Balitsky-Kovchegov (BK) equation. As a result, the BK equation for the dipole density appears as a special case of the nonlinear evolution equation which sums the fan diagrams for BFKL Green's functions in the Möbius representation. We also calculate the corrections $O(1/(N_c^2-1)$ to the triple Pomeron vertex in the space of Möbius functions, and we present a generalization of the BK-equation in the next-to-leading order approximation in the $1/N_c$ expansion.

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arXiv2003

Quark-Antiquark Exchange in $γ^* γ^*$ Scattering

We calculate the high energy behavior of quark-antiquark exchange in $γ^* γ^*$ elastic scattering by summing, to all orders, the leading double logarithmic contributions of the QCD ladder diagrams. Motivation comes from the LEP data for $σ_{tot}^{γ^* γ^*}$ which indicate the need for secondary reggeon exchange. We show that, for large photon virtualities, this exchange is calculable in pQCD. This applies, in particular, to parts of the LEP kinematic region.

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arXiv2003

QCD Saturation and Photoproduction on Proton and Nuclei Targets

We calculate inclusive photoproduction cross-sections for both proton and nuclei targets, using a saturation model derived from an approximate solution to the Balitsky-Kovchegov nonlinear evolution equation. This paper extends our hypothesis, that one can successfully use the dipole picture and saturation models to describe soft processes, instead of the soft Pomeron Regge parametrization. Our fit is compatible with our previous fit to DIS data, and utilizes the same phenomenological parameters as in our paper devoted to soft hadronic interactions. Using the Glauber formalism, and no additional parameters, we calculate the cross-sections for photoproduction on various nuclei, and compare our results with the relevant data.

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arXiv2003

The Bootstrap Conditions for the Gluon Reggeization

Compatibility of gluon Reggeization with s-channel unitarity requires the vertices of the Reggeon interactions to satisfy a series of bootstrap conditions. In order to derive, in the next-to-leading order (NLO), conditions related to the gluon production amplitudes, we calculate the s-channel discontinuities of these amplitudes and compare them with those required by the Reggeization. It turns out that these conditions include the so called strong bootstrap conditions for the kernel and for the impact factors of scattering particles, which were proposed earlier without derivation, and recently were proved to be satisfied. Besides this, there is a new bootstrap condition, which relates a number of Reggeon vertices and the gluon trajectory.

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arXiv2003

The Process gamma* + p -> eta_c + X: A Test for the Perturbative QCD Odderon

The rates of inclusive photo- and electroproduction of the eta_c meson: gamma* + p -> eta_c + X are calculated in the triple Regge region, integrated over the diffractive mass X. For the Regge exchanges we use the hard Pomeron and Odderon, both being calculated in the framework of perturbative QCD. The integrated cross-section depends upon the coupling of the BFKL pomeron to two $C=-1$ odderons, and it is found to be of the order 60 pb for photoproduction and 1.5 pb at Q^2=25 GeV^2.

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arXiv2003

On the Dipole Picture in the Nonforward Direction

We calculate, for nonzero momentum transfer, the dipole formula for the high energy behaviour of elastic and quasielastic scattering of a virtual photon. We obtain an expression of the nonforward photon impact factor and of the nonforward photon wave function, and we give a physical interpretation.

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arXiv2003

The Dipole Picture and Saturation in Soft Processes

We attempt to describe soft hadron interactions in the framework of saturation models, one based upon the Balitsky-Kovchegov non-linear equation and another one due to Golec-Biernat and Wüsthoff. For $pp$, $Kp$, and $πp$ scattering the relevant hadronic wave functions are formulated, and total, elastic cross-sections, and the forward elastic slope are calculated and compared to experimental data. The saturation mechanism leads to reasonable reproduction of the data for the quantities analyzed, except for the forward elastic slope, where the predicted increase with energy is too moderate.

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arXiv2002

NLO Corrections to the Photon Impact Factor: Combining Real and Virtual Corrections

In this third part of our calculation of the QCD NLO corrections to the photon impact factor we combine our previous results for the real corrections with the singular pieces of the virtual corrections and present finite analytic expressions for the quark-antiquark-gluon intermediate state inside the photon impact factor. We begin with a list of the infrared singular pieces of the virtual correction, obtained in the first step of our program. We then list the complete results for the real corrections (longitudinal and transverse photon polarization). In the next step we define, for the real corrections, the collinear and soft singular regions and calculate their contributions to the impact factor. We then subtract the contribution due to the central region. Finally, we combine the real corrections with the singular pieces of the virtual corrections and obtain our finite results.

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