Dipole Cross Section Research Articles

Neutrino structure functions in the QCD dipole picture

In this contribution we present an exploratory QCD analysis of the neutrino structure functions in charged current DIS using the color dipole formalism. The corresponding dipole cross sections are taken from recent phenomenological and theoretical studies in deep inelastic inclusive production, including nuclear shadowing corrections. The theoretical predictions are compared to the available experimental results in the small-x region.

Mechanical Coil Structure of the FAIR SIS 100 Magnets

The SIS 100 magnets of the Nuclotron-type are fast- pulsed superferric cold iron magnets. The dipole coil is a double layer saddle-shaped coil with 16 turns. The cable is a hollow tube NbTi composite cable of about 7.2 mm outer diameter, cooled with two phase helium flow at 4.5 K. A 2D structural analysis of the dipole cross section has been performed to determine the stress levels in the components of the coil package and to suggest an appropriate support structure for the conductor. Different design proposals with the focus on limiting stress in the CuNi cooling tubes and on feasibility of industrial manufacturing procedures have been conceived and analysed. The chosen coil support structure (substrate or comb), together with new insulation and modification of the winding scheme, seems to be an appropriate way to stabilize the coil better and offers important advantages like precise positioning of the conductor, more uniform distribution of loads on the CuNi tubes, an easier winding process on a guiding support, and simplified production procedures. Samples of the new coil structure were produced and tested. The obtained results are presented and discussed.

Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation

Phenomenological models of the dipole cross section that enters in the description of for instance deep inelastic scattering at very high energies have had considerable success in describing the available small-$x$ data in both the saturation region and the so-called extended geometric scaling (EGS) region. We investigate to what extent such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected to describe the nonlinear evolution in $x$ of the dipole cross section in these momentum regions. We find that in the EGS region the BK equation yields results that are qualitatively different from those of phenomenological studies. In particular, geometric scaling around the saturation scale is only obtained at asymptotic rapidities. We find that in this limit the anomalous dimension $\ensuremath{\gamma}(r,x)$ of phenomenological models approaches a limiting function that is universal for a large range of initial conditions. At the saturation scale, this function equals approximately 0.44, in contrast to the value 0.628 commonly used in the models. We further investigate the dependence of these results on the starting distribution, the small-$r$ limit of the anomalous dimension for fixed rapidities and the $x$-dependence of the saturation scale.

Parton distribution function for quarks in ans-channel approach

We use an $s$-channel picture of hard hadronic collisions to investigate the parton distribution function for quarks at small momentum fraction $x$, which corresponds to very high energy scattering. We study the renormalized quark distribution at one loop in this approach. In the high-energy picture, the quark distribution function is expressed in terms of a Wilson-line correlator that represents the cross section for a color dipole to scatter from the proton. We model this Wilson-line correlator in a saturation model. We relate this representation of the quark distribution function to the corresponding representation of the structure function ${F}_{T}(x,{Q}^{2})$ for deeply inelastic scattering.

Unusual features of Drell-Yan diffraction

The cross section of the diffractive Drell-Yan (DY) process, pp->(l-lbar X)p, where the system (l-lbar X) is separated by a large rapidity gap from the recoil proton, is calculated in the light-cone dipole approach. This process reveals unusual features, quite different from what is known for diffractive DIS and nonabelian radiation: (i) the diffractive radiation of a heavy dilepton by a quark vanishes in the forward direction; (ii) the diffractive production of a dilepton is controlled by the large hadronic radius; (iii) in contrast with DIS where diffraction is predominantly soft, the diffractive DY reaction is semihard-semisoft; (iv) as a result of the saturated shape of the dipole cross section, the fraction of diffractive DY events steeply falls with energy, but rises as function of the hard scale. These features are common for other abelian bremsstrahlung processes (higgsstrahlung, Z-strahlung, etc.). Measurements of diffractive DY processes at modern colliders would be a sensitive probe for the shape of the dipole cross section at large separations.

Small-x neutrino–hadron structure functions within the QCD color dipole picture

We present an exploratory QCD analysis of the neutrino structure functions in charged current DIS using the color dipole formalism. The dipole cross sections are taken from recent phenomenological/theoretical studies in deep inelastic inclusive production. The theoretical predictions are compared to the available experimental results in the small-x region, which has never been considered so far.

Saturation physics at HERA and RHIC: An unified description

Abstract One of the frontiers of QCD which are intensely investigated in high energy experiments is the high energy (small x ) regime, where we expect to observe the non-linear behavior of the theory. In this regime, the growth of the parton distribution should saturate, forming a color glass condensate (CGC). In fact, signals of parton saturation have already been observed both in ep deep inelastic scattering at HERA and in deuteron-gold collisions at RHIC. Currently, a global description of the existing experimental data is possible considering different phenomenological saturation models for the two processes within the CGC formalism. In this Letter we analyze the universality of these dipole cross section parameterizations and verify that they are not able to describe the HERA and RHIC data simultaneously. We analyze possible improvements in the parameterizations and propose a new parameterization for the forward dipole amplitude which allows us to describe quite well the small- x ep HERA data on F 2 structure function as well as the dAu RHIC data on charged hadron spectra. It is an important signature of the universality of the saturation physics.

Investigating FL(x,Q2) at fixed energy in the color dipole formalism

At small-x, the structure function F_L(x,Q2) is driven by the gluon content of the nucleon target and consequently it can unravel the underlying QCD dynamics in that region. In this work, one studies its behavior on photon virtuality Q2 at fixed energy within the color dipole formalism for models considering parton saturation effects. The reason is that they resum a wide class of higher-twist contributions, which have important influence in F_L description towards low Q2. It is shown that the geometric scaling property holds for the longitudinal cross section. Moreover, the effective anomalous dimension in scaling dipole cross sections can be investigated by studing both the turn over and the large Q2 regions of the recent experimental measurements.

Design and optimization of the 12.5 T EFDA dipole magnet

The aim of this paper is to provide an overview of a recent study carried out—within the framework of the European Fusion Program—to design a 12.5 T superconducting dipole. By focusing on the CICC based design option, the overall design procedure is presented. In particular, the 2D optimization of the dipole cross section is described including the magneto-static analysis of the winding and iron yoke, the mechanical analysis of the conductor jacket, insulation and outer cylinder, the conductor hot spot analysis, etc. As far as the thermo-hydraulic design is concerned, simulations of nominal as well as offset operating conditions (e.g., magnet quench) are presented with emphasis on their role played in the overall magnet design. For example, diagrams reporting the helium heat removal capabilities, pressure drop, mass flow, etc. are shown and their usefulness as guidance for the magnet designer described.

On the properties of charge-exchange dipole excitations and the T > component of a giant dipole resonance in spherical nuclei

Within the semimicroscopic approach based on the random-phase approximation that takes exactly into account a single-particle continuum and on a phenomenological inclusion of the fragmentation effect, it is proposed to describe the strength functions for charge-exchange giant dipole resonances and cross sections for photoabsorption and for partial “direct + semidirect” (γ, p) reactions in the vicinity of a giant E1 resonance with allowance for the isospin-splitting effect. The results of the calculations performed for some magic and semimagic nuclei without resort to free parameters are compared with available experimental data.

Polarization dependence in ELNES: Influence of probe convergence, collector aperture and electron beam incidence angle

The differential scattering cross section in electron energy loss near edge spectroscopy (ELNES) generally depends on the orientation of the Q wave vector transferred from the incident electron to an atomic core electron. In the case where the excited atom belongs to a threefold, fourfold or sixfold main rotation axis, the dipole cross section depends on the angle of Q with respect to this axis. In this paper, we restrict to this situation called dichroism. Furthermore, if we take into account the relativistic effects due to the high incident electron velocity, this dipole cross section also depends on the angle of Q with respect to the electron beam axis. It is due to these dependences that the shape of measured electron energy loss spectra varies with the electron beam incidence, the collector aperture, the incident beam convergence and the incident electron energy. The existence of a particular beam incidence angle for which the scattering cross section becomes independent of collection and beam convergence semi-angles is clearly underscored. Conversely, it is shown that EELS spectra do not depend on the beam incidence angle for a set of particular values of collection and convergence semi-angles. Particularly, in the case of a parallel incident beam, there is a collection semi-angle (often called magic angle) for which the cross section becomes independent of the beam orientation. This magic angle depends on the incident beam kinetic energy. If the incident electron velocity V is small compared with the light velocity c, this magic angle is about 3.975 θ E ( θ E is the scattering angle). It decreases to 0 when V approaches c. These results are illustrated in the case of the K boron edge in the boron nitride.

Deconvolution of the Co3O4(110) Fuchs–Kliewer phonon spectrum

The Fuchs–Kliewer phonon spectrum of single crystal Co3O4(110) has been treated with a Fourier transform log deconvolution method, which removes multiple scattering features from the single loss spectrum. Auger electron spectroscopy (AES), x-ray photoelectron spectroscopy (XPS) and low-energy electron diffraction (LEED) were first used to characterize the Co3O4 crystal establishing the cleanliness, composition, and order of the (110) surface. High resolution electron energy loss spectroscopy (HREELS) was then used to obtain the phonon spectrum for an incident electron energy of 3.77 eV. Due to the strong dipole cross section for the Fuchs–Kliewer phonon modes, intense multiple electron scattering was detected, which provided a complicated and overlapping combination of all possible loss modes. Deconvolution removed the multiple loss modes to produce well-resolved Fuchs–Kliewer fundamental phonon losses at 218, 373, 598, and 682cm−1 (27.0, 46.2, 74.1, and 84.6 meV). These values are compared to the fundamental loss energies obtained by resolving the overlapping peak structure with standard peak fitting procedures, which confirmed the single loss energies obtained with the deconvolution procedure. Deconvolution results from the four fundamental phonon spectrum of single crystal Co3O4(110) were also compared to those from the simpler spectra of CoO(100) and thin-film CoO(100)–Co3O4 epitaxy and some practical aspects of the deconvolution process discussed in this context.

Colour Dipole Phenomenology

Recent, precise HERA data are analysed in the context of colour dipole models, both with and without gluon saturation. The data on the deep inelastic structure function F2 seem to prefer parameterisations which include saturation effects. That is they indicate that the strong rise with energy of the dipole cross-section, which holds for small dipoles, pertains only for r r s ( x ) where r s ( x ) decreases monotonically as x decreases. The corresponding predictions for the diffractive structure function F 2 D ( 3 ) also hint at saturation, although the data are not accurate enough to be decisive.

Gluon distributions and fits using dipole cross sections

I investigate the relationship between the gluon distribution obtained using a dipole model fit to low-x data on F_2(x,Q^2) and standard gluons obtained from global fits with the collinear factorization theorem at fixed order. I stress the necessity to do fits of this type carefully, and in particular to include the contribution from heavy flavours to the inclusive structure function. I find that the dipole cross-section must be rather steeper than the gluon distribution, which at least partially explains why dipole model fits produce dipole cross-sections growing quite strongly at small x, while DGLAP based fits have valence-like, or even negative, small-x gluons as inputs. However, I also find that the gluon distributions obtained from the dipole fits are much too small to match onto the conventional DGLAP gluons at high Q^2, i.e. approx 50 GeV^2, where the two approaches should coincide. The main reason for this discrepancy is found to be the large approximations made in converting the dipole cross-sections into structure functions using formulae which are designed only for asymptotically small x. The shortcomings in this step affect the accuracy of the extracted dipole cross-sections in terms of size and shape, and hence also in terms of interpretation, at all scales.

Production of forward rapidity photons in high energy heavy ion collisions

We consider production of prompt photons in high energy gold–gold and deuteron–gold collisions in the forward rapidity region of RHIC ( y ∼ 3.8 ). In this kinematics, the projectile partons typically have large x b j while the target partons are mostly at very small x b j , so that the primary partonic collisions involve valence quarks from the projectile and gluons from the target. We take the target nucleus to be a color glass condensate while the projectile deuteron or nucleus is treated as a dilute system of partons. We show that the photon production cross section can be written as a convolution of a quark–nucleus scattering cross section, involving a quark–antiquark dipole, with the leading order quark–photon fragmentation function. We consider different models of the quark–antiquark dipole and show that measurement of photons in the forward rapidity region at RHIC can distinguish between different parameterizations of the dipole cross section as well as help clarify the role of parton coalescence models in hadron production at RHIC.

Heavy quark photoproduction in proton-proton collisions

We calculate the photoproduction of heavy quarks in proton-proton collisions at RHIC, Tevatron, and CERN LHC energies, where the photon reaches energies larger than those accessible at DESY-HERA. The integrated cross section and the rapidity distributions for open charm and bottom production are computed employing sound high energy QCD formalisms. For the linear perturbative QCD approaches we consider both the usual collinear factorization and the ${k}_{\ensuremath{\perp}}$-factorization formalisms, whereas for the nonlinear QCD (saturation) calculations one considers the Golec-Biernat-W\"usthoff and the Iancu-Itakura-Munier parametrizations for the dipole cross section within the color dipole picture.

Gluon Saturation in the Colour Dipole Model?

We use data on the deep inelastic structure function F_2 in order to constrain the cross-section for scattering a colour dipole off a proton. The data seem to prefer parameterisations which include saturation effects. That is they indicate that the strong rise with energy of the dipole cross-section, which holds for small dipoles, pertains only for r < r_s(x) where r_s(x) decreases monotonically as x decreases. Subsequent predicitions for the diffractive structure function F_2^{D(3)} also hint at saturation, although the data are not really sufficiently accurate.

A QCD dipole formalism for forward-gluon production

We derive inclusive and diffractive forward-gluon production in the scattering of a q q ¯ dipole off an arbitrary target in the high-energy eikonal approximation, suitable to study the saturation regime. We show how the inclusive cross-section is related to the total cross-section for the scattering of a colorless pair of gluons on the target: the gluon-production cross-section can be expressed as a convolution between this gg dipole total cross-section and a dipole distribution. We then consider as an application the forward-jet production from an incident hadron and describe forward-jet production at HERA and Mueller–Navelet jets at Tevatron or LHC. We show how these measurements are related to the q q ¯ – gg or gg– gg dipole–dipole cross-sections and why they are therefore well-suited for studying high-energy scattering in QCD.

Radiative parton energy loss and jet quenching in high-energy heavy-ion collisions

We study within the light-cone path integral approach [3] the effect of the induced gluon radiation on high-p_{T} hadrons in high-energy heavy-ion collisions. The induced gluon spectrum is represented in a new form which is convenient for numerical simulations. For the first time, computations are performed with a realistic parametrization of the dipole cross section. The results are in reasonable agreement with suppression of high-p_{T} hadrons in Au+Au collisions at \sqrt{s}=200 GeV observed at RHIC.

Color dipoles andρ,φelectroproduction

We present a detailed comparison of a variety of predictions for diffractive light vector meson production with the data collected at the DESY HERA collider. All our calculations are performed within a dipole model framework and make use of different models for the meson light-cone wave function. There are no free parameters in any of the scenarios we consider. Generally we find good agreement with the data using rather simple Gaussian motivated wave functions in conjunction with dipole cross sections which have been fitted to other data.