In this work we consider the QCD parton saturation models to describe soft interactions at the high energy limit. The total and elastic cross sections as well as the elastic slope parameter are obtained for proton-proton and pion-proton collisions and compared to recent experimental results. The analyses are done within the color dipole formalism taking into account saturation models which have been tested against DIS data. The main point is that the match between soft and hard interaction occurs in the saturation region which can be described by high density QCD approaches. Discussion is performed on the main theoretical uncertainties associated with calculations.
We present the first evaluation of the color dipole diffraction slope from the data on diffractive photo- and electroproduction of vector mesons. The energy and dipole size dependence of the found dipole diffraction slope are consistent with the color dipole gBFKL dynamics.
Forward differential cross-section for diffraction dissociation of virtual photons on nucleon target is calculated in the QCD dipole picture. The numerical estimates are presented and discussed.
Using the QCD dipole picture of BFKL dynamics, the quasi elastic component of the diffractive gamma*-dipole cross-section, dominating at small M^2/Q^2, is calculated.
The contribution to diffraction dissociation of virtual photons due to quasi-elastic scattering of the $q$-$\bar q$ component is calculated in the framework of the QCD dipole picture. Both longitudinal and transverse components of the cross-section are given. It is shown that, at fixed mass of the diffractively produced system, quantum mechanical interference plays an important r\^ ole. Phenomenological consequences are discussed.
The Good-Walker mechanism for diffraction is shown to provide a link between total and diffractive structure functions and to be relevant for QCD calculations at small x_{Bj}. For Deep-Inelastic scattering on a small-size target (cf. an onium) the r\^ ole of Good-Walker ``diffractive eigenstates'' is played by the QCD dipoles appearing in the $1/N_C$ limit of QCD. Hard diffraction is thus related to the QCD tripe-dipole vertex which has been recently identified (and calculated) as being a conformal invariant correlator and/or a closed-string amplitude. An extension to hard diffraction at HERA …
Using the eikonal approximation, we show that inclusive gluon production is related to the scattering of a gluon-gluon dipole while diffractive gluon production in DIS is related to a two-$q\bar q$ dipole scattering amplitude. Hence diffractive photon dissociation cross-sections are observables that provide potential information on dipole correlations, which represent an open issue in high-energy QCD.
The prediction of FL(x,Q2)=0.27F2(x,Q2) in the color-dipole picture based on color-transparency and transverse-size reduction, is consistent with the experimental results from HERA.
Using a combination of S-Matrix and perturbative QCD properties in the small x_{Bjorken} regime, we propose a formulation of hard diffraction unifying the partonic (Ingelman-Schlein) Pomeron, Soft Colour Interaction and QCD dipole descriptions. In particular, we show that all three approaches give an unique and mutually compatible formula for the proton diffractive structure functions incorporating perturbative and non perturbative QCD features.
Starting from a genuinely nonperturbative formulation of photon-proton scattering we discuss which approximations and assumptions are required to obtain the dipole picture of high energy scattering.
We discuss two aspects of the color dipole picture of high energy photon-proton scattering. First we present bounds on various ratios of deep inelastic structure functions resulting from the dipole picture that, together with the measured data, can be used to restrict the kinematical range of its applicability. The second issue that we address is the choice of energy variable in the dipole-proton cross section.
Using the QCD dipole picture of the BFKL pomeron, the cross-section of single diffractive dissociation of virtual photons at high energy and large diffractively excited masses is calculated. The calculation takes into account the full impact-parameter phase-space and thus allows to obtain an exact value of the triple BFKL Pomeron vertex. It appears large enough to compensate the perturbative 6-gluon coupling factor (alpha/pi)^3 thus suggesting a rather appreciable diffractive cross-section.
Compact and well defined formulae for the shadow of the virtual photon interacting with a large nucleus at small $x_{Bj}$ are given in the QCD dipole picture. Two classes of contributions are considered: (a) quasi-elastic interaction of the $q\bar{q}$ dipole and (b) multi-pomeron coupling.
We give a brief representation of the theoretical results from the color dipole picture, covering the total photoabsorption cross section, high-energy $J/ψ$ photoproduction with respect to recent experimental data from the LHCb Collaboration at CERN, and ultra-high energy neutrino scattering, relevant for the ICE-CUBE experiment.
The QCD dipole picture of BFKL dynamics provides an attractive theoretical approach to the study of the QCD (resummed) perturbative expansion of small-x physics and more generally to hard high-energy processes. We discuss applications to the phenomenology of proton structure functions in the HERA range and to the longstanding problem of unitarity corrections, and outline some specific predictions of the dipole picture.
The soft gluon part of a proton wave function is investigated and compared with an onium case. It is argued that at every step of the gluon cascade new color structures appear. Dipole equation kernel emerges when a diquark limit is assumed.
We investigate the mass range of the quark-antiquark fluctuations of the photon that are active in producing the total photoabsorption cross section in the color dipole picture, emphasizing the notion of color transparency and saturation. We consider the implications of measurements at future extensions of the available electron-proton-scattering energy.
We discuss the description of the proton structure function within the dipole factorisation framework. We parametrise the forward dipole amplitude to account for saturation as predicted by the small-x QCD evolution equations. Contrarily to previous models, the saturation scale does not decrease when taking heavy quarks into account. We show that the same dipole amplitude also allows to reproduce diffractive data and exclusive vector meson production.
We study the dipole picture for the description of the deep inelastic scattering, focusing on the structure functions which are driven directly by the gluon distribution. One performs estimates using the effective dipole cross section given by the Glauber-Mueller approach in QCD, which encodes the corrections due to the unitarity effects associated with the saturation phenomenon. We also address issues about frame invariance of the calculations when analysing the observables.
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.
We report on the results obtained in the study of the parton saturation effects, taken into account through the multiscattering Glauber-Mueller approach, applied to the Drell-Yan (DY) process described in the color dipole picture. As a main result, one shows that those effects play an important role in the estimates of the DY differential cross section atRHIC energies.
A personal summary of the discussions which took place at the informal meeting in Amirim, Israel from June 1-4 2000, concerning the dipole picture of small-$x$ physics is presented. The broad aim of the meeting was to address the question ``Has HERA reached a new QCD regime (at small $x$) ?''. The new regime in question is the high-density, but weak-coupling, limit of perturbative QCD.
The QCD-based generalized vector dominance-color-dipole picture (GVD-CDP) provides a coherent picture of low-x DIS, deeply virtual Compton scattering and light as wel as heavy vector-meson production.
We pose the question: how far can we push the QCD dipole model and the idea of QCD saturation to the kinematical regions traditionally associated with soft nonperturbative physics? The answer is that it works sufficiently well allowing a smooth transition from hard (BFKL) pomeron to the soft one.
The relation between the two approaches is discussed both in the linear and nonlinear regimes. It is connected to the gauge invariance and Moebius symmetry in LL perturbative QCD. First corrections beyond the large N approximation are discussed for the nonlinear case.
Based upon the color-dipole picture, we provide closed analytic expressions for the longitudinal and the transverse photoabsorption cross sections at low values of the Bjorken variable of x<0.1. We compare with the experimental data for the longitudinal-to-transverse ratio of the (virtual) photoabsorption cross section and with our previous fit to the experimental data for the total photoabsorption cross section. Scaling in terms of the low-x scaling variable eta(W^2,Q^2) is analyzed in terms of the reduced cross section of deep inelastic scattering.
We study in detail the main features of the unitarized Regge model (CFKS), recently proposed to describe the small-$Q^2$ domain. It takes into account a two-component description with two types of unitarized contributions: one is the multiple Pomeron exchanges contribution, interacting with the large dipole size configurations, and the other one consists on a unitarized dipole cross section, describing the interaction with the small size dipoles. We compare the resulting dipole cross section to that from the saturation model (GBW).
We summarize recent work on low-x deep inelastic scattering. The generalized vector dominance/color-dipole picture (GVD/CDP) implies a scaling behavior for $σ_{γ^* p} (W^2, Q^2)\cong σ_{γ^* p}(η)$, with $η= (Q^2 + m^2_0)/Λ^2 (W^2)$ and yields an excellent representation of the experimental results on $σ_{γ^* p}(η)$.
I briefly review how a three-dimensional picture of parton dynamics is rendered in the impact parameter representation, applied to generalized parton distributions and to the dipole picture of high-energy scattering.
We suggest a simple physical picture for the diffractive parton distributions that appear in diffractive deeply inelastic scattering. In this picture, partons impinging on the proton can have any transverse separation, but only when the separation is small can they penetrate the proton without breaking it up. By comparing the predictions from this picture with the diffractive data from HERA, we determine rough values for the small separations that dominate the diffraction process.
We perform an adjust to the most recent structure function data, considering the QCD dipole picture applied to ep scattering. The structure function F2 at small x and intermediate Q2 can be described by the model containing an economical number of free-parameters, which encodes the hard Pomeron physics. The longitudinal structure function and the gluon distribution are predicted without further adjustments. The data description is effective, whereas a resummed next-to-leading level analysis is deserved.
It is argued that the QCD dipole picture allows to build an unified theoretical description -based on BFKL dynamics- of the total and diffractive nucleon structure functions. This description is in qualitative agreement with the present collection of data obtained by the H1 collaboration. More precise theoretical estimates, in particular the determination of the normalizations and proton transverse momentum behaviour of the diffractive components, are shown to be required in order to reach definite conclusions.
The $F_2$, $F_G$, $R = F_L/F_T$ proton structure functions are derived in the QCD dipole picture. Assuming $k_T$ and renormalization-group factorization, we relate deep-inelastic proton scattering to deep-inelastic onium scattering. We get a three-parameter fit of the 1994 H1 data in the low-$x,$ moderate $Q^2$ range. The ratios $F_G/F_2$ and $R$ are predicted without further adjustment. The dipole picture of BFKL dynamics is shown to provide a relevant model for quantitatively describing the proton structure functions at HERA. The predictions for $F_2$ and $F_G$ are compatible with the next-t…
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.
Onium-onium scattering at high energy is used to illustrate a dipole picture of high energy hard scattering in the large $N_c$ limit. Single and double BFKL pomeron exchanges are calculated in the leading logarithmic approximation. An expression is given for the triple pomeron coupling when one of the pomeron's momentum is zero while the other two have momentum transfer, t. This expression is explicit and could be evaluated numerically. It has a $(-t)^{-{1\over 2}}$ singularity at t=0.
We study in detail the main features of the unitarized Regge model (CFKS), recently proposed to describe the small-$Q^2$ domain. It takes into account a two-component description with two types of unitarized contributions: one is the multiple pomeron exchange contribution, interacting with the large dipole configurations, and the other one consists of a unitarized dipole cross section, describing the interaction with the small size dipoles. We analyze the ratio between soft and hard pieces as a function of the virtuality, and also compare the resulting dipole cross section to that from the sat…
Using the QCD dipole picture of the hard BFKL pomeron, we derive the general expressions of the elastic and inelastic components of the proton diffractive structure functions. We obtain a good 7 parameter fit (including a secondary reggeon contribution) to data taken at HERA by the H1 and ZEUS collaborations. The main characteristic features of the model in reproducing the data are discussed, namely the effective pomeron intercept, the scaling violations and the beta dependence. A difference obtained in the separate H1 and ZEUS fits leads us to analyse directly the differences between both mea…
This is the first of two papers in which we study real and virtual photon-proton scattering in a nonperturbative framework. We classify different contributions to this process and identify the leading contributions at high energies. We then study the renormalisation of the photon-quark-antiquark vertex that occurs in the leading contributions. We find something like the dipole picture in one of these contributions but also find two correction terms which can potentially become large at small photon virtualities. In the second paper we will discuss the additional approximations and assumptions …
The AGL equation includes all multiple pomeron exchanges in the double logarithmic approximation (DLA) limit, leading to an unitarized gluon distribution in the small $x$ regime. This equation was originally obtained using the Glauber-Mueller approach. We demonstrate in this contribution that the AGL equation can also be obtained from the dipole picture. Our conclusion is that the AGL equation is a good candidate for an unitarized evolution equation at small $x$ in the DLA limit.
Using the QCD dipole picture of the BFKL pomeron, the gluon contribution to the cross-section for single diffractive dissociation in deep-inelastic high-energy scattering is calculated. The resulting contribution to the proton diffractive structure function integrated over $t$ is given in terms of relevant variables, $x_{\cal P}, Q^2, $ and $β= x_{Bj}/x_{\cal P}.$ It factorizes into an explicit $x_{\cal P}-$dependent Hard Pomeron flux factor and structure function. The flux factor is found to have substantial logarithmic corrections which may account for the recent measurements of the Pomeron …
We pursue the intriguing possibility that larger-size instantons build up diffractive scattering, with the marked instanton-size scale $<ρ> \approx 0.5$ fm being reflected in the conspicuous ``geometrization'' of soft QCD. As an explicit illustration, the known instanton contribution to DIS is transformed into the intuitive colour dipole picture. With the help of lattice results, the $q \bar{q}$-dipole size r is carefully increased towards hadronic dimensions. Unlike pQCD, one now observes a competition between two crucial length scales: the dipole size r and the size $ρ$ of the background ins…
Recently Kovner and Lublinsky proposed a set of equations which can be viewed as dual to JIMWLK evolution. We show that these dual equations have a natural dipole-like structure, as conjectured by Kovner and Lublinsky. In the high energy large N_c limit these evolution equations reduce to equations previously derived in the dipole model. We also show that the dual evolution kernel is scheme dependent, although its action on the weight functional describing a high energy state gives a unique result.
The total $γ^*γ^*$ cross-section is derived in the Leading Order QCD dipole picture of BFKL dynamics, and compared with the one from 2-gluon exchange. The Double Leading Logarithm approximation of the DGLAP cross-section is found to be small in the phase space studied. Cross sections are calculated for realistic data samples at the $e^+e^-$ collider LEP and a future high energy linear collider. Next to Leading order corrections to the BFKL evolution have been determined phenomenologically, and are found to give very large corrections to the BFKL cross-section, leading to a reduced sensitivity …
In this contribution we discuss distinct approaches for the high density QCD (hdQCD) and the demonstration of the equivalence between the AGL approach and the K approach is presented. Our conclusion is that the AGL equation is a good candidate for an unitarized evolution equation at high densities in the DLA limit.
The AGL equation includes all multiple pomeron exchanges in the double logarithmic approximation (DLA) limit, leading to an unitarized gluon distribution in the small x regime. This equation was originally obtained using the Glauber-Mueller approach. We demonstrate in this paper that the AGL equation and, consequently, the GLR equation, can also be obtained from the dipole picture in the double logarithmic limit, using an evolution equation, recently proposed, which includes all multiple pomeron exchanges in the leading logarithmic approximation. Our conclusion is that the AGL equation is a go…
This is the second of two papers in which we study real and virtual photon-proton scattering in a nonperturbative framework. In the first paper we have identified the leading contributions to this process at high energies and have derived expressions for them which take into account the renormalisation of the photon-quark-antiquark vertex. In the present paper we investigate the approximations and assumptions that are necessary to obtain the dipole model of high energy scattering from the results derived in the first paper. We discuss the gauge invariance of different contributions to the scat…
The scaling in $σ_{γ^*p}$ cross sections (for $Q^2/W^2 << 1$) in terms of the scaling variable $η= (Q^2 + m^2_0)/Λ^2 (W^2)$ is interpreted in the generalized vector dominance/color-dipole picture (GVD/CDP). The quantity $Λ^2 (W^2)$ is identified as the average gluon transverse momentum absorbed by the $q \bar q$ state, $<\vec l^{~2}> = (1/6) Λ^2 (W^2)$. At any $Q^2$, for $W^2 \to \infty$,the cross sections for virtual and real photons became universal, $σ_{γ^*p}(W^2,Q^2)/σ_{γp}(W^2) \to 1$.
In this presentation, we obtain the corresponding universal function to the diffractive process and show the cross section exhibits the geometrical scaling. It is observed the diffractive theory according to the color dipole approach at small-$x$ is a convenient framework that reveals the color transparency and the saturation phenomena. Also we calculate the contribution of heavy quark productions in the diffractive cross section for high energy that is determined by the small size dipole configuration. The ratio of the diffractive cross section to the total cross section in the electron-proto…
The transverse size of q q-bar fluctuations of the longitudinal photon is reduced relative to the transverse size of q q-bar fluctuations of the transverse photon. This implies R(W2, Q2) = 0.375 or, equivalently, FL/F2 = 0.27 at x<<0.1 and Q2 sufficiently large, while R(W2, Q2) = 0.5, if this effect is not taken into account. Forthcoming experimental data from HERA will allow to test this prediction.
We discuss two different models for the impact parameter dependent dipole cross section: one based on DGLAP evolution and the other inspired by the Balitsky-Kovchegov equation. The parameters are determined from fits to data on the total gamma* p cross section measured at HERA. The impact parameter dependent saturation scale is extracted. Predictions are then confronted with HERA data on exclusive diffractive vector meson production and deeply virtual Compton scattering. Finally, predictions are given for the cross sections of exclusive photoproduced J/psi and Upsilon mesons, and Z^0 bosons, e…
In this paper we demonstrate that the dense system of partons (gluons) can be produced in dilute-dilute system scattering, using the example of dipole-dipole collisions. This increase in density stems from the intensive gluon cascades that can be described by the enhanced BFKL Pomeron diagrams (Pomeron loops). For the first time we found the analytical solution to the equation for diffraction production in the dipole-dense parton system scattering, using the simplified BFKL kernel. Having this solution as well as the solution to Balitsky- Kovchegov equation we developed technique that allowed …
For photon virtualities of $Q^2 \gsim 20 {\rm GeV}^2$, the results of the (hard Pomeron) fit in the tensor-Pomeron model in terms of the variables $Q^2$ and the virtual-photon-proton energy squared, $W^2$, provide empirical evidence for the validity of the Color Dipole Picture (CDP). Consistency of the CDP with the perturbative QCD (pQCD) improved parton model implies the prediction of $C_2 = ε_0 \cong 0.30$ for the exponent $C_2$ of the energy-squared dependence in agreement with the results of the fits. For $Q^2 \lsim 20 GeV^2$, the CDP yields a parameter-free smooth transition from $Q^2 \gs…
We provide predictions for the rapidity distributions of exclusive photoproduced J/psi and Upsilon mesons, and Z^0 bosons, at the Tevatron and LHC. We use the equivalent-photon approximation with the photon-proton cross sections given by the impact parameter dependent dipole saturation model, which has already been shown to give a good description of a wide variety of HERA data. We derive the quark-antiquark light-cone wave functions of timelike neutral electroweak bosons. An essential difference is pointed out between the amplitude for timelike heavy boson photoproduction and the amplitude fo…
The transverse size of q q-bar fluctuations of a longitudinally polarized photon is reduced relative to the transerve size of q q-bar fluctuation of a transversely polarized photon. This implies a model-independent prediction of the ratio R(W2,Q2)=sigma_L/sigma_T=0.375, or, equivalently, F_L/F_2=0.27, for x=Q2/W2<<1 and Q2 sufficiently large, while R(W2,Q2)=0.50, if this effect is ignored. Experimental data from HERA confirm the transverse-size reduction.
The transverse size of q q-bar fluctuations of the longitudinal photon is reduced relative to the transverse size of q q-bar fluctuations of the transverse photon. This implies R(W^2, Q^2) = 0.375 or, equivalently, F_L(W^2,Q^2)/F_2(W^2,Q^2) = 0.27 for x = Q^2/W^2 << 1 and Q^2 sufficiently large, while R(W^2, Q^2) = 0.5, if this effect is not taken into account. Forthcoming experimental data from HERA will allow to test this prediction.
We present a simultaneous analysis, within an impact parameter dependent saturated dipole model, of exclusive diffractive vector meson (J/psi, phi and rho) production, deeply virtual Compton scattering and the total gamma* p cross section data measured at HERA. Various cross sections measured as a function of the kinematic variables Q^2, W and t are well described, with little sensitivity to the details of the vector meson wave functions. We determine the properties of the gluon density in the proton in both longitudinal and transverse dimensions, including the impact parameter dependent satur…
In the color dipole gBFKL dynamics we predict a strikingly different Q^2 and energy dependence of the diffraction slope for the elastic production of ground state V(1S) and radially excited V'(2S) light vector mesons. The color dipole model predictions for the diffraction slope for ρ^0 and ϕ^0 production are in a good agreement with the data from the fixed target and collider HERA experiments. We present how a different form of anomalous energy and Q^2 dependence of the diffraction slope for V'(2S) production leads to a different position of the node in radial wave function and discuss a possi…
