We analyze deep inelastic scattering at small Bjorken x, using the approximate conformal invariance of QCD at high energies. Hard pomeron exchanges are resummed eikonally, restoring unitarity at large values of the phase shift in the dual AdS geometry. At weak coupling this phase is imaginary, corresponding to a black disk in AdS. In this saturated regime, cross sections exhibit geometric scaling and have a simple universal form, which we test against available experimental data for the proton structure function F_2(x,Q^2). We predict, in particular, the dependence of the cross section on the scaling variable (Q/Q_s)^2 in the deeply saturated region, where Q_s is the usual saturation scale. We find agreement with current data on F_2 in the kinematical region 0.5 < Q^2 < 10 GeV^2, x < 10^-2, with an average 6% accuracy. We conclude by discussing the relation of our approach with the commonly used dipole formalism.
I describe the parton picture at strong coupling emerging from the gauge/gravity duality, with emphasis on the universality of the phenomenon of parton saturation. I discuss several consequences of this picture for the phenomenology of a strongly coupled quark-gluon plasma, which are potentially relevant for heavy ion collisions at RHIC and LHC.
In a previous paper, we have analyzed high energy QCD from AdS-CFT and proved the saturation of the Froissart bound (a purely QCD proof of which is still lacking). In this paper we describe the calculation in more physical terms and map it to QCD language. We find a remarkable agreement with the 1952 Heisenberg description of the saturation (pre-QCD!) in terms of shockwave collisions of pion field distributions. It provides a direct map between gauge theory physics and the gravitational physics on the IR brane of the Randall-Sundrum model. Saturation occurs through black hole production on the…
For gauge theories which admit a dual string description, we analyze deep inelastic scattering at strong 't Hooft coupling and high energy, in the vicinity of the unitarity limit. We discuss the onset of unitarity corrections and determine the saturation line which separates weak scattering from strong scattering in the parameter space of rapidity and photon virtuality. We discover that the approach towards unitarity proceeds through two different mechanisms, depending upon the photon virtuality Q^2 : single Pomeron exchange at relatively low Q^2 and, respectively, multiple graviton exchanges …
We use the holographic dual of a finite-temperature, strongly-coupled, gauge theory with a small number of flavors of massive fundamental quarks to study meson excitations and deep inelastic scattering (DIS) in the low-temperature phase, where the mesons are stable. We show that a high-energy flavor current with nearly light-like kinematics disappears into the plasma by resonantly producing mesons in highly excited states. This mechanism generates the same DIS structure functions as in the high temperature phase, where mesons are unstable and the current disappears through medium-induced parto…
We present a model based on the concept of saturation for small $Q^2$ and small $x$. With only three parameters we achieve a good description of all Deep Inelastic Scattering data below $x=0.01$. This includes a consistent treatment of charm and a successful extrapolation into the photoproduction regime. The same model leads to a roughly constant ratio of diffractive and inclusive cross section.
In $1/N_c$ expansion, analyticity and crossing lead to crossing even and odd ($C=\pm 1$) vacuum exchanges at high-energy, the {\em Pomeron} and the {\em Odderon}. We discuss how, using {\em String/Gauge duality}, these can be identified with a reggeized {\em Graviton} and the anti-symmetric {\em Kalb-Ramond fields} in $AdS$ background. With confinement, these Regge singularities interpolate with glueball states. We also discuss unitarization based on eikonal sum in $AdS$.
Saturation of gluon distribution is a consequence of the non-linear evolution equations of QCD. Saturation implies the existence of so called saturation momentum which is defined as a gluon density per unit rapidity per transverse area. At large energies for certain kinematical domains saturation momentum is the only scale for physical processes. As a consequence different observables exhibit geometrical scaling (GS). We discuss a number of examples of GS in different reactions.
We propose a new description of inclusive diffraction in deep inelastic scattering (DIS). The diffractive structure functions are expressed in the dipole picture and contain heavy-quark contributions. The dipole scattering amplitude, a saturation model fitted on inclusive DIS data, features a saturation scale Q_s(x) larger than 1 GeV for x=10^{-5}. The q\bar{q}g contribution to the diffractive final state is modeled in such a way that both the large-Q^2 and small-beta limits are implemented. In the regime xpom<0.01 in which saturation is expected to be relevant, we obtain a parameter-free desc…
We successfully describe the HERA-data on diffractive deep inelastic scattering using a saturation model which has been applied in our earlier analysis of the inclusive $ep$-scattering data. No further parameters are needed. Saturation already turned out to be essential in describing the transition from large to small values of $Q^2$ in inclusive scattering. It is even more important for diffractive processes and naturally leads to a constant ratio of the diffractive versus inclusive cross sections. We present an extensive discussion of our results as well as detailed comparison with data.
We analyse the dissociation of a photon in diffractive deep inelastic scattering in the kinematic regime where the diffractive mass is much bigger than the photon virtuality. We consider the dominant q\bar{q}g component keeping track of the transverse momentum of the gluon which can be measured as a final-state jet. We show that the diffractive gluon-jet production cross-section is strongly sensitive to unitarity constraints. In particular, in a model with parton saturation, this cross-section is sensitive to the scale at which unitarity effects become important, the saturation scale. We argue…
In this paper we investigate the saturation physics in diffractive deep inelastic electron-ion scattering. We estimate the energy and nuclear dependence of the ratio $σ^{diff}/σ^{tot}$ and predict the $x_{\pom}$ and $β$ behavior of the nuclear diffractive structure function $F_{2,A}^{D(3)}(Q^2, β, x_{IP})$. Moreover, we analyze the ratio $R^{diff}_{A1,A2}(Q^2, β, x_{IP}) = F_{2,A1} ^{D(3)}/F_{2,A2} ^{D(3)}$, which probes the nuclear dependence of the structure of the Pomeron. We show that saturation physics predicts that approximately 37 % of the events observed at eRHIC should be diffractive.
The analytical treatment of the nonperturbative QCD dynamics is one of main open questions of the strong interactions. Currently, it is only possible to get some qualitative information about this regime considering other QCD-like theories, as for example the N=4 super Yang-Mills (SYM), where one can perform calculations in the nonperturbative limit of large 't Hooft coupling using the Anti-de Sitter space/Conformal field theory (AdS/CFT). Recently, the high energy scattering amplitude was calculated in the AdS/CFT approach, applied to deep inelastic scattering (DIS) and confronted with the $F…
Considering the high-energy limit of the QCD gluon distribution inside a nucleus, we calculate the proton-nucleus total inelastic cross section using a simplified dipole model. We show that, if gluon saturation occurs in the nuclear surface region, the total cross section of proton-nucleus collisions increases more rapidly as a function of the incident energy compared to that of a Glauber-type estimate. We discuss the implications of this with respect to recent ultra-high-energy cosmic ray experiments.
Gluon distributions of colliding hadrons saturate as a result of the non-linear evolution equations of QCD. As a consequence there exists the so called saturation momentum, which is related to the gluon density per unit rapidity per transverse area. When saturation momentum is the only scale for physical processes, different observables exhibit geometrical scaling (GS). We show a number of examples of GS and its violation in different reactions.
We investigate the softwall AdS/CFT model. We specifically looked at the Pomeron, leading Regge contribution to a scattering process and used it to fit deep inelastic scattering data from the HERA collaboration. We find that the model fits the data with much more success than the purely conformal case, and find similar success to previous confinement models.
We investigate the role of unitarization effects in virtual photon-proton (γ^*p) interactions at small x. The q\bar{q}-fluctuation of the initial photon is separated into a small distance and a large distance component and a model for the unitarization of each component is proposed. The Born approximation for the small size component is calculated using QCD perturbation theory. Reggeon diagram technique is used in order to obtain a self-consistent scheme for both total γ^*p cross section and diffractive production. The model gives a good description of HERA data in the small-x region, with a s…
Consistency of the previously suggested color-dipole representation of deep-inelastic scattering (DIS_) and vector-meson production at low x with DGLAP evolution allows one to predict the exponent of the W^2 dependence of the saturation scale Lambda_sat^2(W^2) ~ (W^2)^C-2. One finds C_2^theory = 0.27 in agreement with the model-independent analysis of the experimental data from HERA on deep-inelastic electron scattering.
Saturation effects in diffractive deep inelastic scattering
University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；The University of Kansas（堪萨斯大学）；The University of Helsinki（赫尔辛基大学）
The solution to the BFKL equation grows like a power of center of mass energy, s, violating unitarity conditions at high energies. The growth of the cross section can be tamed by taking into account multiple pomeron exchanges. This is known as saturation and it is expressed in the Balitsky-Kovchegov equation. Conservation of energy should also slow down the growth of the cross section, and our aim in this work is to study the effects of enforcing energy conservation in DIS-events. Using the dipole picture, onium-onium collisions can be viewed, in the large N_c and the leading logarithmic limit…
We use the AdS/CFT correspondence and the holographic softwall model to investigate the Deep Inelastic Scattering (DIS) in the exponentially small $x$ (Bjorken Parameter) regime. We calculate the corresponding structure functions for scalar fields. Using these results we studied the problem of the saturation line in the strong interactions. Our results are consistent with those achieved using other models.
We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the three-dimensional hyperbolic space H3, which is the impact parameter space for high energy scattering in…
By using the AdS/CFT correspondence we study the deep inelastic scattering of an R-current off a N=4 supersymmetric Yang-Mills (SYM) plasma at finite temperature and strong coupling. Within the supergravity approximation valid when the number of colors is large, we compute the structure functions by solving Maxwell equations in the space-time geometry of the AdS_5 black three-brane. We find a rather sharp transition between a low energy regime where the scattering is weak and quasi-elastic, and a high-energy regime where the current is completely absorbed. The critical energy for this transiti…
Analyzing recent ALICE data on inelastic pp scattering at the LHC energies we show that charged particle distributions exhibit geometrical scaling (GS). We show also that the inelastic cross-section is scaling as well and that in this case the quality of GS is better than for multiplicities. Moreover, exponent $λ$ characterizing the saturation scale is for the cross-section scaling compatible with the one found in deep inelastic ep scattering at HERA. Next, by parametrizing charged particles distributions by the Tsallis-like formula, we find a somewhat unexpected solution that still exhibits G…
We show that HERA data for the inclusive structure function F_2(x,Q^2) at small Bjorken-x and Q^2 can be reasonably well described by a color-dipole model with an AdS/CFT-inspired dipole-proton cross section. The model contains only three free parameters fitted to data. In our AdS/CFT-based parameterization the saturation scale varies in the range of 1-3 GeV becoming independent of energy/Bjorken-x at very small x. This leads to the prediction of x-independence of the F_2 and F_L structure functions at very small x. We provide predictions for F_2 and F_L in the kinematic regions of future expe…
We show how the AGBS model, originally developed for deep inelastic scattering applied to HERA data on the proton structure function, can also describe the RHIC data on single inclusive hadron yield for $d+Au$ and $p+p$ collisions through a new simultaneous fit. The single inclusive hadron production is modeled through the color glass condensate, which uses the quark(and gluon)--condensate amplitudes in momentum space. The AGBS model is also a momentum space model based on the asymptotic solutions of the BK equation, although a different definition of the Fourier transform is used. This aspect…
The geometric scaling property observed in the HERA data at small x, that the deep inelastic scattering (DIS) total cross-section is a function of only the variable Q^2*x^λ, has been argued to be a manifestation of the saturation regime of QCD and of the saturation scale Q^2_s(x) x^{-λ}. We show that this implies a similar scaling in the context of diffractive DIS and we observe, for several diffractive observables, that the experimental data from HERA confirm the expectations of this scaling.
Progresses towards the calculation and the understanding of NLO/NLL contributions to Deep Inelastic Scattering at low x with gluon saturation are being reviewed.
We calculate deep inelastic structure functions for mesons in the D3-D7 brane model, that incorporates flavour to the AdS/CFT correspondence. We consider two different prescriptions for the hadronic current dual: a gauge field in the AdS bulk and a gauge field on the D7 brane. We also calculate elastic form factors in both cases. We compare our results with other holographic models.
We study the semi-inclusive hadron production in deep inelastic scattering at small $x$. A transverse momentum dependent factorization is found consistent with the results calculated in the small-$x$ approaches, such as the color-dipole framework and the color glass condensate, in the appropriate kinematic region at the lowest order. The transverse momentum dependent quark distribution can be studied in this process as a probe for the small-$x$ saturation physics. Especially, the ratio of quark distributions as a function of transverse momentum at different $x$ demonstrates strong dependence o…
Deep inelastic scattering at low x can be described by essentially only two fitted parameters. The interpretation of J/Psi photoproduction in terms of the gluon structure function is elaborated upon.
String theory has long ago been initiated by the quest for a theoretical explanation of the observed high-energy ``Reggeization'' of strong interaction amplitudes. In terms of quantum field theory, it is the so-called ``soft'' regime, where the coupling constant is expected to be large and thus perturbative calculations inadequate. However, since then, no convincing derivation of the link between gauge field theory at strong coupling and string theory has come out. This 35-years-old puzzle is thus still unsolved. We discuss how modern tools like the AdS/CFT correspondence give a new insight on…
We review the recent finding of the two-plateau momentum distribution of sea quarks in deep inelastic scattering off nuclei in the saturation regime. The diffractive plateau which dominates for small $\bp$ measures precisely the momentum distribution of quarks in the beam photon, the rôle of the nucleus is simply to provide an opacity. The plateau for truly inelastic DIS exhibits a substantial nuclear broadening of the momentum distribution. Despite this nuclear broadening, the observed final state and initial state sea quark densities do coincide exactly. We emphasize how the saturated sea is…
At low $x \cong Q^2/W^2 << 1$, in deep inelastic scattering, the photon fluctuates into a $q \bar q$ vector state that interacts via two gluons with the proton. The energy dependence is determined by the saturation scale, in our approach given by $Λ^2_{sat} (W^2) \sim (W^2)^{C_2}$. Imposing DGLAP evolution, we find $C_2^{theory} = 0.27$ in agreement with the model-independent analysis of the HERA data. Different values of the exponent $C_2$ are correlated with different ratios of the longitudinal to transverse structure function. This stresses the need for experiments to separate longitudinal …
We derive the two-plateau momentum distribution of final state (FS) quarks produced in deep inelastic scattering (DIS) off nuclei in the saturation regime. The diffractive plateau which dominates for small transverse momentum p measures precisely the momentum distribution of quarks in the beam photon, the role of the nucleus is simply to provide an opacity. The plateau for truly inelastic DIS exhibits a substantial nuclear broadening of the FS momentum distribution. We discuss the relationship between the FS quark densities and the properly defined initial state (IS) nuclear quark densities.Th…
Within the gauge/gravity correspondence, we discuss the general formulation of the shockwave metric which is dual to a 'nucleus' described by the strongly-coupled N=4 SYM theory in the limit where the number of colors Nc is arbitrarily large. We emphasize that the 'nucleus' must possess Nc^2 degrees of freedom per unit volume, so like a finite-temperature plasma, in order for a supergravity description to exist. We critically reassess previous proposals for introducing transverse inhomogeneity in the shockwave and formulate a new proposal in that sense, which involves no external source but re…
We review QCD based descriptions of diffractive deep inelastic scattering emphasizing the role of models with parton saturation. These models provide natural explanation of such experimentally observed facts as the constant ratio of diffractive and total DIS cross sections as a function of the Bjorken variable x and Regge factorization of diffractive parton distributions.
We use recently proposed method of ratios to assess the quality of geometrical scaling in deep inelastic scattering for different forms of the saturation scale. We consider original form of geometrical scaling (motivated by the Balitski-Kovchegov (BK) equation with fixed coupling) studied in more detail in our previous paper, and four new hypotheses: phenomenologically motivated case with $Q^2$ dependent exponent $λ$ that governs small $x$ dependence of the saturation scale, two versions of scaling (running coupling 1 and 2) that follow from the BK equation with running coupling, and diffusive…
Our approach to low-x deep inelastic scattering based on the ell-perp factorization of perturbative QCD (the color-dipole picture) yields parameter-free absolute predictions for J/Psi production. The connection of J/Psi production to the low-x saturation scale and to the gluon structure function is clarified.
We examine the process of Deep Inelastic Scattering (DIS) in the small-x limit, where Pomeron exchange dominates. Using the AdS/CFT correspondence, we study Pomeron exchange in the dual string theory in AdS space, which allows us to study DIS at strong coupling. Two possibilities are examined, a purely conformal model, and a model with a hard-wall cutoff introduced to take into account the effects of confinement. Comparing our calculations with HERA DIS data, we find a very good agreement not only at large $Q^2$ dominated by conformal symmetry, but due to our strong coupling approach which all…
A modification of the saturation model of deep inelastic scattering at small x which includes the Altarelli-Parisi (DGLAP) evolution is presented. Significant improvement of the description of the structure function F_2 at large Q^2 is achieved and a good description of diffractive data is preserved.
We calculate the light cone wave functions for a virtual photon to split into quark-antiquark states, including for the first time quark masses at one loop accuracy. These wave functions can be used to calculate cross sections for several precision probes of perturbative gluon saturation at the Electron-Ion Collider. Using these wave functions we derive, for the first time, the dipole picture DIS cross sections at one loop for longitudinal and transverse virtual photons including quark masses. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requiremen…
Saturation and geometrical scaling (GS) of gluon distributions are a consequence of the non-linear evolution equations of QCD. We argue that in pp GS holds for the inelastic cross-section rather than for the multiplicity distributions. We also discuss possible fluctuations of the proton saturation scale in pA collisions at the LHC.
Results from the large hadron collider (LHC) show that no available Monte Carlo simulation incorporates our pre-LHC knowledge of soft and hard diffraction in a way that could be reliably extrapolated to LHC energies. As a simulation is needed to establish triggers, perform underlying event corrections and calculate acceptances, the lack of a robust simulation affects all measurements at the LHC. Particularly affected are the measurements of processes with large diffractive rapidity gaps, which constitute about one quarter of the inelastic cross section. In this paper, a previously described ph…
In the holographic or AdS/CFT dual to QCD, the Pomeron is identified with a Reggeized Graviton in $AdS_5$. We emphasize the importance of confinement, which in this context corresponds to a deformation of $AdS_5$ geometry in the IR. The holographic Pomeron provides a very good fit to the combined data from HERA for Deep Inelastic Scattering at small $x$, lending new confidence to this AdS dual approach to high energy diffractive scattering.
The role of local higher-twist ($τ> 3$) spin-1/2 fermionic operators of the strongly coupled ${\cal {N}}=4$ supersymmetric Yang-Mills theory on the symmetric and antisymmetric deep inelastic scattering (DIS) structure functions is investigated. The calculations are carried out in terms of the duality between ${\cal {N}}=4$ SYM theory and type IIB supergravity on AdS$_5 \times S^5$. Particularly, we explicitly obtain the structure functions for single-trace spin-1/2 fermionic operators in the 20$^*$ and 60$^*$ irreducible representations of $SU(4)_R$, corresponding to twists 4 and 5, respective…
I discuss the saturation regime of QCD: the weak-coupling regime that describes large parton densities inside hadrons and the resulting high-energy behavior of scattering amplitudes. I briefly review past successes in the context of deep inelastic scattering at HERA and forward particle production at RHIC, and I present some recent progresses that significantly improved our understanding of high-energy scattering in QCD.
Recent developments in theory and phenomenology relevant to deep inelastic lepton scattering are reviewed, concentrating on the following topics: Predicted behaviour of non-singlet and polarized structure functions at small $x$; Theoretical studies of saturation and unitarity effects at small $x$ in quarkonium scattering; Renormalons and higher twist contributions; Next-to-leading-order calculations of jet cross sections; Forward jet production as a probe of small-$x$ dynamics.
In large-mass diffraction in deep inelastic scattering, we study the gluon jet close to the rapidity gap and show that its transverse momentum spectrum is peaked around a value which caracterizes the onset of S-matrix unitarity. We argue that such a measurement of diffractive jets could help understanding if at the present energies, unitarity comes as a consequence of saturation.
We study exclusive dijet production in coherent diffractive processes in deep inelastic scattering and real (and virtual) photon-hadron ($γ^{(*)}$-h) collisions in the Color Glass Condensate formalism at leading order. We show that the diffractive dijet cross section is sensitive to the color-dipole orientation in the transverse plane, and is a good probe of possible correlations between the $q\bar{q}$-dipole transverse separation vector $\r$ and the dipole impact parameter $\b$. We also investigate the diffractive dijet azimuthal angle correlations and $t$-distributions in $γ^{(*)}$-h collisi…
In Part I (in this journal) we argued that the structure function $F_2^{γp}(x,Q^2)$ in deep inelastic $ep$ scattering, regarded as a cross section for virtual $γ^*p$ scattering, has a saturated Froissart-bounded form behaving as $\ln^2 (1/x)$ at small $x$. This form provides an excellent fit to the low $x$ HERA data, including the very low $Q^2$ regions, and can be extrapolated reliably to small $x$ using the natural variable $\ln(1/x)$. We used our fit to derive quark distributions for values of $x$ down to $x=10^{-14}$. We use those distributions here to evaluate ultra-high energy (UHE) cros…
Following recent progresses in the understanding of high-energy scattering in QCD, we derive the first phenomenological consequences of Pomeron loops, in the context of both inclusive and diffractive deep inelastic scattering. In particular, we discuss diffusive scaling, a new scaling law that emerges for sufficiently high energies and up to very large values of $Q^2,$ well above the proton saturation momentum.
We study the scaling properties in deep inelastic scattering using the most recent combined structure function data $F_2$ from the H1 and ZEUS collaborations. We also perform a direct fit to the $F_2$ data inspired by the scaling properties. Our analysis favours the QCD saturation mechanism from the Balitski Kovchegiv equation wuth running coupling.
Deeply inelastic scattering of electrons off nuclei can determine whether parton distributions saturate at HERA energies. If so, this phenomenon will also tell us a great deal about how particles are produced, and whether they equilibrate, in high energy nuclear collisions.
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.
The charm and beauty quark production in deep inelastic scattering at low values of the Bjorken variable x is considered in the DGLAP improved saturation model. After fitting parameters of the model to the structure function F_2, the heavy quark contributions Fc_2 and Fb_2 are predicted. A good description of the data is found. Predictions for the longitudinal structure function F_L and the diffractive structure function FD_2 are also presented.
We demonstrate that hard dijet production via coherent inelastic diffraction is a promising channel for probing gluon saturation at the Electron-Ion Collider. By $inelastic$ diffraction we mean a process in which the two hard jets - a quark-antiquark pair generated by the decay of the virtual photon - are accompanied by a softer gluon jet, emitted by the quark or the antiquark. This process can be described as the elastic scattering of an effective gluon-gluon dipole. The cross section takes a factorised form, between a hard factor and a unintegrated ("Pomeron") gluon distribution describing t…
The AdS/CFT correspondence in principle gives a new approach to deep inelastic scattering as formulated by Polchinski and Strassler. Subsequently Brower, Polchinski, Strassler and Tan (BPST) computed the strong coupling kernel for the vacuum (or Pomeron) contribution to total cross sections. By identifying deep inelastic scattering with virtual photon total cross section, this allows a self consistent description at small-$x$ where the dominant contribution is the vacuum exchange process. Here we formulate this contribution and compare it with HERA small-$x$ DIS scattering data. We find that t…
Nuclear shadowing corrections to the structure functions of deep inelastic scattering on intermediate-mass nuclei are calculated at very small values of Bjorken x and small values of Q^2 (Q^2<5 Gev^2). The two-component approach developed in previous works of authors for a description of the nucleon structure functions of deep inelastic scattering is used. It is shown that the hard component of the nucleon structure functions that arises, in terms of the colour dipole model, from qq-pairs with a high transverse momentum, is almost not shadowed. It is shown that a change of the slope of the sha…
In the context of both inclusive and diffractive deep inelastic scattering, we derive the first phenomenological consequences of the inclusion of Pomeron loops in the QCD evolution equations towards high energy. We discuss the transition between the well-known geometric scaling regime and the new diffusive scaling, that emerges for sufficiently high energies and up to very large values of Q^2, well above the proton saturation momentum.
