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 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.
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.
Combining the QCD dipole model with the Good and Walker picture, we formulate diffractive dissociation of a photon of virtuality Q^2 off a hadronic target, in the kinematical regime in which Q is close to the saturation scale and much smaller than the invariant mass of the diffracted system. We show how the obtained formula compares to the HERA data and discuss what can be learnt from such a phenomenology. In particular, we argue that diffractive observables in these kinematics provide useful pieces of information on the saturation regime of QCD.
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.
In the framework of the recently proposed saturation picture, we examine in a systematic way whether the nuclear modification factor measured for d-Au collisions at RHIC may be simply explained. The Cronin peak which is obtained at mid-rapidity around $k_{\bot}\simeq 3$ GeV may be reproduced at the proper height only by boosting the saturation momentum by an additional nuclear component as already shown in the literature. In this respect, mid-rapidity RHIC data cannot necessarily be seen as a probe of the saturation picture. The large rapidity ($η\simeq 3$) region allows us to test the shape o…
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…
In these proceedings, I shall review the basic concepts of perturbative QCD in its high-energy limit, emphasising the approach to the unitarity limit, usually referred to as {\em saturation}. I shall explain the basic framework showing the need for saturation, first, from a simple picture of the high-energy behaviour, then, giving a short derivation of the equation driving this evolution. In the second part, I shall exhibit an analogy with statistical physics and show how this allows to derive {\em geometric scaling} in QCD with saturation. I shall finally consider the effects of gluon-number …
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 perf…
Based on the color-dipole picture, we present a successful parameter-free prediction for the recent high-energy $J/ψ$ photoproduction data from the Large Hadron Collider. The experimental data provide empirical evidence for the transition from color transparency to saturation.
Using the Good and Walker picture, we derive a simple formula for diffractive dissociation that can apply to recent data collected at HERA in the low Q2 regime.
In this talk I discuss the high energy asymptotics of QCD scattering, and its similarity to a reaction-diffusion process. I also discuss detailed numerical studies of the mean field approximation to this picture, i.e., the Balitsky-Kovchegov equation.
I discuss recent results on the Color Glass Condensate which is a dense saturated gluonic state and appears as the universal picture of hadrons or nuclei at very high energies.
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.
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.
In this paper we study the description of saturation in Balitsky, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (B-JIMWLK) picture when restricted to observables made up only from dipole operators. We derive a functional form of the evolution equation for the dipole probability distribution and find a one-parameter family of exact solutions to the dipole evolution equations.
The Color Glass Condensate picture of the nuclear wave function at small-x successfully predicted the suppressed production of high-pT particles at forward rapidities in deuteron-gold collisions at RHIC. This triggered more efforts which resulted in theoretical improvements and predictions for different observables which will provide further phenomenological tests. I review recent theoretical developments and discuss the resulting predictions.
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 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…
The measurement of the proton structure function at HERA is often seen as a hint for the observation of saturation in high-energy QCD e.g. through the observation of geometric scaling. Accordingly, the dipole picture provides a powerful framework in which the QCD-based saturation models can be confronted to the data. In this paper, we give a parametrisation of proton structure function which is directly constrained by the dynamics of QCD in its high-energy limit and fully includes the heavy quark effects. We obtain a good agreement with the available data. Furthermore, to the contrary of vario…
We introduce a saturation model for photon-photon interactions, based on a QCD dipole picture of high energy scattering. The two-dipole cross-section is assumed to satisfy the saturation property. This pomeron-like contribution is supplemented with QPM and non-pomeron reggeon contributions. The model gives a very good description of the data on the gamma-gamma total cross-section, on the photon structure function F_2^gamma(x,Q^2) at low x and on the gamma*-gamma* cross-section.
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 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 additiona…
A saturation model for the total gamma-gamma and gamma*-gamma* cross-sections and for the real photon structure function F_2^gamma(x,Q^2) is described. The model is based on a QCD dipole picture of high energy scattering. The two-dipole cross-section is assumed to satisfy the saturation property with the saturation radius taken from the GBW analysis of the gamma*-p interaction at HERA. The model is combined with the QPM and non-pomeron reggeon contributions an it gives a very good description of the data on the gamma-gamma total cross-section, on the photon structure function F_2^gamma(x,Q^2) …
We review the theoretical interpretation of deep-inelastic electron-proton scattering at low values of the Bjorken variable $x \simeq Q^2/W^2 \lsim 0.1$. The process proceeds via the interaction of quark-antiquark $(q \bar q)$ color-dipole fluctuations of the (virtual) photon with the proton. In terms of the forward Compton scattering amplitude, two reaction channels contribute to the interaction of the $q \bar q$ color dipole with the gluon field in the proton. Dependent on the kinematics, there is either {\it color transparency}, corresponding to a cancellation of the amplitudes for the two …
We show that the HERA data for the inclusive structure function F_2(x,Q^2) for x < 0.01 and 0.045 < Q^2 < 45 GeV^2 can be well described within the color dipole picture, with a simple analytic expression for the dipole-proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger th…
Including the new HERA data, the $γ^* p$ total cross section is analysed in the generalized vector dominance/colour-dipole picture (GVD/CDP) that contains scaling in $η= (Q^2 + m^2_0) / Λ^2 (W^2)$, where $Λ^2 (W^2)$ is an increasing function of $W^2$. At any $Q^2$, for $W^2 \to \infty$, the cross sections for virtual and real photons become identical, $σ_{γ^* p} (W^2, Q^2) / σ_{γp} (W^2) \to 1$. The gluon density deduced from the colour-dipole cross section fulfills the leading order DGLAP relationship. Evolution à la DGLAP breaks down for $η\lsim 0.1$.
We discuss the recent claim that hadron multiplicities measured at RHIC energies are directly described in terms of gluon degrees of freedom fixed from the initial conditions of central heavy ion collisions. The argument is based on the parton saturation scenario expected to be valid at high parton densities and on the assumption of conserved gluon number. Alternatively we conjecture that "bottom-up" equilibration before hadronization modifies this picture, due to nonconservation of the number of gluons.
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 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…
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…
A simple model for nuclear structure functions in the region of small x and small and moderate $Q^2$, is presented. It is a parameter-free extension, in the Glauber-Gribov approach to nuclear collisions, of a saturation model for the nucleon. A reasonable agreement with experimental data on ratios of nuclear structure functions is obtained. Nuclear effects in the longitudinal-to-transverse cross section ratios are found to be small. Predictions of the model for values of $x$ smaller than those available to present experiments are given. The unintegrated gluon distribution and the behaviour of …
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 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…
Constraining the Dipole Amplitude at NLO with HERA Data and Probing Gluon Saturation in SIDIS
Department of Physics, University of Jyv\"askyl\"a, P.O. Box 35, 40014 University of Jyv\"askyl\"a, Finland；Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
We discuss recent developments towards next-to-leading order (NLO) accuracy in the dipole picture. We review recent NLO results for exclusive vector meson production and diffractive structure functions, and discuss how it is becoming possible to describe both inclusive and exclusive DIS data simultaneously within the Color Glass Condensate framework at NLO accuracy. These developments will make it possible to probe the gluon saturation phenomena in detail especially when nuclear-DIS data from the EIC become available.
We present a detailed examination of the color-dipole picture (CDP) of low-$x$ deep inelastic scattering. We discriminate model-independent results, not depending on a specific parameterization of the dipole cross section, from model-dependent ones. The model-independent results include the ratio of the longitudinal to the transverse photoabsorption cross section at large $Q^2$, or equivalently the ratio of the longitudinal to the unpolarized proton structure function, $F_L (x,Q^2)=0.27 F_2 (x, Q^2)$, as well as the low-$x$ scaling behavior of the total photoabsorption cross section $σ_{γ^*p} …
Deep inelastic electron scattering (DIS) from nucleons at low values of the Bjorken variable $x \cong Q^2/W^2 \lsim ~ 0.1$ proceeds via fluctuations of the photon into quark-antiquark dipole states that subsequently interact with the gluon field in the nucleon. Dependent on the interaction energy, $W$, the color-gauge-invariant dipole interaction with the gluon field in the nucleon, for any fixed dipole size, contains the limits of i) color transparency and ii) saturation, where "saturation" stands for the approach to a hadronlike dipole-proton interaction cross section. All essential features…
We demonstrate that the dipole-hadron cross-section computed from the non-linear evolution equation for the Colour Glass Condensate saturates the Froissart bound in the case of a fixed coupling and for a small dipole (Q^2 >> Lambda_{QCD}^2). That is, the cross-section increases as the logarithm squared of the energy, with a proportionality coefficient involving the pion mass and the BFKL intercept (alpha_s N_c/pi)4 ln 2. The pion mass enters via the non-perturbative initial conditions at low energy. The BFKL equation emerges as a limit of the non-linear evolution equation valid in the tail of …
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…
We study coherent diffractive dijet production in electron-hadron and electron-nucleus collisions within the dipole picture. We provide semi-analytic results for the differential cross section and elliptic anisotropy in the angle between dijet transverse momentum and hadron recoil momentum. We demonstrate the direct relation between angular moments of the dipole amplitude in coordinate space and angular moments of the diffractive dijet cross sections. To perform explicit calculations we employ two different saturation models, extended to include the target geometry. In the limit of large photo…
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 corresp…
We present an analysis of the most precise set of HERA data within the color dipole formalism, by using an analytical gluon density, based on the double-logarithm approximation of the DGLAP equations in the asymptotic limit of the scaling variable, $σ=\log{(1/x)}\log{(\log{(Q^2/Q_ 0^2)})}\rightarrow \infty$. Fits to data, including charm and bottom quarks are performed and demonstrate the efficiency of the model in describing the reduced cross section, $σ_{r}$, in the wide range $Q^2:(1.5,500)$ GeV$^2$ for two dipole models including parton saturation effects. We also give predictions to $F_{2…
An extensive phenomenological study of the Drell-Yan (DY) process in $pp$ collisions at various energies is performed in the color dipole framework. Besides previously studied $γ^*$ production we have also included the $Z^0$ contribution relevant at large dilepton invariant masses. We investigate the DY cross section differential in invariant mass, rapidity and transverse momentum of the dilepton pair in $pp$ collisions at RHIC and LHC. We consider three different phenomenological models for the dipole cross section and found a reasonable agreement with the available data. As a further test of…
In this work we estimate the heavy quark production in the interaction of ultra high energy cosmic rays in the atmosphere, considering that the primary cosmic ray is a proton or a photon. At these energies the saturation momentum Q_{sat}^2 stays above the hard scale μ_c^2=4m_c^2, implying charm production probing the saturation regime. In particular, we show that the ep HERA data presents a scaling on τ_c = (Q^2+μ_c^2)/Q_{sat}^2. We derive our results considering the dipole picture and the Color Glass Condensate formalism, which one shows to be able to describe the heavy quark production in ph…
In this paper we perform a numerical study of the tranverse expansion of hadronic scattering amplitudes in the dipole picture of high energy QCD. We go beyond the mean field approximation by including fluctuations and also wave function saturation effects, and the evolution with both a fixed and a running coupling is investigated. We also study the nonperturbative aspects, and as has been predicted earlier, our results indicate that the Froissart-Martin bound is saturated once confinement effects are included in the evolution. Thus the total cross section increases proportional to the square o…
A study on the prompt photon production within the QCD color dipole picture with emphasis in $pp$ and $pA$ collisions at the LHC energy regimes is performed. We present predictions for the differential cross section as a function of photon transverse momentum at different rapidity bins considering updated phenomenological color dipole models, which take into account the QCD gluon saturation physics. The results are directly compared to the recent experimental measurements provided by CMS and ATLAS Collaborations, showing a reasonable agreement in all rapidity bins with no free parameters. Spec…
We have studied the color dipole picture for the description of the deep inelastic process, mainly the structure functions which are driven directly by the gluon distribution. Estimates for those functions are obtained using the effective dipole cross section given by the Glauber-Mueller approach in QCD, encoding the corrections due to the unitarity effects associated with the saturation phenomenon. Frame invariance is verified in the calculations of the observables when analysing the experimental data.
We calculate the inclusive and diffractive photoproduction of heavy quarks in proton-proton collisions at Tevatron and LHC energies, where the photon reaches energies larger than those ones accessible at DESY-HERA. The integrated cross section and the rapidity distributions for charm and bottom production are computed within the color dipole picture employing three phenomenological saturation models based on the Color Glass Condensate formalism. Our results demonstrate that the experimental analyzes of these reactions is feasible and that the cross sections are sensitive to the underlying part…
It is observed that K-/pi in A+A and possibly p+p and pbar+p collisions follows an interesting systematic in omega, the pion transverse energy per unit of rapidity and transverse overlap area. The systematics show a linear increase of K-/pi with omega in the AGS and SPS energy regime and a saturation at RHIC energy. The systematics indicate that omega might be the relevant variable underlying K-/pi. At high energy, the omega variable is related to the gluon saturation scale in high density QCD, and perhaps to the initial energy density in the Bjorken picture.
Theory Center, IPNS, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构（KEK））；Graduate Institute for Advanced Studies, SOKENDAI（SOKENDAI高级研究研究生院）
Topological quantization of vector meson anomalous couplings
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；International Centre for Theoretical Physics Asia-Pacific (ICTP-AP)（亚太理论物理中心）；Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS)（中国科学院大学太极引力波宇宙实验室（北京/杭州））
We develop an asymptotic perturbation theory for the large logarithmic behavior of the non-linear integro-differential equation describing the soft correlations of QCD jet measurements, the Banfi-Marchesini-Smye (BMS) equation. This equation captures the late-time evolution of radiating color dipoles after a hard collision. This allows us to prove that at large values of the control variable (the non-global logarithm, a function of the infra-red energy scales associated with distinct hard jets in an event), the distribution has a gaussian tail. We compute the decay width analytically, giving a…
We discuss stiffening of dense matter in two color QCD (QC$_2$D) where hadrons are mesons and diquark baryons. We study two models which describe a transition of matter from the Bose-Einstein-Condensation regime at low density to the Bardeen-Cooper-Schrieffer regime at high density. The first model is based on coherent states of diquarks, and the second is the Nambu-Jona-Lasinio model with diquark pairing terms. We particularly focus on how quark states are occupied as baryon density increases. We find that, due to the occupied quark levels, the ideal gas picture of diquarks breaks down at den…
The quark saturation behavior at low $Q^2$ is shown in a numeric solution of the DGLAP equation with parton recombination corrections, which resembles the widely discussed JIMWLK saturation of gluons. Our calculation suggests that the partonic saturation can be interpreted as a dynamical balance between the splitting and the fusion processes of partons, without any other condensation mechanisms added. The nuclear shadowing saturation at small $x$ resulted from the proposed quark saturation is also discussed.
