We perform the first dipole picture fit to HERA inclusive cross section data using the full next-to-leading order (NLO) impact factor combined with an improved Balitsky-Kovchegov evolution including the dominant effects beyond leading logarithmic accuracy at low $x$. We find that three different formulations of the evolution equation that have been proposed in the recent literature result in a very similar description of HERA data, and robust predictions for future deep inelastic scattering experiments. We find evidence pointing towards a significant nonperturbative contribution to the structure function for light quarks, which stresses the need to extend the NLO impact factor calculation to massive quarks.
We compute single inclusive hadron production in proton-proton and proton-nucleus collisions consistently within the CGC framework. The parameters in the calculations are obtained from electron-proton DIS and standard nuclear geometry. We obtain a good description of the DIS data without an anomalous dimension in the initial condition of the BK evolution and get a good agreement with the available single inclusive proton-proton and proton-nucleus data.
We determine the initial condition for the small-$x$ evolution equation (BK) from the HERA deep inelastic scattering data using a new parametrization that also keeps the unintegrated gluon distribution positive. The obtained dipole amplitude and its uncertainty estimate can be used to compute single inclusive particle production in proton-proton and proton-nucleus collisions. We argue that one has to use consistently the proton transverse area measured in DIS and the total inelastic cross section when calculating the single inclusive cross section. This leads to a midrapidity nuclear modificat…
I give a brief overview of the effective theory for the Color Glass Condensate, which is the high-density gluonic matter which controls high-energy scattering in QCD in the vicinity of the unitarity limit. I concentrate on fundamental phenomena, like gluon saturation, unitarization, and geometric scaling, and the way how these are encoded in the formalism. I emphasize the importance of the next-to-leading order corrections, especially the running of the coupling, for both conceptual and phenomenological issues. I survey the implications of the CGC theory for the HERA physics and its phenomenol…
Deep inelastic scattering (DIS) total cross section data at small-x as measured by the HERA experiments is well described by Balitsky-Kovchegov (BK) evolution in the leading order dipole picture. Recently the full Next-to-Leading Order (NLO) dipole picture total cross sections have become available for DIS, and a working factorization scheme has been devised which subtracts the soft gluon divergence present at NLO. We report our recently published work in which we make the first comparisons of the NLO DIS total cross sections to HERA data. The non-perturbative initial condition to BK evolution…
We calculate the small-$x$ evolution of protons with finite size by solving numerically the JIMWLK evolution equation. The initial condition is constrained by the HERA measurements of charm reduced cross section and of exclusive vector meson production. We compute the energy dependence of diffractive cross sections in order to access the energy evolution of the event-by-event fluctuating proton density profile. The fundamental problems arising from the regime sensitive to non-perturbatively large dipoles are also discussed.
I introduce the concept of the Color Glass Condensate. I review data from HERA and RHIC which suggest that such a universal form of matter has been found.
Deeply virtual meson production at HERA and at the EIC within the Color Glass Condensate EFT
CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院）；Dipartimento di Fisica, Università della Calabria（卡塔尼亚大学物理系）；INFN, Gruppo Collegato di Cosenza（意大利国家核物理研究所科森扎协作组）；National Centre for Nuclear Research (NCBJ)（波兰国家核研究中心）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学）
In a previous publication, we have established a collinearly-improved version of the Balitsky-Kovchegov (BK) equation, which resums to all orders the radiative corrections enhanced by large double transverse logarithms. Here, we study the relevance of this equation as a tool for phenomenology, by confronting it to the HERA data. To that aim, we first improve the perturbative accuracy of our resummation, by including two classes of single-logarithmic corrections: those generated by the first non-singular terms in the DGLAP splitting functions and those expressing the one-loop running of the QCD…
The Impact-Parameter dependent Color Glass Condensate (b-CGC) dipole model is based on the Balitsky-Kovchegov non-linear evolution equation and improves the Iancu-Itakura-Munier dipole model by incorporating the impact-parameter dependence of the saturation scale. Here we confront the model to the recently released high precision combined HERA data and obtain its parameters. The b-CGC results are then compared to data at small-x for the structure function, the longitudinal structure function, the charm structure function, exclusive vector meson (J/ψ, ϕ, ρ) production and Deeply Virtual Compton…
We compute the perturbative one-to-three Pomeron vertex in the colour glass condensate using the extended generalized leading logarithmic approximation in high energy QCD. The vertex is shown to be a conformal four-point function in two-dimensional impact parameter space. Our result can be used to compare different theoretical descriptions of the colour glass condensate.
We show that the colour glass condensate dipole model of Iancu, Itakura and Munier, improved to include the impact parameter dependence, gives a good fit to the total gamma* p cross section measured at HERA if the anomalous dimension at the saturation scale, gamma_s, is treated as a free parameter. We find that the optimum value of gamma_s = 0.46 is close to the value determined from numerical solution of the Balitsky-Kovchegov equation. The impact parameter dependent saturation scale is generally less than 0.5 GeV^2 in the HERA kinematic regime for the most relevant impact parameters b ~ 2-3 …
We compute cross sections for incoherent and coherent diffractive J/$Ψ$ and $Ψ(2S)$ production in ultraperipheral heavy ion collisions. The dipole models used in these calculations are obtained by fitting the HERA deep inelastic scattering data and compared with available electron-proton diffraction measurements. We obtain a reasonably good description of the available ALICE data. We find that the normalization of the ultraperipheral cross section has large model dependence, but the rapidity dependence is more tightly constrained.
The Impact-Parameter dependent Color Glass Condensate (b-CGC) and Saturation (IP-Sat) dipole models incorporate key features of small-x physics properties and match smoothly to the perturbative QCD regime at large $Q^2$ for a given $x$. Although both models include saturation effects and depend on impact-parameter, the former is based on the non-linear BK equation, while the latter is based on DGLAP evolution. After confronting the models to the recently released high precision combined HERA data, we show that in both models, the typical impact-parameter probed in the total $γ^{*}p$ cross-sect…
We confront the colour glass condensate motivated dipole model parameterization of Iancu, Itakura and Munier with the available HERA data on the diffractive structure function F2D3 and with existing dipole model parameterizations. Reasonably good agreement is found with only two adjustable parameters. We caution against interpreting the success of the model as compelling evidence for low-x perturbative saturation dynamics.
Perturbative Quantum Chromodynamics (pQCD) predicts that the small-$x$ gluons in a hadron wavefunction should form a Color Glass Condensate (CGC), which has universal properties, which are the same for all hadrons or nuclei. Assuming this property, in this paper we cross relate the current CGC descriptions of the $ep$ HERA data and $dAu$ RHIC data. In particular, we use the quark dipole scattering amplitude recently proposed by Kharzeev, Kovchegov and Tuchin (KKT) to explain the high $p_T$ particle suppression observed in $dAu$ collisions at RHIC in our calculations of the proton and longitudi…
The proton structure function F_2(x,Q^2) for x < 0.01 and 0.045< Q^2 < 45 GeV^2, measured in the deep inelastic scattering at HERA, can be well described within the framework of the Color Glass Condensate.
We provide quantitative predictions for the rapidity, centrality and energy dependencies of inclusive charged-hadron productions for the forthcoming LHC measurements in nucleus-nucleus collisions based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives very good descriptions of the first data from the LHC for the inclusive charged-hadron production in proton-proton collisions, the deep inelastic scattering at HERA at small Bjorken-x, and the hadron multiplicities in nucleus-nucleus collisions at RHIC.
The exclusive photoproduction of vector mesons ($J/ψ$ and $ϕ$) are investigated by taking into account the next-to-leading order corrections in the framework of Color Glass Condensate. We confront the next-to-leading order modified dipole amplitude with the HERA data finding good agreement. Our studies show that the $χ^2/d.o.f$ from leading order, running coupling and collinearly improved next-to-leading order dipole amplitudes are 2.159, 1.097, and 0.932 for the elastic cross section, and 2.056, 1.449, and 1.357 for differential cross section. The outcomes indicate that the higher-order corre…
I review the physical and mathematical foundations for the theoretical description of the hadron wavefunction at small $x$ as a Colour Glass Condensate. In this context, I discuss the phenomenon of gluon saturation and some of its remarkable consequences: a new ``geometric scaling'' for $F_2$, which has been recently identified at HERA, and the unitarization of the hadronic cross-sections at high energy. I show that by combining saturation and confinement one obtains cross-sections which saturate the Froissart bound.
We use an anti-de Sitter/Quantum Chromodynamics (AdS/QCD) holographic light-front wavefunction for the $ρ$ and $ϕ$ mesons, in conjunction with the Color Glass Condensate (CGC) dipole cross-section whose parameters are fitted to the most recent 2015 high precision HERA data on inclusive Deep Inelastic Scattering (DIS), in order to predict the cross-sections for diffractive $ρ$ and $ϕ$ electroproduction. Our results suggest that the holographic meson light-front wavefunction is able to give a simultaneous description of the $ρ$ and $ϕ$ production data provided we use a set of light quark masses …
We extract the leading twist-2 and subleading twist-3 Distribution Amplitudes (DAs) of the rho meson using the HERA data on diffractive rho photoproduction. We do so using several Colour Glass Condensate (CGC) inspired and a Regge inspired dipole models. We find that our extracted twist-2 DA is not much model dependent and is consistent with QCD Sum Rules and lattice predictions. The extracted twist-3 DA is more model dependent but is still consistent with the Sum Rules prediction.
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, the description of the experimental data of these experiments is possible considering different phenomenological saturation models f…
The forthcoming LHC measurement of hadron multiplicity in proton-nucleus collisions is a crucial test of the k_t factorization and gluon saturation based models. Here, we provide quantitative predictions for the pseudorapidity distribution of charged particles produced in minimum bias proton-nucleus collisions at the LHC based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives good descriptions of the LHC and RHIC data for the charged-hadron multiplicities in both proton-proton and nucleus-nucleus collisions, and also the deep inelastic scattering at…
We show that particle production in proton-nucleus (pA) collisions in the Color Glass Condensate model can be related to Deep Inelastic Scattering of leptons on protons/nuclei (DIS). The common building block is the quark antiquark (or gluon-gluon) dipole cross section which is present in both DIS and pA processes. This correspondence in a sense generalizes the standard leading twist approach to pA collisions based on collinear factorization and perturbative QCD, and allows one to express the pA cross sections in terms of a universal quantity (dipole cross section) which, in principle, can be …
In this letter we update our predictions for exclusive $J/Ψ$ and $Υ$ photoproduction in proton-proton and nucleus - nucleus collisions at the Run 2 LHC energies obtained with the color dipole formalism and considering the impact parameter Color Glass Condensate model (bCGC) for the forward dipole - target scattering amplitude. A comparison with the LHCb data on rapidity distributions and photon - hadron cross sections is presented. Our results demonstrate that the current data can be quite well described by the bCGC model, which takes into account nonlinear effects in the QCD dynamics and repr…
Unintegrated gluon distributions sensitive to the transverse spatial distribution of gluons in the proton are extracted from data on exclusive and diffractive final states at HERA in the dipole approach. These unintegrated gluon distributions can be used to compute inclusive hadron production in p+p collisions at the LHC. In this paper, we consider a number of saturation models with differering dynamical assumptions that give good fits to the available HERA data. We apply these models to study the rapidity and transverse momentum dependence of the LHC data up to $\sqrt{s} = 7$ TeV. We examine …
In the recent experiments like DIS at HERA or the heavy-ion experiments at RHIC, and also in expected LHC at CERN, the number of involved partons is very large, due to the high energy and/or the high number of participants of those experiments. These high parton densities should in principal lead to an extremely huge multiparticle production, but experimentally we have seen that this is not the case. So there should be a mechanism that reduces the number of created particle. Here, I review the problem of parton saturation and its implications through three in principal different approaches, bu…
We compute the rate for diffractive $ϕ$ electro-production using the Color Glass Condensate dipole model. The model parameters are obtained from fits to the most recent combined HERA data on inclusive deep inelastic scattering. As for the $ϕ$ meson, we use an AdS/QCD holographic light front wavefunction. Our predictions are compared to the available data collected at the HERA collider.
Perturbative Quantum Chromodynamics (pQCD) predicts that the small-$x$ gluons in a hadron wavefunction should form a Color Glass Condensate (CGC), characterized by a saturation scale $Q_s (x, A)$ which is energy and atomic number dependent. In this paper we study the predictions of CGC physics for electron - ion collisions at high energies. We consider that the nucleus at high energies acts as an amplifier of the physics of high parton densities and estimate the nuclear structure function $F_2^A(x,Q^2)$, as well as the longitudinal and charm contributions, using a generalization for nuclear ta…
Using the color glass condensate formalism, we study the nuclear modification of forward $J/ψ$ and $D$ meson production in high energy proton-nucleus collisions at the LHC. We show that relying on the optical Glauber model to obtain the dipole cross section of the nucleus from the one of the proton fitted to HERA DIS data leads to a smaller nuclear suppression than in the first study of these processes in this formalism and a better agreement with experimental data.
In the recent years we have seen a lot of activity around systems and experiments, like DIS at HERA or the heavy-ion experiments at RHIC, involving a large number of partons due to the high enery and/or the high number of participants of those experiments. The main problem in this regime is that of the high parton densities. In fact, in most of the models of multiparticle production, two contributions to the multiplicity are considered: one proportional to the number of participant nucleons, $N_{part}$, and a second one proportional to the number of collisions, $N_{part}^{4/3}$. In order to ge…
CGC Fit to HERA DIS and Forward Hadron Production in p+p Collisions
Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）；Doctoral School of Exact and Natural Sciences, Jagiellonian University（雅盖隆大学数理博士学院）；Department of Physics, Temple University（天普大学物理系）；RIKEN-BNL Research Center, Brookhaven National Laboratory（布鲁克海文国家实验室理研-布鲁克海文研究中心）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理部）
At very high energies or small values of Bjorken x, the density of partons, per unit transverse area, in hadronic wavefunctions becomes very large leading to a saturation of partonic distributions. When the scale corresponding to the density per unit transverse area, the saturation scale Q_s, becomes large (Q_s\gg Λ_{QCD}), the coupling constant becomes weak (α_S(Q_s)\ll 1) which suggests that the high energy limit of QCD may be studied using weak coupling techniques. This simple idea can be formalized in an effective theory, the Color Glass Condensate (CGC), which describes the behavior of th…
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…
This is a personal summary of the meeting "Saturation, the Color Glass Condensate and Glasma: What Have we Learned from RHIC?" that took place at BNL in May 2010. The purpose of the meeting was to discuss the status of high density QCD and parton saturation, and to review the progress that RHIC has allowed in the field.
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…
We study the production of heavy quarkonium states in high energy proton-nucleus collisions. Following earlier work of Blaizot, Fujii, Gelis, and Venugopalan, we systematically include both small $x$ evolution and multiple scattering effects on heavy quark pair production within the Color Glass Condensate (CGC) framework. We obtain for the first time expressions in the Non-Relativistic QCD (NRQCD) factorization formalism for heavy quarkonium differential cross sections as a function of transverse momentum and rapidity. We observe that the production of color singlet heavy quark pairs is sensit…
Exclusive production of transversely polarized heavy vector mesons in deep inelastic scattering at high energy is calculated at next-to-leading order accuracy in the Color Glass Condensate framework. In addition to the first QCD correction proportional to the strong coupling constant $α_s$, we systematically also include the first relativistic correction proportional to the heavy quark velocity squared $v^2$. When combined with our previously published results for longitudinal vector meson production at next-to-leading order accuracy, these results make phenomenological calculations of heavy v…
This thesis studies gluon saturation in hadronic matter at high energy by calculating next-to-leading order (NLO) corrections to inclusive and diffractive deep inelastic scattering cross sections in the Color Glass Condensate (CGC) effective field theory. We demonstrate that the large soft gluon logarithm is correctly factorized into the Balitsky-Kovchegov (BK) renormalization group equation by accurately connecting the NLO scattering kinematics to the rapidity scale of the dipole amplitude in the scattering. This brings the perturbative expansion under control and enables us to do precision c…
