The early stages of heavy ion collisions are dominated by high density systems of gluons that carry each a small fraction $x$ of the momenta of the colliding nucleons. A distinguishing feature of such systems is the phenomenon of "saturation" which tames the expected growth of the gluon density as the energy of the collision increases. The onset of saturation occurs at a particular transverse momentum scale, the "saturation momentum", that emerges dynamically and that marks the onset of non-linear gluon interactions. At high energy, and for large nuclei, the saturation momentum is large compared to the typical hadronic scale, making high density gluons amenable to a description with weak coupling techniques. This paper reviews some of the challenges faced in the study of such dense systems of small $x$ gluons, and of the progress made in addressing them. The focus is on conceptual issues, and the presentation is both pedagogical, and critical. Examples where high gluon density could play a visible role in heavy ion collisions are briefly discussed at the end, for illustration purpose.
Considering the low-temperature ($T$) and high-baryon-number-density ($n_B$) region of the QCD phase diagram, we present a model for the first-order phase transition between the quark-gluon plasma (QGP) and the recently proposed colour superconducting phase. We study nucleation of a droplet of the superconducting phase within the metastable QGP gas. Numerical results for the activation energy, radius and other physical parameters of the droplets, at various temperatures, densities and gap parameters, are given. We have estimated the latent heat of the phase transition. In the $T-n_B$ plane, we…
I review the current status of lattice Monte-Carlo computations of the equation of state of QCD, our current understanding of the thermalization process at collider energies, and two new theoretical developments, one pertaining to the ab-initio calculation of the low-$x$ gluon structure of heavy nuclei, the other to the chaotic behavior of QCD. At the end I give a brief overview of the status of various quark-gluon plasma signatures.
Quantum Chromo Dynamics (QCD), the theory of strong interactions, predicts a transition of the usual matter to a new phase of matter, called Quark-Gluon Plasma (QGP), at sufficiently high temperatures. The non-perturbative technique of defining a theory on a space-time lattice has been used to obtain this and other predictions about the nature of QGP. Heavy ion collisions at the Large Hadron Collider in CERN can potentially test these predictions and thereby test our theoretical understanding of confinement. This brief review aims at providing a glimpse of both these aspects of QGP.
New fits of the unintegrated gluon density obtained from CCFM evolution to HERA $F_2(x,Q^2)$ data are presented. Also predictions of the unintegrated gluon density of the real photon are presented.
This note is a physics manual for a recent numerical implementation of k_t-factorization with running-coupling BK unintegrated gluon distributions. We also compile some results for Pb+Pb collisions at \sqrt{s} = 2.75 TeV, such as predictions for the centrality dependence of the charged particle multiplicity and transverse energy. The model can further be used to obtain initial conditions for hydrodynamic simulations of A+A collisions at the LHC.
We study the gluon parton densities [parton distribution functions (PDFs), transverse momentum distributions (TMDs), generalized parton distributions (GPDs)] and form factors in soft-wall AdS/QCD. We show that the power behavior of gluon parton distributions and form factors at large values of the light-cone variable and large values of square momentum is consistent with quark counting rules. We also show that the transverse momentum distributions derived in our approach obey the model-independent Mulders-Rodrigues inequalities without referring to specific model parameters. All gluon parton d…
We investigate the implication of uncertainties in the unintegrated gluon distribution for the predictions for central exclusive production of scalars at hadron colliders. We use parameterizations of the kT-unintegrated gluon density obtained from the Linked Dipole Chain model, applying different options for the treatment of non-leading terms. We find that the luminosity function for central exclusive production is very sensitive to details of the transverse momentum distribution of the gluon which, contrary to the kT-integrated distribution, is not very well constrained experimentally.
We study the emergence of color superconductivity in the theory of the strong interaction at supranuclear densities. To this end, we follow the renormalization group (RG) flow of dense strong-interaction matter with two massless quark flavors from the fundamental quark and gluon degrees of freedom at high energies down to the non-perturbative low-energy regime which is found to be governed by the dynamical formation of diquark states. With the strong coupling at the initial RG scale as the only input parameter, we compute the (chirally symmetric) scalar diquark condensate and analyze its scali…
We report on the lattice computation of the Landau gauge gluon propagator at finite temperature, including the non-zero Matsubara frequencies. Moreover, the corresponding Källén-Lehmann spectral density is computed, using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement are also discussed.
We calculate the energy and hydrostatic pressure densities of a hot quark-gluon plasma in thermal equilibrium through diagrammatic analyses of the statistical average, $\langle Θ_{μν} \rangle$, of the energy-momentum-tensor operator $Θ_{μν}$. To leading order at high temperature, the energy density of the long wave length modes is consistently extracted by applying the hard-thermal-loop resummation scheme to the operator-inserted no-leg thermal amplitudes $\langle Θ_{μν} \rangle$. We find that, for the long wave length gluons, the energy density, being positive, is tremendously enhanced as com…
We discuss a method to extract the Källén-Lehmann spectral density of a particle (be it elementary or bound state) propagator and apply it to compute gluon spectral densities from lattice data. Furthermore, we also consider the interpretation of the Landau-gauge gluon propagator at finite temperature as a massive-type bosonic propagator.
We derive here the equation of state for quark matter with a nontrivial vacuum structure in QCD at finite temperature and baryon density. Using thermofield dynamics, the parameters of thermal vacuum and the gluon condensate function are determined through minimisation of the thermodynamic potential, along with a self-consistent determination of the effective gluon and quark masses. The scale parameter for the gluon condensates is related to the SVZ parameter in the context of QCD sum rules at zero temperature. With inclusion of quarks in the thermal vacuum the critical temperature at which the…
The decay of colour neutral 2-gluon systems in qqbar and 2q2qbar has been simulated with the Monte-Carlo method, taking into account an effective 1-gluon exchange interaction between the emitted quarks, which was folded with a 2-gluon density determined self-consistently. Finite 2-gluon densities were obtained with a mean square radius <r^2> of about 0.5 fm^2. These give a significant contribution to the 2-gluon field correlators and the gluon propagator from lattice QCD. By solving a relativistic Schroedinger equation the binding potential of the 2-gluon density is computed. By the relation 2…
The gluon density in nuclei, G^A(x), is poorly constrained at all x from the current DIS and Drell-Yan data. In this paper, we point out that J/psi production measured in proton-nucleus collisions at sqrt(s)=38.8 GeV by the E866 collaboration puts stringent constraints on the x-dependence of the G^W/G^Be ratio in the x=0.02-0.1 range. The E866 data suggest a rather mild x-dependence of G^W/G^Be, and consequently tend to favour DS and HKM sets, rather than the DSg, EKS, and EPS parametrizations which exhibit a large shadowing and anti-shadowing.
Color-octet contributions to the associate $J/ψ+γ$ production are found to be negligible, compared to the ordinary color-singlet contribution. Within the color-singlet model the $J/ψ+γ$ production in the leading order is possible only through gluon-gluon fusion process. Therefore, the associate $J/ψ+γ$ production remains to be useful as a clean channel to probe the unpolarized and polarized gluon distribution inside proton (and photon), and to study heavy quarkonia production mechanism. We discuss in detail the associate production of $J/ψ+γ$ at $p \overline{p}$ (or $pp$) and $ep$ colliders. B…
The $Q^2$ dependence of the ratios of nuclear structure functions $F_2^A$ is studied by performing QCD evolution of nuclear parton distribution functions. The log $Q^2$ slope of these ratios is very sensitive to the nuclear gluon distribution function. Taking different parametrizations, we show that the NMC data on the $Q^2$ dependence of $F_2^{\rm Sn}/F_2^{\rm C}$ rule out the case where nuclear shadowing (suppression) of gluons at $x\sim 0.01$ is much larger than the shadowing observed in the ratio $F_2^A/F_2^{\rm D}$. We also take into account modifications to the DGLAP evolution by includi…
We present our results on open beauty production in proton-nucleus collisions for the recent LHC $p$Pb run at $\sqrt{s_{NN}}$=5 TeV. We have analysed the effect of the modification of the gluon PDFs in nucleus at the level of the nuclear modification factor. Because of the absence of measurement in $pp$ collisions at the same energy, we also propose the study of the forward-to-backward yield ratio in which the unknown proton-proton yield cancel. Our results are compared with the data obtained by LHCb collaboration and show a good agreement.
We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1 percent over a range…
Using constituent quark model constraints we calculate the gluon and sea content of pions solely in terms of their valence density and the known sea and gluon densities of the nucleon. The resulting small-x predictions for g^{pi}(x,Q^2) and \bar{q}^{pi}(x,Q^2) are unique and parameter free, being entirely due to QCD dynamics. Similar ideas are applied for calculating the gluon and sea content of kaons which, for our suggested choice of the kaon's valence densities, turn out to be identical to the ones of the pion.
We study the associated production of real (isolated) or virtual photons (with their subsequent leptonic decay) and hadronic jets in proton-proton collisions at the LHC using the $k_T$-factorization approach of QCD. The consideration is based on the off-shell quark-gluon QCD Compton scattering subprocesses. In the case of virtual photon production, the contributions from Z boson exchange as well as gamma*-Z interference with the full spin correlations are included. The transverse momentum dependent (TMD) quark and gluon densities in a proton are determined from the Kimber-Martin-Ryskin prescri…
We apply dynamical string models of heavy-ions collisions at high energies to the analysis of event-by-event fluctuations. Main attention is devoted to a new variable proposed to study "equilibration" in heavy-ions collisions. Recent results of the NA49 collaboration at CERN SPS are compared with predictions of the Quark-Gluon String Model (QGSM), which gives a good description of different aspects of multiparticle production for collisions of nucleons and nuclei. It is shown that the new observable and other results of the NA49 analysis of event-by-event fluctuations are correctly reproduced …
The energy densities achieved during central collisions of large nuclei at the AGS may be high enough to allow the formation of quark--gluon plasma. We propose that most collisions at AGS energies produce superheated hadronic matter, but in rare events a droplet of quark--gluon plasma is nucleated. We estimate the probability of this to occur based on homogeneous and inhomogeneous nucleation theory and discuss possible experimental signals.
Unintegrated gluon densities in nuclei, dipole-nucleus cross-sections and quark densities are numerically investigated in the high-colour limit, with the scattering on a heavy nucleus exactly described by the sum of fan diagrams of BFKL pomerons. The initial condition for the evolution in rapidity is quickly forgotten, and the gluon density presents a "supersaturation" pattern, as previous studies indicated. Both dipole-nucleus cross-sections and quark densities present the expected saturation features. Identifying the position in transverse momentum $l$ of the maximum of the gluon distributio…
The phenomenology of gluon saturation at small parton momentum fraction, Bjorken-x, in the proton and in the nucleus is introduced. The experimentally-accessible kinematic domains at the nucleus-nucleus colliders RHIC and LHC are discussed. Finally, the saturation hints emerging from measurements at RHIC and the perspectives for LHC are described.
The collective modes of QCD at temperatures and densities above its phase-transition are analyzed for isotropic systems as well as for systems having an anisotropy in momentum-space using the HTL approximation. For isotropic systems, results for the thermodynamic pressure and entropy at finite densities based on a phenomenological description of lattice calculations at vanishing densities are derived and compared to those following from different methods. From the resulting equation of state the mass-radius relationship of so-called quark-stars and other applications are investigated. It is sh…
In a previous report we used the Linked Dipole Chain model unintegrated gluon densities to investigate the uncertainties in the predictions for central exclusive production of scalars at hadron colliders. Here we expand this investigation by also looking at other parameterizations of the unintegrated gluon density, and look in more detail on the behavior of these at small k_T. We confirm our conclusions that the luminosity function for central exclusive production is very sensitive to this behavior. However, we also conclude that the available densities based on the CCFM and LDC evolutions are…
Unraveling the inner dynamics of gluons and quarks inside nucleons is a primary target of studies at new-generation colliding machines. Finding an answer to fundamental problems of Quantum ChromoDynamics, such as the origin of nucleon mass and spin, strongly depends on our ability of reconstructing the 3D motion of partons inside the parent hadrons. We present progresses and challenges in the extraction of TMD parton densities, with particular attention to the ones describing polarization states of gluons, which still represent an largely unexplored field. Then, we highlight connections with c…
The idea of the meson cloud approach in the chiral quark model has been extended to include gluon cloud in order to achieve the parton densities in the nucleon, based on the constitute quark framework. The splitting function of the quark to the quark-meson and quark-gluon at low $Q^2$ value are used to obtain parton densities in the constituent quark. The phenomenological constituent model is employed to extract the parton distributions in the proton at low $Q^2$ value. Since we have access to the parton densities at low $Q^2$, we are able to obtain $F_{2}(x,Q^2)$ structure function at low $Q^…
We calculate the cross section of a single inclusive gluon production in deep inelastic scattering at very high energies in the saturation regime, where the parton densities inside hadrons and nuclei are large and the evolution of structure functions with energy is nonlinear. The expression we obtain for the inclusive gluon production cross section is generated by this nonlinear evolution. We analyze the rapidity distribution of the produced gluons as well as their transverse momentum spectrum given by the derived expression for the inclusive cross section. We propose an ansatz for the multipl…
The initial stages of relativistic heavy ion collisions are studied numerically in the framework of a 2+1 dimensional classical Yang-Mills theory. We calculate the energy and number densities and momentum spectra of the produced gluons. The model is also applied to non central collisions. The numerical results are discussed in the light of RHIC measurements of energy and multiplicity and other theoretical calculations. Some problems of the present approach are pointed out.
The energy densities achieved during central collisions of large nuclei at Brookhaven's AGS may be high enough to allow the formation of quark--gluon plasma. Calculations based on relativistic nucleation theory suggest that rare events, perhaps one in every 10$^2$ or 10$^3$, undergo the phase transition. Experimental ramifications may include an enhancement in the ratio of pions to baryons, a reduction in the ratio of deuterons to protons, and a larger source size as seen by hadron interferometry.
We update our previous studies of nuclear-matter effects on J/Psi production in proton-nucleus for the recent LHC pPb runs at sqrt(s_NN)=5 TeV. We have analysed the effects of the modification of the gluon PDFs in nucleus, using an exact kinematics for a 2->2 process, namely g+g->J/Psi+g as expected from LO pQCD. This allows to constrain the transverse-momentum while computing the nuclear modification factor for different rapidities, unlike with the usual simplified kinematics. Owing to the absence of measurement in pp collisions at the same sqrt(s_NN) and owing to the expected significant unc…
At high temperatures and densities the nuclear matter undergoes a phase transition to a new state of matter called quark gluon plasma (QGP). This new state of matter which existed in the universe after a few microsecond of the big bang can be created in the laboratory by colliding two nuclei at relativistic energies. In this presentation we will discuss how the the properties of QGP can be extracted by analyzing the spectra of photons, dileptons and heavy flavours produced in nuclear collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies.
We present the results of a QCD fit to global data on deep-inelastic polarised lepton-hadron scattering. We find that it is possible to fit the data with strongly broken SU(2) flavour for the polarised sea densities. This can easily be tested in $W$ production at polarised RHIC. The data fails to pin down polarised singlet sea quark and gluon densities. We explore the uncertainties in detail and show that improvement in statistics, achievable at polarised HERA for measurement of A_1 at moderately low values of x, have large payoffs in terms of the improvement in measurement of gluon and sea qu…
We study properties of high energy factorisable gluon densities focusing on saturation effects. In particular we show that the property of saturation of unintegrated gluon density allows for introduction of thermodynamical entropy associated with production of gluons. This is due to the observation that saturation scale acts like a mass of a gluon which related with temperature via thermodynamical relations allows for calculations of entropy. We also show that obtained entropy behaves like multiplicity of produced gluons.
The recently proposed nonlinear evolution equation \cite{Kutak:2013hda} for unintegrated gluon densities valid for large values of the QCD coupling constant $\barα _s$ is presented. In particular we outline its derivation, numerical solution and obtained saturation scale.
We have made next to leading order QCD fit to the deep inelastic spin asymmetries on nucleons and we have determined polarised quark and gluon densities. The functional form for such distributions was inspired by the unpolarised ones given by MRST (Martin, Roberts, Stirling and Thorne) fit. In addition to usually used data points (averaged over $Q^2$) we have also considered the sample containing points with the same $x$ and different $Q^2$. Our fits to both groups of data give very similar results. For the integrated quantities we get rather small gluon polarisation. For the non averaged data…
Motivated by forthcoming p-Pb experiments at Large Hadron Collider which require both knowledge of gluon densities accounting for saturation and for processes at a wide range of $p_t$ we study basic momentum space evolution equations of high energy QCD factorization. Solutions of those equations might be used to form a set of gluon densities to calculate observables in generalized high energy factorization. Moreover in order to provide a framework for predictions for exclusive final states in p-Pb scattering with high $p_t$ we rewrite the equation for the high energy factorizable gluon density…
We use the TMD quark densities of the proton to investigate unpolarized Drell-Yan lepton pair production in proton-proton collisions at the LHC energies. We investigate the case where the gluon-to-quark splitting occurs at the last evolution step and calculate the TMD sea quark density as a convolution of the CCFM-evolved gluon distribution and the TMD gluon-to-quark splitting function which contains all single logarithmic small-x corrections to the sea quark evolution for any order of perturbation theory. Based on the O(alpha) production amplitude of quark-antiquark annihilation calculated ac…
Exploiting recently obtained analytic solutions of classical Yang-Mills equations for higher order perturbations in the field of the dilute object (proton), we derive the complete first saturation correction to the single inclusive semi-hard gluon production in high energy proton-nucleus collisions by applying the Lehmann-Symanzik-Zimmermann reduction formula. We thus finalize the program started by Balitsky (see Ref.~\cite{Balitsky:2004rr}) and independently by Chirilli, Kovchegov and Wertepny (see Ref.~\cite{Chirilli:2015tea}) albeit using a very different approach to carry out our calculati…
The claims for production of high energy densities and possible new states of matter in collisions of nuclei by George F. Bertsch (Science, {\bf 265} (1994) 480-481) are examined and compared with simple explanations of the data which have appeared in the literature.
In order to determine polarized parton densities in nucleon we have made fits using all experimental data on spin asymmetries measured in the deep inelastic scattering on different nucleon targets. We have used in our analysis next to leading order QCD corrections in bar{MS} renormalization scheme. The functional forms of polarized densities are based on the fit to unpolarized deep inelastic data made by the MRST group (MRST 99). We have concentrated on different models for gluon spin distributions. In the best fit we get for gluon polarization (at Gev^{2}) Delta G=-1.0 +/- 0.6. The obtained r…
We investigate the sea quark polarization in the nucleon by means of a combined next to leading order analysis to the recently enlarged set of inclusive and semi-inclusive polarized deep inelastic scattering data. Using the Lagrange multiplier method, we asses the uncertainty inherent to the extraction of the different spin dependent parton densities in a QCD global fit, and the impact of the increased set of semi-inclusive data now available. We comment on future prospects at RHIC and JLAB and their potential impact in the future determination of polarized parton densities.
Inclusive as well as exclusive emissions in forward and central directions of rapidity are widely recognized as excellent channels to access the proton structure at small-x. In this regime, to describe nucleons structure, it is necessary to use kT-unintegrated distributions. In particular, at large transverse momenta, the x-evolution of the so-called unintegrated gluon distribution is driven by the Balitsky-Fadin-Kuraev-Lipatov equation, within the framework of the high-energy factorization (HEF). Recent analyses on the diffractive electroproduction of ρmesons have corroborated the underlying …
The coherent hadron production analogous to Cherenkov radiation of photons gives rise to the ring-like events. Being projected on the ring diameter they produce the two-bump structure recently observed for the away-side jets at RHIC. The position of the peaks and their height determine such properties of the hadronic medium as its nuclear refractive index, the parton density, the free path length and the energy loss of Cherenkov gluons. Cherenkov gluons may be responsible for the asymmetry of dilepton mass spectra near rho-meson observed in experiment. Beside comparatively low energy gluons ob…
We study the production and equilibration of the gluon-minijet plasma expected to be formed in the central region of ultrarelativistic heavy-ion collisions at the BNL-RHIC and the CERN-LHC by solving a self-consistent relativistic transport equation. We compute the minijet production within perturbative QCD. Subsequent collisions among the semi-hard partons are treated by considering the elastic gg -> gg processes with screening of the long wavelength modes taken into account. We determine the time $τ_{eq}$ where close to ideal hydrodynamic flow sets in, and find rather similar numbers for cen…
We investigate the transverse momentum dependent (TMD) quark and gluon distribution functions in the modified chiral quark model ($χQM$). Calculations of the TMD quark and gluon densities, using the modified $χQM$ are done for the first time in this article. For this propose we first formulate the TMD interactions that occur in the $χQM$ at low $Q^2$ scale ($Q^2=0.35~ GeV^2$) and then obtain the TMD parton distributions inside the proton, considering the interactions. To this end, we need to compute the TMD bare quark distributions. These TMD bare densities are calculated, using the solution o…
We consider the associated production of Higgs boson and hadronic jet(s) in $pp$ collisions at the LHC for the first time using the $k_T$-factorization approach. Our analysis is based on the off-shell gluon-gluon fusion subprocess, where non-zero transverse momenta of initial gluons are taken into account and covers $H \to γγ$, $H \to ZZ^* \to 4l$ (with $l = e,μ$) and $H \to W^+ W^- \to e^\pm μ^\mp ν\bar ν$ decay channels. The transverse momentum dependent (TMD) gluon densities in a proton are taken from Catani-Ciafaloni-Fiorani-Marchesini evolution equation. To simulate the kinematics of the …
A new type of parametrization for parton distribution functions in a proton, based on their $Q^2$-evolution at large and small $x$ values, is constructed. In our analysis, the valence and nonsinglet parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, respectively. For the singlet quark and gluon densities momentum conservation is taken into account. Then, using the Kimber-Martin-Ryskin prescription, we extend the consideration to Transverse Momentum Dependent (TMD, or unintegrated) gluon and quark distributions in a proton, which currently plays an important role in a number of pheno…
The properties of the quark-gluon plasma(QGP) in the presence of baryon chemical potential are studied using the Field Correlator Method(FCM). At low densities the QGP thermodynamics with the colormagnetic confinement and the Polyakov line interaction is in good agreement with lattice data,and the speed of sound satisfies $C_s^2\leq \frac13$,but in the intermediate range of densities the speed of sound displays a singular behaviour and one needs density modifications of the Polyakov line interaction to avoid instabilities. In particular for $μ_q >0.5$ GeV there exists a region in the $(μ, T)$ …
Lattice quantum chromodynamics (QCD), defined on a discrete space time lattice, leads to a spectacular non-perturbative prediction of a new state of matter, called quark-gluon plasma (QGP), at sufficiently high temperatures or equivalently large energy densities. The experimental programs of CERN, Geneva and BNL, New York of relativistic heavy ion collisions are expected to produce such energy densities, thereby providing us a chance to test the above prediction. After a brief introduction of the necessary theoretical concepts, I will present a critical review of the experimental results alrea…
There is a major need to better constrain nuclear parton densities in order to provide reliable perturbative QCD predictions at the LHC as well as to probe possible non-linear evolution at small values of x. In these proceedings, we discuss how the production of prompt photons at large rapidity in p-p and d-Au collisions at RHIC (sqrt(s_NN)=200 GeV) is sensitive to the nuclear modifications of gluon distributions at x~0.001 and at rather low scales, Q^2~10 GeV^2. The nuclear production ratio, R_dAu=sigma(d+A->gamma+X)/(2A sigma(p+p->gamma X), is computed for isolated prompt photons at NLO usin…
Some of the new developments in the theory of heavy ion collisions are reviewed. Much of the last progress have been triggered by the high energies available at RHIC. In the near future, the LHC will extend the energy reach in heavy ions by a factor thirty and give access to new QCD regimes characterized by large densities and temperatures and corresponding modified evolution equations.
We investigate the inclusive Higgs boson production in proton-proton collisions at high energies in the framework of kt-factorization QCD approach. The attention is focused on the dominant off-shell gluon-gluon fusion subprocess, where the transverse momentum of incoming gluons are taken into account. The transverse momentum dependent (or unintegrated) gluon densities of the proton are determined using the CCFM evolution equation as well as the Kimber-Martin-Ryskin prescription. We study the theoretical uncertainties of our calculations and perform the comparison with the results of traditiona…
The behavior of the structure function at high energies (high densities) is directly associated to the gluon distribution. In this paper we analyze the asymptotic behavior of the structure function at very high densities considering a leading and a higher twist relation between these two quantities. We verify that (a) if the leading twist relation between the structure function and the gluon distribution is used, we recover the black disc limit, and (b) a softer behavior is predicted if a higher twist relation between $F_2$ and $xG$ is considered. While the first behavior is well-established b…
