We calculate the inclusive gluon correlation function for arbitrary number of gluons with full rapidity and transverse momentum dependence for the initial glasma state of the p-p, p-A and A-A collisions. The formula we derive via superdiagrams generates cumulants for any number of gluons. Higher order cumulants contain information on correlations between multiple gluons, and they are necessary for calculations of higher dimensional ridges as well as flow coefficients from multi-particle correlations.
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.
RHIC experiments have recently measured the azimuthal correlation function of forward di-hadrons. The data show a disappearance of the away-side peak in central d+Au collisions, compared to p+p collisions, as was predicted by saturation physics. Indeed, we argue that this effect, absent at mid-rapidity, is a consequence of the small-x evolution into the saturation regime of the Gold nucleus wave function. We show that the data are well described in the Color Glass Condensate framework.
We calculate the classical single-gluon production amplitude in nucleus-nucleus collisions including the first saturation correction in one of the nuclei (the projectile) while keeping multiple-rescattering (saturation) corrections to all orders in the other nucleus (the target). In our approximation only two nucleons interact in the projectile nucleus: the single-gluon production amplitude we calculate is order-g^3 and is leading-order in the atomic number of the projectile, while resumming all order-one saturation corrections in the target nucleus. Our result is the first step towards obtain…
We calculate the triple- and quadruple-gluon inclusive distributions with arbitrary rapidity and azimuthal angle dependences in the gluon saturation regime by using glasma diagrams. Also, we predict higher-dimensional ridges in triple- and quadruple-hadron correlations for p-p and p-Pb collisions at LHC, which have yet to be measured. In p-p and p-Pb collisions at the top LHC energies, gluon saturation is expected to occur since smaller Bjorken-$x$ values are being probed. Glasma diagrams, which are enhanced at small-$x$, include the gluon saturation effects, and they are used for calculating …
Correlations between the momenta of the final state hadrons measured in proton or nucleus collisions contain information that sheds light on the initial conditions and evolutionary dynamics of the collision system. These correlation measurements have revealed the long-range rapidity correlations in p-p and p-Pb systems, and they have also made it possible to extract the elliptic flow coefficient from hadron correlation measurements. In this work, we calculate five- and six-gluon correlation functions in the framework of saturation physics by using superdiagrams. We also derive the cumulant exp…
We perform a numerical study of higher order saturation corrections to the dilute-dense approximation for multi-particle production in high-energy hadronic collisions in the framework of the Color Glass Condensate. We compare semi-analytical results obtained by performing a leading order expansion in the dilute field of the projectile with numerical simulations of the full Classical Yang-Mills dynamics for a number of phenomenologically relevant observables. By varying the saturation momentum of the target and the projectile, we establish the regime of validity of the dilute-dense approximatio…
We show that, in the saturation/Color Glass Condensate framework, odd azimuthal harmonics of the two-gluon correlation function with a long-range separation in rapidity are generated by the higher-order saturation corrections in the interactions with the projectile and the target. At the very least, the odd harmonics require three scatterings in the projectile and three scatterings in the target. We derive the leading-order expression for the two-gluon production cross section which generates odd harmonics: the expression includes all-order interactions with the target and three interactions w…
We consider double $gg\rightarrow g$ production in the presence of a bias on the unintegrated gluon distribution of the colliding hadron or nuclei. Such bias could be due to the selection of configurations with a greater number of gluons or higher mean transverse momentum squared or, more generally, due to a modified spectral shape of the gluon distribution in the hadrons. Hence, we consider reweighted functional averages over the stochastic ensemble of small-x gluons. We evaluate explicitly the double inclusive gluon transverse momentum spectrum in high-energy collisions, and their azimuthal …
We demonstrate that the recent forward-forward dijet correlation data measured by the ATLAS collaboration for proton-proton and proton-lead collisions are consistent with the broadening effects due to both the gluon saturation and the resummation of large logarithms of the hard scale (the so-called Sudakov logarithms). We find that both effects are necessary to describe the experimental results.
We modified the gluon saturation model by rescaling the momentum fraction according to saturation momentum and introduced the Cooper-Frye hydrodynamic evolution to systematically study the pseudo-rapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at BNL Relativistic Heavy Ion Collider (RHIC). The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.
We examine the origins of azimuthal correlations observed in high energy proton-nucleus collisions by considering the simple example of the scattering of uncorrelated partons off color fields in a large nucleus. We demonstrate how the physics of fluctuating color fields in the color glass condensate (CGC) effective theory generates these azimuthal multiparticle correlations and compute the corresponding Fourier coefficients v_n within different CGC approximation schemes. We discuss in detail the qualitative and quantitative differences between the different schemes. We will show how a recently…
We determine the distribution of linearly polarized gluons of a dense target at small $x$ by solving the B-JIMWLK rapidity evolution equations. From these solutions we estimate the amplitude of $\sim \cos 2ϕ$ azimuthal asymmetries in DIS dijet production at high energies. We find sizeable long-range in rapidity azimuthal asymmetries with a magnitude in the range of $v_2=\langle\cos 2ϕ\rangle \sim 10\%$.
Annihilation process of proton and antiproton to guark antiquark pair accompanied by emission of two additional gluon jets with intermediate state of vector meson is considered.Strong azimuthal correlation is revealed of two gluonic jets,effectively created in the same plane.Some applications to cosmic ray events and to LHC experiments are discussed.
We study saturation effects in the production of dijets in p-p and p-Pb collisions using the framework of high energy factorization. We focus on central-forward jet configurations, which allow for probing gluon density at low longitudinal momentum fraction. We find significant suppression of the central-forward jet decorrelations in p-Pb compared to p-p, which we attribute to saturation of gluon density in nuclei.
We investigate the azimuthal correlations of the glasma in p-p collisions at $\sqrt{s_{\mathrm{NN}}}=7$ TeV by using the CGC formalism. As expected, the azimuthal correlations show two peaks at $Δϕ=0$ and $π$ which represent collimation production in CGC. Beyond that, azimuthal correlations show fine structures, i.e. bumps or shoulders between the two peaks, when at least one gluon has small $x$. The structures are demonstrated to be associated with saturation momentum, and likely appear at transverse momentum around $2Q_{\mathrm{sp}}=1.8$ GeV$/$c.
Color flux tubes (quark-gluon strings), formed at early stages of hadron-hadron collisions, may overlap in case of sufficiently high densities and interact, producing long-range azimuthal correlations. In the hypothesis of repulsive interaction, each string may acquire, before the hadronization, the additional transverse boost, which is an efficient sum of all accounted string-string interactions. This modifies transverse momenta to the particles formed in string decay, leading to modification of event-wise observables, like azimuthal asymmetry of two-particle correlations, over a wide range o…
The production of a hard dijet with small transverse momentum imbalance in semi-inclusive DIS probes the conventional and linearly polarized Weizsaecker-Williams (WW) Transverse Momentum Dependent (TMD) gluon distributions. The latter, in particular, gives rise to an azimuthal dependence of the dijet cross-section. In this paper we analyze the feasibility of a measurement of these TMDs through dijet production in DIS on a nucleus at an Electron-Ion Collider. We introduce the MCDijet Monte-Carlo generator to sample quark-antiquark dijet configurations based on leading order parton level cross-…
The paper presents a system of nonlinear Lorentz-invariant equations. The behavior of their localized solutions is analogous to the processes of formation of azimuthal-anisotropic elliptical flows of quark-gluon plasma and hadron jets. In contrast to the hydrodynamic models of an ideal fluid, the elliptic flow in this model has a significant negative acceleration. The presence of the negative acceleration allows us to propose a hypothesis about the direct elliptic flow of photons as braking radiation QGP.
The impact parameter dependent gluon distribution of the proton xG(x,Q^2,b) is investigated in a loop-loop correlation model that respects the S-matrix unitarity condition in impact parameter space. We find low-x saturation of G(x,Q^2,b) as a manifestation of S-matrix unitarity. The integrated gluon distribution xG(x,Q^2) does not saturate because of the growth of the effective proton radius with decreasing x.
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 Weizsaecker-Williams transverse momentum dependent (TMD) gluon distributions can be probed in the production of a hard dijet in semi-inclusive DIS. This process is sensitive not only to the conventional but also to the linearly polarized gluon distribution. The latter gives rise to an azimuthal dependence of the dijet cross section and therefore can be distinguished from the former. Feasibility study of a measurement of these TMDs through dijet production at a future electron-ion collider shows that the extraction of the distribution of linearly polarized gluons with a statistical accuracy…
We derive all order soft gluon resummation in dijet azimuthal angular correlation in hadronic collisions at the next-to-leading logarithmic level. The relevant coefficients for the Sudakov resummation factor, the soft and hard factors, are calculated. The theory predictions agree well with the experimental data from D0 Collaboration at the Tevatron. This provides a benchmark calculation for the transverse momentum dependent QCD resummation for jet productions in hadron collisions and can be readily applied at the CERN LHC.
A new geometrical scaling method with gluon saturation rapidity limit is proposed to study the gluon saturation feature of the central rapidity region of relativistic nuclear collisions. The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. We take advantage of the gluon saturation model with geometric scaling of the rapidity limit to investigate the net baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions. Predictions for net-baryon rapidity distribution…
In this letter we suggest the generalization of $k_T$-factorization formula for inclusive gluon production for the dense-dense parton system scattering. It turnes out that the soft gluon production with transverse momentum $p_T$ is suppressed by additional Sudakov-like factor that depends on $p^2_T/Q^2_s$ ratio in a good agreement with the first numerical calculation in Colour Glass Condensate approach by J.P. Blaizot, T. Lappi and Y. Mehtar-Tan.
We show that gluon saturation gives rise to a strong modification of the scaling in both the nuclear mass number $A$ and the virtuality $Q^2$ of the vector meson production cross-section in exclusive deep-inelastic scattering off nuclei. We present qualitative analytic expressions for how the scaling exponents are modified as well as quantitative predictions that can be tested at an Electron-Ion Collider.
We consider the influence of parton saturation in the Color Glass Condensate on the back-to-back azimuthal correlations of high $p_T$ hadrons in $pA$ (or $dA$) collisions. When both near--side and away--side hadrons are detected at mid-rapidity at RHIC energy, the effects of parton saturation are constrained to transverse momenta below the saturation scale $p_T \leq Q_s$; in this case the back-to-back correlations do not disappear but exhibit broadening. However when near-side and away-side hadrons are separated by several units of rapidity, quantum evolution effects lead to the depletion of b…
In high energy proton-nucleus collisions, the gluon saturation effects from the nucleus are fully incorporated into the light-like Wilson lines. The gluon saturation effects from the proton, which are anticipated to be important either in the extreme high energy limit or towards the dense-dense (nucleus-nucleus) collision regimes, have been studied perturbatively within the Color Glass Condensate effective theory in previous papers of this series. A configuration-by-configuration expression for the single inclusive semi-hard gluon production including the first saturation correction was obtain…
We investigate hadrons and direct photon production in pp collisions at the LHC energy within the color-dipole approach. We show that greatest sensitivity to gluon saturation effects is reached at very forward rapidities in pp collisions at LHC (\sqrt{s}=14 TeV). The discrepancies among various saturation models (fitted to HERA data) results can be about a factor of 2-3 at forward rapidities. We found that the ratio of direct-photon to pion production can be about 20-10 at forward rapidities η=7-8. Therefore, direct photon production at forward rapidities should provide a rather clean probe as…
Back-to-back dijet cross-sections in deeply inelastic scattering (DIS) at small $x_{\rm Bj}$ are suppressed by many-body multiple scattering and screening effects arising from gluon saturation at high parton densities. They are similarly sensitive in these kinematics to large Sudakov logarithms from soft gluon radiation. Uncovering novel physics in this DIS channel therefore requires understanding the interplay of the two phenomena. In this work, we compute the small $x_{\rm Bj}$ inclusive dijet DIS cross-section in back-to-back kinematics at next-to-leading order (NLO) in the Color Glass Cond…
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 study coherent and incoherent diffractive hadron production in high energy quarkonium--heavy nucleus collisions as a probe of the gluon saturation regime of QCD. Taking this process as a model for pA collisions, we argue that the coherent diffractive gluon production, in which the target nucleus states intact, exhibits a remarkable sensitivity to the energy, rapidity and atomic number dependence. The incoherent diffractive gluon production is less sensitive to the details of the low-x dynamics but can serve as a probe of fluctuations in the color glass condensate. As a quantitative measure …
Recent data on the azimuthal and transverse momentum dependence of high-pT>10 GeV pion nuclear modification factors in nuclear collisions at RHIC/BNL and LHC/CERN are analyzed in terms of a wide class of jet-energy loss models and a variety of transverse expanding collective flow backgrounds. RHIC data at 200 AGeV are found to be surprisingly consistent with rather different dE/dx models when coupled to recent 2+1D minimally viscous QGP flow field predictions. However, extrapolations to LHC, with parameters fixed at RHIC, favor running coupling QCD based energy-loss models over fixed coupling …
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…
We compute two-particle production in p+A collisions and extract azimuthal harmonics, using the dilute-dense formalism in the Color Glass Condensate framework. The multiple scatterings of the partons inside the projectile proton on the dense gluons inside the target nucleus are expressed in terms of Wilson lines. They generate interesting correlations, which can be partly responsible for the signals of collectivity measured at RHIC and at the LHC. Most notably, while gluon Wilson loops yield vanishing odd harmonics, quark Wilson loops can generate sizable odd harmonics for two particle correla…
The azimuthal anisotropies of the collective transverse flow of hadrons are investigated in a large range of heavy-ion collision energy within the Parton-Hadron-String Dynamics (PHSD) microscopic transport approach which incorporates explicit partonic degrees of freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD as well as dynamical hadronization and hadronic dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ with bombarding energy is successfully described in terms of…
We calculate the cross section for diffractive hadron production in deep inelastic scattering off heavy nuclei in the framework of gluon saturation/color glass condensate. We analyze the kinematic region of the future Electron-Ion Collider. We argue that coherent and incoherent diffractive channels are very sensitive to the structure of the nuclear matter at low $x$. This expresses itself in a characteristic dependence of the cross sections on rapidity and transverse momentum of the produced hadron and on the nuclear weight. We also discuss dependence on the scattering angle and argue that bot…
The leading order single inclusive soft gluon production in high energy proton-nucleus (pA) collisions has been studied by various approaches for more than two decades. The first correction due to the gluon saturation in proton was analytically attempted recently through a diagrammatic approach in which only partial results were obtained. An important feature of the first saturation correction is that it includes both initial state and final state interactions. In this paper, we present the complete result derived from the Color Glass Condensate framework. Our approach is to analytically solve…
We investigate the azimuthal asymmetry v2 of produced pions in pp and pA collisions at both RHIC and SPS energies. In our approach, based on the pQCD parton model and the light-cone QCD-dipole formalism, the azimuthal asymmetry results from a correlation between the color-dipole orientation and the impact parameter of the collision. We introduce the color-dipole orientation within an improved Born approximation and the saturation model which satisfies available DIS data, showing that the azimuthal asymmetry of partons and pions is very sensitive to the choice of the model, and that it is reduc…
We investigate the impact of soft gluon resummation on the azimuthal angle correlation between the total and relative momenta of two energetic final state particles (jets). We show that the initial and final state radiations induce sizable $\cos(ϕ)$ and $\cos (2ϕ)$ asymmetries in single jet and dijet events, respectively. We numerically evaluate the magnitude of these asymmetries for a number of processes in collider experiments, including diffractive dijet and dilepton production in ultraperipheral $pA$ and $AA$ collisions, inclusive and diffractive dijet production at the EIC and inclusive d…
In this letter we complement previous studies on exclusive vector meson photoproduction in hadronic collisions presenting a comprehensive analysis of the $t$ - spectrum measured in exclusive $ρ$ and $J/Ψ$ photoproduction in $pA$ collisions at the LHC. We compute the differential cross sections considering two phenomenological models for the gluon saturation effects and present predictions for $pPb$ and $pCa$ collisions. Moreover, we compare our predictions with the recent preliminary CMS data for the exclusive $ρ$ photoproduction. We demonstrate that the gluon saturation models are able to des…
We propose a method to introduce Sudakov effects to the unintegrated gluon density promoting it to be hard scale dependent. The advantage of the approach is that it guarantees that the gluon density is positive definite and that the Sudakov effects cancel on integrated level. As a case study we apply the method to calculate angular correlations and $R_{pA}$ ratio for p+p vs. p+Pb collision in the production of forward-forward dijets.
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.
We consider a novel mechanism for J/Psi production in nuclear collisions arising due to the high density of gluons. We calculate the resulting J/Psi production cross section as a function of rapidity and centrality. We evaluate the nuclear modification factor and show that the rapidity distribution of the produced J/Psi's is significantly more narrow in AA collisions due to the gluon saturation effects. Our results indicate that gluon saturation in the colliding nuclei is a significant source of J/Psi suppression that can be disentangled from the quark-gluon plasma effects.
We calculate the unintegrated gluon distribution at low intrinsic transverse momenta and its parameters are found from the best description of the SPS and LHC data on the $pp$ collision in the soft kinematical region. It allows us to study the saturation of the gluon density at low $Q^2$ more carefully and find the saturation scale.
We show that instanton calculations in QCD become theoretically well defined in the gluon saturation environment which suppresses large size instantons. The effective cutoff scale is determined by the inverse of the saturation scale. We concentrate on two most important cases: the small-x tail of a gluon distribution of a high energy hadron or a large nucleus and the central rapidity region in a high energy hadronic or heavy ion collision. In the saturation regime the gluon density in a single large ultrarelativistic nucleus is high and gluonic fields are given by the classical solutions of th…
We report on the interesting possibility of instanton-driven gluon saturation in lepton-nucleon scattering at small Bjorken-x. The explicitly known instanton gauge field serves as a concrete realization of an underlying non-perturbative saturation mechanism associated with strong classical fields. The conspicuous, intrinsic instanton size scale known from lattice simulations, turns out to determine the saturation scale. The ``colour glass condensate'' can be identified in our approach with the QCD-sphaleron state, dominating instanton-induced processes in the softer regime.
Parton distributions in the small $x$ region are numerically predicted by using a modified DGLAP equation with the GRV-like input distributions. We find that gluon recombination at twist-4 level obviously suppresses the rapid growth of parton densities with $x$ decrease. We show that before the saturation scale $Q^2_s$ is reached, saturation and partial saturation appear in the small $x$ behavior of parton distributions in nucleus and free proton, respectively. The antishadowing contributions to the saturation phenomena are also discussed.
We present an overview of theoretical aspects of the phenomenon of gluon saturation in high energy scattering in Quantum Chromo Dynamics. Then we review the state-of-the-art of saturation-based phenomenological approaches to the study and characterisation of the initial state of ultra-relativistic heavy ion collisions performed at RHIC and the LHC. Our review focuses mostly in the Color Glass Condensate effective theory, although we shall also discuss other approaches in parallel.
Large angle gluon radiations induced by multiple parton scatterings contribute to dijet production in deeply inelastic scattering off a large nucleus at the Electron-Ion Collider. Within the generalized high-twist approach to multiple parton scattering, such contributions at the leading order in perturbative QCD and large Bjorken momentum fraction $x_B$ can be expressed as a convolution of the multiple parton scattering amplitudes and the transverse momentum dependent (TMD) two-parton correlation matrix elements. We study this medium-induced dijet spectrum and its azimuthal angle correlation u…
We evaluate the unintegrated gluon distribution of the proton starting from a parametrization of the color dipole cross section including DGLAP evolution and saturation effects. To this end, we perform the Fourier-Bessel transform of $σ(x,r)/α(r)$. At large transverse momentum of gluons we match the so-obtained distribution to the logarithmic derivative of the collinear gluon distribution. We check our approach by calculating the proton structure function $F_L(x,Q^2)$ finding good agreement with HERA data.
We show that the inclusion of parton density effects in the perturbative small-x evolution reduces the strength of the powerlike growth of total hadronic cross sections.
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.
