Kirill Tuchin
We discuss a novel mechanism for J/Psi$ production in nuclear collisions arising due to the high density of gluons. We demonstrate that gluon saturation in the colliding nuclei is a dominant source of J/Psi suppression and can explain its experimentally observed rapidity and centrality dependence.
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We study J/psi production at RHIC and LHC energies with both initial production and regeneration. We solve the coupled set of transport equation for the J/psi distribution in phase space and the hydrodynamic equation for evolution of quark-gluon plasma. At RHIC, continuous regeneration is crucial for the J/psi momentum distribution while the elliptic flow is still dominated by initial production. At LHC energy, almost all the initially created J\psis are dissociated in the medium and regeneration dominates the J/psi properties.
The transverse momentum dependence of J/Psi suppression in relativistic heavy ion collisions is calculated from initial state gluon rescattering not only with nucleons but also with prompt gluons produced in nucleon-nucleon collisions in the early phase of the reaction. The second mechanism is new and turns out to be important in a description of the data for central collisions.
Centrality dependence of J/psi production in Au-Au collisions at 200 GeV nucleon-nucleon center of mass energy is studied using the Glauber model plus the kinetic formation model. Initial J/psi production and destruction by incoming nucleons are described by the Glauber model. J/psi-charm equilibration in the gluon plasma is described by the kinetic formation model. We explore the possibility of J/psi suppression suggested by the recent PHENIX data. We show that the J/psi yield monotonically decreases with increasing centrality in the kinetic formation model when the charm mass is smaller than…
All measured Feynman x_f distributions of the ratio, R, of j_psi production in nuclei relative to production on protons fall off with x_f. They show [2] that absorption of charmonium cannot be the only source of j_psi suppression and that energy loss of the constituents of the incident proton prior to the j_psi production, because of the exponential sqrt(s) dependence of the charmonium cross section, should not be neglected. Including the effects of initial state energy loss we find that the latest measured Pb-Pb j_psi cross sections do not provide any evidence for deconfinement.
Finite size effect on gluon dissociation of J/psi in relativistic heavy ion collisions
本文用袋模型研究纵向有限尺寸对夸克物质热力学量及J/psi胶子解离率的影响，发现解离率在特定尺寸L_m处最大，并分析了尺寸依赖的抑制行为。
The enhanced suppression of $J/ψ$ production at large $x_F$ in $pA$ collisions is studied in the framework of gluon depletion at large $x_1$. The nonperturbative process that modifies the gluon distribution as the gluons propagate in nuclear matter is described by an evolution equation with a kernal to be determined by phenomenology. With nuclear shadowing and anti-shadowing taken into account, the effect on the gluon distribution is shown to be a depletion in excess of 40% at $x_1 \approx 0.8$ for $A > 100$. There is a small amount of enhancement of the gluon distribution at small $x_1$, but …
Using a multiphase transport model, we study the relative importance of J/psi suppression mechanisms due to plasma screening, gluon scattering, and hadron absorption in heavy ion collisions at the Relativistic Heavy Ion Collider. We find that for collisions between heavy nuclei such as Au+Au, both plasma screening and gluon scattering are important. As a result, the effect due to absorption by hadrons becomes relatively minor. The final J/psi survival probability in these collisions is only a few percent. In the case of collisions between light nuclei such as S+S, the effect of plasma screenin…
Using a nonrelativistic potential model, we calculate the cross section for the leading-order gluon dissociation of J/psi by including the full gluon wave function. We find that the resulting cross section as a function of gluon energy is reduced by about a factor of three at its maximum value compared to that calculated in the dipole approximation that is usually adopted in theoretical studies. The effect of the reduced cross section on the J/psi dissociation width at finite temperature is also discussed.
We calculate the inclusive J/Psi production in heavy ion collisions including the effects of gluon saturation in the wave functions of the colliding nuclei. We argue that the dominant production mechanism in proton--nucleus and nucleus--nucleus collisions for heavy nuclei is different from the one in hadron-hadron interactions. We find that the rapidity distribution of primary J/Psi production is more peaked around midrapidity than the analogous distribution in elementary pp collisions. We discuss the consequences of this fact on the experimentally observed J/Psi suppression in Au-Au collision…
We derive the formulae for the cross section of J/Psi production in high energy pA and AA collisions taking into account the gluon saturation/color glass condensate effects. We then perform the numerical calculations of the corresponding nuclear modification factors and find a good agreement between our calculations and the experimental data on J/Psi production in dA collisions. We also observe that cold nuclear modification effects alone cannot describe the data on J/Psi production in AA collisions. Additional final state suppression (at RHIC) and enhancement (at LHC) mechanisms are required …
We investigate possible mass shift and width broadening of J/psi in hot gluonic matter using QCD sum rule. Input values of gluon condensates at finite temperature are extracted from lattice QCD data for the energy density and pressure. Although stability of the moment ratio is achieved only up to T/Tc ~ 1.05, the gluon condensates cause a decrease of the moment ratio, which results in change of spectral properties. Using the Breit-Wigner form for the phenomenological side, we find that mass shift of J/psi just above Tc can reach maximally 200 MeV and width can broaden to dozens of MeV.
We explore the effects of shadowing on inclusive J/psi and Upsilon(1S) production at AFTER@LHC. We also present the rates as a function of p_T and rapidity for p+Pb and Pb+p collisions in the proposed AFTER@LHC rapidity acceptance.
It is shown that the study of the ω-ρinterference pattern in the J/psi -> (rho+omega)eta -> pi+pi-eta decay provides evidence for the large (nearly 90 degrees) relative phase between the isovector one-photon and three-gluon decay amplitudes.
The only experimental information on the parton distribution of kaons was obtained from the scarce kaon-induced Drell-Yan cross section data. From these data, evidence for a valence $u$ quark distribution of kaon softer than that of pion was found. We study the feasibility to extract kaon's valence quark distribution via the existing kaon-induced J/psi production data. We compare the NA3 data on the K- / pi- and K+ / pi+ ratios for J/psi production on a platinum target with theoretical calculations based on the color-evaporation model. We show that the NA3 data on J/psi production provide an i…
The gluon-exchange contribution to $J/ψ$-nucleon scattering is shown to yield a sizeable scattering length of about -0.25 fm, which is consistent with the sparse available data. Hadronic corrections to gluon exchange which are generated by $ρπ$ and $D\bar D$ intermediate states of the $J/ψ$ are shown to be negligible. We also propose a new method to study $J/ψ$-nucleon elastic scattering in the reaction $π^+ d\to J/ψp p$.
We update our previous work of a Langevin-with-interaction model for charmonium in heavy-ion collisions, by considering the effect due to recombination. We determine the contribution to J/psi yields from charm-anticharm pairs whose constituent quarks originate from two different hard processes. Like the surviving J/psi states, the recombinant J/psi also undergo both a stochastic interaction, determined by a hydrodynamical simulation of the heavy-ion collision, and an interaction determined by the heavy quark-antiquark potentials measured on the lattice for appropriate temperatures. From the re…
It is argued that the search of the J/psi --> f0(980)omega and J/psi --> a0(980)rho decays and the more precise definition of B(J/psi --> f0(980)phi) are the urgent purposes in the J/ψspectroscopy. It is shown that the study of the omega-rho0 interference pattern in the J/psi --> (ρ^0+ω)eta --> pi+pi-eta decay provides evidence for the large (nearly pi/2) relative phase between the isovector one-photon and three-gluon decay amplitudes .
The nonlinear effect of gluon depletion in the collision of large nuclei can be large. It is due to multiple scatterings among comoving partons initiated by primary scattering of partons in the colliding nuclei. The effect can give rise to substantial suppression of $J/ψ$ production in very large nuclei, even if the linear depletion effect is insignificant for the collisions of nuclei of smaller sizes. This mechanism offers a natural explanation of the enhanced suppression in the Pb-Pb data recently observed by NA50.
The space-time evolution of J/psi production in central Au+Au collisions at RHIC energy is investigated in a transport model. Both gluon dissociation and continuous regeneration of J/psis inside deconfined state are considered.
The depletion of gluons as the parton flux traverses a nucleus in a heavy-ion collision can influence the production rate of heavy-quark states. Thus the suppression of $J/ψ$ can be due to gluon depletion in the initial state in addition to nuclear and hadronic absorption in the final state. A formalism is developed to describe the depletion effect. It is shown that, without constraints from other experimental facts beside the $J/ψ$ suppression data in $pA$ and $AB$ collisions, it is not possible to determine the relative importance of depletion vs absorption. Possible relevance to the enhance…
We estimate the survival probability of $J/ψ$ in relativistic heavy-ion collisions, using both short-distance QCD and nuclear absorption mechanism. The suppression is found to be almost 100 percent for a thermally equilibrating quark-gluon plasma. The measurement of such a huge suppression of $J/ψ$ may suggest the existence of a deconfined partonic medium, possibly a thermalised quark-gluon plasma, at RHIC.
Prompt gluons are an additional source for charmonium suppression in nuclear collisions, in particular for nucleus-nucleus collisions. These gluons are radiated as bremsstrahlung in N-N collisions and interact inelastically with the charmonium states while the nuclei still overlap. The spectra and mean number <n_g> of the prompt gluons are calculated perturbatively and the gluon-Psi inelastic cross section is estimated. The integrated cross sections for AB --> J/Psi (Psi')X for p-A and A-B collisions and the dependence on transverse energy for S-U and Pb-Pb can be described quantitatively with…
To study the stability of heavy quarkonia in quark-gluon plasma, we use a color-singlet Q-Qbar potential determined previously to be a well-defined linear combination of the free energy F_1 and the internal energy U_1. Using the lattice gauge results of Kaczmarek et al., the dissociation temperatures of J/psi and chi_b in quenched QCD are found to be 1.62Tc and 1.18Tc respectively, in good agreement with spectral function analyses. The dissociation temperature of J/psi in full QCD with 2 flavors is 1.42Tc. Thus, the presence of dynamical quarks in full QCD lowers the dissociation temperature o…
We calculate the Wilson coefficients of all dimension 6 gluon operators with non zero spin in the correlation function between two heavy vector currents. For the twist-4 part, we first identify the three independent gluon operators, and then proceed with the calculation of the Wilson coefficients using the fixed point gauge. Together with the previous calculation of the Wilson coefficients for the dimension 6 scalar gluon operators by Nikolaev and Radyushkin, our result completes the list of all the Wilson coefficients of dimension 6 gluon operators in the correlation function between heavy ve…
The production and space-time evolution of heavy quarks and J/psi in the quark gluon plasma is studied within the partonic transport model Boltzmann Approach to MultiParton Scatterings (BAMPS). This framework allows interactions among all partons: gluons, light quarks and heavy quarks. Heavy quarks, in particular, interact with the rest of the medium via binary scatterings with a running coupling and a more precise Debye screening which is derived from hard thermal loop calculations. We compare our results of the elliptic flow and nuclear modification factor not only to experimental data of he…
The experimental results on the pion, strangeness and J/psi production in high energy nuclear collisions are discussed. The anomalous energy dependence of pion and strangeness production is consistent with the hypothesis that a transition to a deconfined phase takes place between the top AGS (15 AGeV) and the SPS (200 AGeV) energies. The J/psi production systematics at the SPS can be understood assuming that the J/psi mesons are created at hadronization according to the available hadronic phase space. This new interpretation of the J/psi data allows one to establish a coherent picture of high …
J/psi production and collective flow is studied with a coalescence model based on phase space distribution of charm quarks from a multi-phase transport model simulation of relativistic heavy ion collisions. Both the yield and the flow of J/psi particles are sensitive to charm quark final state interactions. As the charm quark rescattering cross section increases from 3 mb to 10 mb, J/psi elliptic flow increases faster than corresponding light hadron elliptic flows. The v_2(p_t) of J/psi crosses that of D mesons to reach a value that is about the peak value of the D meson flow but at a higher p…
Two decades ago Matsui and Satz suggested that Debye screening in the quark-gluon plasma would result in J/psi suppression in heavy ion collisions. Much has happened in the subsequent years, and the picture of quark-gluon plasma at present is rapidly evolving - what does it imply for the J/psi suppression? What are the recent RHIC and SPS results trying to tell us? What else has to be done? This talk is an attempt to address these questions.
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 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…
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.
We investigate the masses of the lowest c\bar{c} states, the J/psi and eta_c, in nuclear matter using QCD sum rules. Up to dimension four, the differences between the operator product expansions in vacuum and in medium arise from the density-dependent change in the gluon condensate and from a new contribution proportional to the nucleon expectation value of the twist-2 gluon operator. Both terms together give an attractive shift of about 5-10 MeV to the J/psi and eta_c masses in nuclear matter.
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 extract the pole positions, hadronic and gamma-gamma widths of sigma and f_0(980, from pi-pi and gamma-gamma scattering data using an improved analytic K-matrix model. Our results favour a large gluon component for the sigma and a \bar ss or/and gluon component for the f_0(980) but neither a large four-quark nor a molecule component. Gluonium sigma_B production from J/psi, phi radiative and D_s semi-leptonic decays are also discussed.
We study the charmonium suppression in different evolutions of quark gluon plasma (QGP) based on the transport model. In the colliding energies of Large Hadron Collider, charmonium final yields are dominated by the recombination of charm and anti-charm quarks in the deconfined phase. Heavy quark diffusions depend less on the shear viscosity of the bulk medium, which makes the J/psi nuclear modification factor in the entire pT bin shows weak dependence on the shear viscosity of QGP. However, charmonium with high transverse momentum pT, can only be produced in the early stage of nuclear collisio…
Cold nuclear matter effects on J/psi production in proton-nucleus and nucleus-nucleus collisions are evaluated taking into account the specific J/psi production kinematics at the partonic level, the shadowing of the initial parton distributions and the absorption in the nuclear matter. We consider two different parton processes for the c-cbar pair production: one with collinear gluons and a recoiling gluon in the final state and the other with initial gluons carrying intrinsic transverse momentum. Our results are compared to RHIC observables. The smaller values of the nuclear modification fact…
Using the color-singlet free energy F_1 and total internal energy U_1 obtained by Kaczmarek et al. for a static quark Q and an antiquark Qbar in quenched QCD, we study the binding energies and wave functions of heavy quarkonia in a quark-gluon plasma. By minimizing the grand potential in a simplified schematic model, we find that the proper color-singlet Q-Qbar potential can be obtained from the total internal energy U_1 by subtracting the gluon internal energy contributions. We carry out this subtraction in the local energy-density approximation in which the gluon energy density can be relate…
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…
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…
The Color-Octet Model has been used successfully to analyze many problems in heavy quarkonium production. We examine some of the conceptual and practical problems of the soft gluon emission process in the Color-Octet Model. We use a potential model to describe the initial and final states in the soft gluon emission process, as the emission occurs at a late stage after the production of the heavy quark pair. It is found in this model that the soft gluon M1 transition, 1S0(8)->3S1(1), dominates over the E1 transition, 3PJ(8)->3S1(1), for J/psi and psi' production. Such a dominance may help resol…
We present a new calculation of the pi-J/psi dissociation cross sections within the Constituent Quark-Meson Model recently introduced. To discuss the absorption of J/psi in heavy-ion collisions, we assume the J/psi to be produced inside a thermalized pion gas, as discussed by Bjorken, and introduce the corrections due to absorption by nuclear matter as well. We fit the absorption length of the J/psi to the data obtained at the CERN SPS by the NA50 Collaboration for Pb-Pb collisions. Collisions of lower centrality allow us to determine the temperature and the energy density of the pion gas. For…
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.
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.
Gluon Saturation Effects in Exclusive Heavy Vector Meson Photoproduction
本研究在高能极限下对比线性与非线性演化方程计算质子和Pb靶的专属重矢量介子光致产生，发现Pb靶的$J/ψ$产生数据明显支持包含胶子饱和效应的演化。
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…
J/psi-pair production at NLL in TMD factorisation at the LHC
本文在TMD因子化框架下计算LHC上J/ψ对产生至NLL精度，给出LHCb接收度内的横动量分布、PDF不确定性及线性极化胶子导致的方位角调制预言。
In central collisions at RHIC, the initial production of heavy quarks will for the first time yield multiple pairs of c-cbar in each central event. If a region of deconfined quarks and gluons is subsequently formed, a new mechanism for the formation of heavy quarkonium bound states will be activated. This will result from the mobility of heavy quarks in the deconfined region, such that bound states can be formed from a quark and an antiquark which were originally produced in separate incoherent interactions. Our model estimates of this effect predict a dramatic increase in the number of observ…
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 …
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…
In order to understand the J/psi suppression arising from the possible occurrence of the quark-gluon plasma in high-energy heavy-ion collisions, it is necessary to have a comprehensive picture how the J/psi and its precursors are produced, what their properties after production are, and how the J/psi and its precursors propagate inside nuclear matter. There are unresolved questions in the descriptions of J/psi production and propagation. We outline some of these questions and discuss the approaches for their resolution.
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 present new results based on an improved version of the Glauber model, used to describe the nuclear absorption of J/psi in reactions between nuclei at high energy. The excitation of the colour degrees of freedom of nucleons, due to collisions mediated by one-gluon exchange, is taken into account. It is found that the proposed mechanism leads to larger nuclear absorption of J/psi than previously considered.
Probing gluon saturation through inclusive hadron production in DIS
本研究在色玻璃凝聚框架下计算半包容深度非弹性散射截面，验证于HERA数据，预测EIC上饱和效应导致显著核抑制，可约束BK演化初始条件，表明SIDIS对非线性QCD动力学敏感。
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…
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.
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…
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