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 introduced color field domain model that captures key features of the observed azimuthal correlations can be understood in the CGC effective theory as a model of non-Gaussian correlations in the target nucleus.
We present a good description of recent experimental data on forward di-hadron azimuthal correlations measured in deuteron-gold collisions at RHIC, where monojet production has been observed. Our approach is based on the Color Glass Condensate effective theory for the small-x degrees of freedom of the nuclear wave function, including the use of non-linear evolution equations with running QCD coupling. Our analysis provides further evidence for the presence of saturation effects in RHIC data.
We analyse the azimuthal structure of two gluon correlations in the Color Glass Condensate including those effects that result from relaxing the shockwave approximation for the target. Working in the Glasma graph approach suitable for collisions between dilute systems, we compute numerically the azimuthal distributions and show that both even and odd harmonics appear. We study their dependence on model parameters, energy of the collision, pseudorapidity and transverse momentum of the produced particles, and length of the target. While the contribution from non-eikonal corrections vanishes with…
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…
Simple power counting arguments in the dilute-dense framework of the Color Glass Condensate (CGC) Effective Field Theory predict that even and odd azimuthal anisotropy harmonics of two-particle correlations in proton-nucleus collisions at the LHC will respectively satisfy v^2_{2n} ~ N_{ch}^0 and v^2_{2n+1} ~ N_{ch}, where N_{ch} denotes the number of charged particles. We show that these expectations are borne out qualitatively, and even quantitatively, within systematic uncertainties, for v_2 and v_4 in comparisons with data from the ATLAS collaboration. We also observe that ATLAS data for th…
We demonstrate that the striking systematics of two-particle azimuthal Fourier harmonics $v_2$ and $v_3$ in ultrarelativistic collisions of protons, deuterons and helium-3 ions off gold nuclei measured by the PHENIX Collaboration [arXiv:1805.02973] at the Relativistic Heavy Ion Collider (RHIC) is reproduced in the Color Glass Condensate (CGC) effective field theory. This contradicts the claim in [arXiv:1805.02973] that their data rules out initial state based explanations. The underlying systematics of the effect, as discussed previously in [arXiv:1705.00745,arXiv:1706.06260,arXiv:1801.09704],…
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…
We calculate azimuthal correlations in dAu collisions at different rapidities and centralities and argue that experimentally observed depletion of the back-to-back pick can be quantitatively explained by gluon saturation in the Color Glass Condensate of the Gold nucleus.
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 discuss azimuthal correlations in $dAu$ collisions at different rapidities and centralities and argue that experimentally observed depletion of the back-to-back peak can be quantitatively explained by gluon saturation in the Color Glass Condensate of the Gold nucleus.
We derive forward inclusive dijet production in the scattering of a dilute hadron off an arbitrary dense target, whose partons with small fraction of momentum x are described by a Color Glass Condensate. Both multiple scattering and non-linear QCD evolution at small-x are included. This is of relevance for measurements of two-particle correlations in the proton direction of proton-nucleus collisions at RHIC and LHC energies. The azimuthal angle distribution is peaked back to back and broadens as the momenta of the measured particles gets closer to the saturation scale.
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 collimation of di-hadrons with large rapidity separations in high multiplicity p+p collisions at the LHC is described in the Color Glass Condensate (CGC) effective theory [1] by N_c^2 suppressed multi-ladder QCD diagrams that are enhanced α_S^(-8) due to gluon saturation in hadron wavefunctions. We show that quantitative computations in the CGC framework are in good agreement with data from the CMS experiment on per trigger di-hadron yields and predict further systematics of these yields with varying trigger pT and charged hadron multiplicity. Radial flow generated by re-scatteri…
Considering a dilute-dense situation suitable for pA collisions, we compute in the Color Glass Condensate the correlation between azimuthal asymmetries, specifically the squared second Fourier coefficient $v_2^2$, and the total multiplicity in the event. We also analyse the correlation between $v_2^2$ and the mean squared transverse momentum of particles in the event. In both cases, we find that the correlations are generally very small, consistent with the observations. We also note an interesting sharp change in the value of $v_2^2$ and its correlations as a function of the width of the tran…
We perform an exploratory study of the role of coherent, medium-induced energy loss in azimuthal angular correlations in dihadron production in Deep Inelastic Scattering (DIS) at small $x$ where the target proton/nucleus is modeled as a Color Glass Condensate. In this approach coherent radiative energy loss is part of the higher order corrections to the leading order dihadron production cross section. We include the effects of both gluon saturation and coherent radiative energy loss and show that radiative cold-matter energy loss has a significant effect on the so-called coincidence probabilit…
We study exclusive dijet production in coherent diffractive processes in deep inelastic scattering and real (and virtual) photon-hadron ($γ^{(*)}$-h) collisions in the Color Glass Condensate formalism at leading order. We show that the diffractive dijet cross section is sensitive to the color-dipole orientation in the transverse plane, and is a good probe of possible correlations between the $q\bar{q}$-dipole transverse separation vector $\r$ and the dipole impact parameter $\b$. We also investigate the diffractive dijet azimuthal angle correlations and $t$-distributions in $γ^{(*)}$-h collisi…
We discuss azimuthal correlations in double inclusive hadron production in high energy $dA$ collisions at RHIC. We argue that the leading logarithmic approximation is inadequate for description of experimental data. Realistic shape of the azimuthal correlation function is obtain only if we keep terms that are finite in the rapidity difference between the produced hadrons. Likewise, transverse momentum dependence of parton distribution functions in both deuteron and nucleus must be retained. We observe depletion of the back-to-back correlations in central $dAu$ collisions in the forward directi…
We investigate inclusive prompt photon and semi-inclusive prompt photon-hadron production in high energy proton-nucleus collisions using the Color Glass Condensate (CGC) formalism which incorporates non-linear dynamics of gluon saturation at small x via Balitsky-Kovchegov equation with running coupling. For inclusive prompt photon production, we rewrite the cross-section in terms of direct and fragmentation contributions and show that the direct photon (and isolated prompt photon) production is more sensitive to gluon saturation effects. We then analyze azimuthal correlations in photon-hadron …
Measuring correlations between forward dijets in deuteron-gold collisions at RHIC will further test the Color Glass Condensate (CGC) picture of the nuclear wavefunction at small-x, which successfully predicted the suppressed production of high-p_T particles at forward rapidities in d+Au collisions: R_dA<1. I present predictions for the correlation in azimuthal angle between forward dijets in the CGC framework, with both multiple scatterings and non-linear QCD evolution at small-x taken into account.
The ridge signal, which is long-ranged in rapidity, in the di-hadron correlations in high-multiplicity p-p and p-A collisions opened up a whole new research area in high-energy QCD. Although the ridge had been observed in A-A collisions and interpreted as a result of the radial flow of quark-gluon plasma, it had not appeared until recently in the data of small collision systems such as p-p and p-A, nor had it been predicted theoretically or seen in the event generators. There are two competing approaches that attempt to explain the systematics of the di-hadron ridge signal; hydrodynamics and g…
In the Color Glass Condensate formalism, we evaluate the 3-dipole correlator up to the $\frac{1}{N_c^4}$ order with $N_c$ being the number of colors, and compute the azimuthal cumulant $c_{123}$ for 3-particle productions. In addition, we discuss the patterns appearing in the $n$-dipole formula in terms of $\frac{1}{N_c}$ expansions. This allows us to conjecture the $N_c$ scaling of $c_n\{m\}$, which is crosschecked by our calculation of $c_2\{4\}$ in the dilute limit.
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…
Quark-antiquark pair (or dijet) production at the electron-ion collider (EIC) has been argued to be one of most important processes that allowing to access the Weizsäcker-Williams (WW) gluon distributions at small $x$ limit. Within the framework of Color Glass Condensate (CGC) effective field theory (EFT), we calculated the dijet cross sections and the azimuthal correlations by including the Sudakov resummations, numerical results shown that the back-to-back correlations are significantly suppressed when the Sudakov resummations are taken into account. In addition, by using the solutions of ru…
We study the azimuthal asymmetries for quark pair production in proton-nucleus collisions using a hybrid approach in which the nucleus is treated in the Color Glass Condensate (CGC) framework while the Lipatov approximation is applied on the proton side. Our treatment goes beyond the large N_c limit. We particularly focus on the so-called correlation limit where the imbalance of the transverse momentum of the quark pair is much smaller than the out-going individual quark transverse momenta. In this kinematic region, a matching between the hybrid approach and a factorization in terms of transve…
We demonstrate that the recent measurement of azimuthally collimated, long range rapidity ("ridge") correlations in $\sqrt{s}=13$ TeV proton-proton (p+p) collisions by the ATLAS collaboration at the LHC are in agreement with expectations from the color glass condensate effective theory of high energy QCD. The observation that the integrated near side yield as a function of multiplicity is independent of collision energy is a natural consequence of the fact that multiparticle production is driven by a single semi-hard saturation scale in the color glass condensate framework. We argue further th…
We perform a detailed comparison of long range rapidity correlations in the Color Glass Condensate framework to high multiplicity di-hadron data in proton-proton and proton-lead collisions from the CMS, ALICE and ATLAS experiments at the LHC. The overall good agreement thus far of the non-trivial systematics of theory with data is strongly suggestive of gluon saturation and the presence of subtle quantum interference effects between rapidity separated gluons. In particular, the yield of pairs collimated in their relative azimuthal angle $Δϕ\sim 0$, is sensitive to the shape of unintegrated glu…
We use the spinor helicity formalism to calculate the cross section for production of three partons of a given polarization in Deep Inelastic Scattering (DIS) off proton and nucleus targets at small Bjorken x. The target proton or nucleus is treated as a classical color field (shock wave) from which the produced partons scatter multiple times. We reported our result for the final expression for the production cross section and studied the azimuthal angular correlations of the produced partons in [1]. Here we provide the full details of the calculation of the production cross section using the …
We show that for a finite number of emitting sources, the Color Glass Condensate produces substantial elliptic azimuthal anisotropy, characterized by $v_2$, for two and four particle correlations for momentum greater than or of the order the saturation momentum. The flow produced has the correct semi-quantitative features to describe flow seen in LHC experiments with p-Pb and pp collisions. This flow is induced by quantum mechanical interference between the waves of produced particles, and the flow itself is coupled to fluctuations in the positions of emitting sources. We shortly discuss gener…
The eccentricity in coordinate-space at midrapidity of the overlap zone in high-energy heavy-ion collisions predicted by the $k_\perp$-factorization formalism is generically larger than expected from scaling with the number of participants. We provide a simple qualitative explanation of the effect which shows that it is not caused predominantly by edge effects. We also show that it is quite insensitive to ``details'' of the unintegrated gluon distribution functions such as the presence of leading-twist shadowing and of an extended geometric scaling window. The larger eccentricity increases the…
We study azimuthal asymmetries in diffractive J/$ψ$ production in ultraperipheral heavy-ion collisions at RHIC and LHC energies using the color glass condensate effective theory. Our calculation successfully describes azimuthal averaged $J/ψ$ production cross section measured by STAR and ALICE. We further predict very large $\cos 2ϕ$ and $\cos 4ϕ$ azimuthal asymmetries for diffractive $J/ψ$ production both in UPCs at RHIC and LHC energies and in eA collisions at EIC energy. These novel polarization dependent observables may provide complementary information for constraining gluon transverse sp…
Gluonic nucleon energy correlators and fracture functions for Color Glass Condensate
University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Shandong University（山东大学）；École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Chulalongkorn University（朱拉隆功大学）
It was argued in arXiv:1805.09342 and arXiv:1807.00825 that the systematics of the azimuthal anisotropy coefficients $v_{2,3}$ measured in ultrarelativistic light-heavy ion collisions at RHIC and the LHC can be described in an initial state dilute-dense Color Glass Condensate (CGC) framework. We elaborate here on the discussion in these papers and provide further novel results that strengthen their conclusions. The underlying mathematical framework and numerical techniques employed are very similar to those in the CGC based IP-Glasma model used previously as initial conditions for heavy-ion co…
Tracing Gluon Saturation through Hadronization at EIC
Central China Normal University（华中师范大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Shandong University（山东大学）；École Polytechnique, Institut Polytechnique de Paris（巴黎理工学院巴黎综合理工学校）
We study two-particle long-range rapidity correlations arising in the early stages of heavy ion collisions in the saturation/Color Glass Condensate framework, assuming for simplicity that one colliding nucleus is much larger than the other. We calculate the two-gluon production cross section while including all-order saturation effects in the heavy nucleus with the lowest-order rescattering in the lighter nucleus. We find four types of correlations in the two-gluon production cross section: (i) geometric correlations, (ii) HBT correlations accompanied by a back-to-back maximum, (iii) away-side…
We study the initial, high-energy scatterings in heavy ion collisions using the saturation/Color Glass Condensate framework. We focus on two-particle long-range rapidity correlations which are modeled as two-gluon correlations. We calculate the two-gluon production cross section using the saturation framework in the heavy-light ion regime, including all-order saturation effects in the heavy nucleus while considering only two-orders in the light ion. The two-gluon production cross section generates four types of long-range in rapidity correlations: (i) geometric correlations, (ii) Hanbury Brown…
We provide the first calculation of two-gluon production at mid-rapidity in ultra-peripheral collisions in the Color Glass Condensate framework. To estimate systematic uncertainty associated with poor understanding of the wave function of the nearly real photon, we consider two diametrically different models: the dilute quark-antiquark dipole approximation and a vector meson, in which color charge density is approximated by McLerran-Venugopalan model. In the experimentally relevant range, the target nucleus can be faithfully approximated by a highly saturated state. This simplification enables…
Azimuthal angular correlations between produced hadrons/jets in high energy collisions are a sensitive probe of the dynamics of QCD at small x. Here we derive the triple differential cross section for inclusive production of 3 polarized partons in DIS at small x using the spinor helicity formalism. The target proton or nucleus is described using the Color Glass Condensate (CGC) formalism. The resulting expressions are used to study azimuthal angular correlations between produced partons in order to probe the gluon structure of the target hadron or nucleus. Our analytic expressions can also be …
We compute multi-gluon production in the Color Glass Condensate approach in dilute-dense collisions, p$A$, extending previous calculations up to four gluons. We include the contributions that are leading in the overlap area of the collision but keep all orders in the expansion in the number of colors. We develop a diagrammatic technique to write the numerous color contractions and exploit the symmetries to group the diagrams and simplify the expressions. To proceed further, we use the McLerran-Venugopalan and Golec-Biernat-Wüsthoff models for the projectile and target averages, respectively. W…
The study of azimuthal correlations in particle production at forward rapidities in proton-nucleus collisions provides direct information about high gluon density effects, like gluon saturation, in the nuclear wavefunction. In the kinematical conditions for proton-lead collisions at the LHC, the forward di-hadron production is dominated by partonic processes in which a gluon from the proton splits into a pair of gluons, while undergoing multiple scattering off the dense gluon system in the nucleus. We compute the corresponding cross-section using the Colour Glass Condensate effective theory, w…
Following an explicit example, we present the chain of steps required for an event-by-event description of hadron production in high energy hadronic and nuclear collisions. We start from incoming nuclei, described in the Color Glass Condensate effective theory, whose collision creates the gluon fields of the glasma. Individual gluons are then sampled from the gluon fields' Husimi (smeared Wigner) distributions, and clustered using a new spacetime based algorithm. Clusters are fed into the Herwig event generator, which performs the hadronization, conserving energy and momentum. We discuss the p…
We compute the differential cross-section for inclusive prompt photon$+$quark production in deeply inelastic scattering of electrons off nuclei at small $x$ ($e+A$ DIS) in the framework of the Color Glass Condensate effective field theory. The result is expressed as a convolution of the leading order (in the strong coupling $α_{\mathrm{s}}$) impact factor for the process and universal dipole matrix elements, in the limit of hard photon transverse momentum relative to the nuclear saturation scale $Q_{s,A}(x)$. We perform a numerical study of this process for the kinematics of the Electron-Ion C…
We study ridge correlations of the glasma in pp collisions at $\sqrt{s_{\mathrm{NN}}}=7$ TeV by using the color glass condensate (CGC) formalism. The azimuthal collimation at long range rapidity is intrinsic to glasma dynamics and is reproduced here. When rapidity window enlarges, ridge correlations in two dimensional $Δy$-$Δϕ$ distribution and one dimensional $Δϕ$ distribution at long range rapidity gap are enhanced. The enhancements are demonstrated to be the contributions of source gluons. The quantum evolution of the gluons presents unique correlation patterns in differential correlation f…
At leading-order, the standard dilute-dense Color Glass Condensate formula used for two-particle correlations in proton-nucleus collisions, whose symmetries prevent the generation of odd azimuthal anisotropy harmonics, is the dilute projectile limit of the dense-dense formalism. However, when the projectile is genuinely dilute, the complete formulation contains additional contributions at the same leading order in the strong coupling constant. In this work we investigate those low projectile density contributions that are relevant when the particles are produced at forward rapidities. We find …
Using a model based on the Color Glass Condensate framework and the dilute-dense factorization, we systematically study the azimuthal angular correlations between a heavy flavor meson and a light reference particle in proton-nucleus collisions. The obtained second harmonic coefficients (also known as the elliptic flows) for $J/ψ$ and $D^0$ agree with recent experimental data from the LHC. We also provide predictions for the elliptic flows of $Υ$ and $B$ meson, which can be measured in the near future at the LHC. This work can shed light on the physics origin of the collectivity phenomenon in t…
It is shown that odd harmonic azimuthal correlations, including the directed flow $v_1$, in forward two-particle production in peripheral proton-nucleus ($pA$) collisions can arise simply from the radial nuclear profile of a large nucleus. This requires consideration of the C-odd part of the gluonic generalized transverse momentum dependent (GTMD) correlator of nucleons in the nucleus. The gluonic GTMD correlator is the Fourier transform of an off-forward hadronic matrix element containing gluonic field strength tensors that are connected by gauge links. It is parametrized in terms of various …
We study open heavy flavor meson production in proton-nucleus (pA) collisions at RHIC and LHC energies within the Color Glass Condensate framework. We use the unintegrated gluon distribution at small Bjorken's x in the proton obtained by solving the Balitsky-Kovchegov equation with running coupling correction and constrained by global fitting of HERA data. We change the initial saturation scale of the gluon distribution for the heavy nucleus. The gluon distribution with McLerran-Venugopalan model initial condition is also used for comparison. We present transverse momentum spectra of single D …
We study the disappearance of the away-side peak of the di-hadron correlation function in p+A vs p+p collisions at forward rapidities, when the scaterring process presents a manifest dilute-dense asymmetry. We improve the state-of-the-art description of this phenomenon in the framework of the Color Glass Condensate (CGC), for hadrons produced nearly back-to-back. In that case, the gluon content of the saturated nuclear target can be described with transverse-momentum-dependent gluon distributions, whose small-$x$ evolution we calculate numerically by solving the Balitsky-Kovchegov equation wit…
During the 2008 run RHIC provided high luminosity in both p+p and d+Au collisions at $\sqrt{s_{NN}}=200GeV$. Electromagnetic calorimeter acceptance in STAR was enhanced by the new Forward Meson Spectrometer (FMS), and is now almost contiguous from $-1<η<4$ over the full azimuth. This large acceptance provides sensitivity to the gluon density in the nucleus down to $x\approx 10^{-3}$. Measurements of the azimuthal correlation between a forward $π^0$ and an associated particle at large rapidity are sensitive to the low-$x$ gluon density. Data exhibit the qualitative features expected from gluon …
We study the properties of the cross section for two-gluon production in heavy-light ion collisions derived in our previous paper on the subject in the saturation/Color Glass Condensate framework. Concentrating on the energy and geometry dependence of the corresponding correlation functions we find that the two-gluon correlator is a much slower function of the center-of-mass energy than the one- and two-gluon production cross sections. The geometry dependence of the correlation function leads to stronger azimuthal near- and away-side correlations in the tip-on-tip U+U collisions than in the si…
Probing gluon saturation with forward di-hadron correlations in proton-nucleus collisions
SUBATECH UMR 6457 (IMT Atlantique, Universite de Nantes, IN2P3/CNRS)（SUBATECH联合研究单位6457（大西洋理工大学，南特大学，法国国家科学研究中心））；University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；Center for Frontiers in Nuclear Science, Stony Brook University（纽约州立大学石溪分校核科学前沿中心）；Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）；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-BNL研究中心）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）；CFNS, Department of Physics and Astronomy, Stony Brook University（纽约州立大学石溪分校物理与天文学系核科学前沿中心）；Higgs Center for Theoretical Physics, The University of Edinburgh（爱丁堡大学希格斯理论物理中心）；Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics（粒子物理研究所夸克和轻子物理重点实验室）
