I present the first isolation of azimuth quadrupole components from published $v_2(p_t)$ data (called elliptic flow) as spectra on transverse rapidity $y_t$ for identified pions, kaons and lambdas/protons from minimum-bias Au-Au collisions at 200 GeV. The form of the spectra on $y_t$ indicates that the three hadron species are emitted from a common boosted source with boost $Δy_{t0} \sim 0.6$. The quadrupole spectra have a Lévy form similar to the soft component of the single-particle spectrum, but with significantly reduced ($\sim 0.7\times$) slope parameters $T$. Comparison of quadrupole spectra with single-particle spectra suggests that the quadrupole component comprises a small fraction ($< 5$%) of the total hadron yield, contradicting the hydrodynamic picture of a thermalized, flowing bulk medium. The form of $v_2(p_t)$ is, within a constant factor, the product of $p'_t$ ($p_t$ in the boost frame) times the ratio of quadrupole spectrum to single-particle spectrum. That ratio in turn implies that above 0.5 GeV/c the form of $v_2(p_t)$ is dominated by the hard component of the single-particle spectrum (interpreted as due to minijets). It is therefore unlikely that so-called {\em constituent-quark scaling} attributed to $v_2$ is relevant to soft hadron production mechanisms (e.g., chemical freezeout).
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.
Large elliptic flow at RHIC seems to indicate that ideal hydrodynamics provides a good description of Au-Au collisions, at least at the maximum RHIC energy. The medium formed has been interpreted as a nearly perfect (low-viscosity) liquid, and connections have been made to gravitation through string theory. Recently, claimed observations of large flow fluctuations comparable to participant eccentricity fluctuations seem to confirm the ideal hydro scenario. However, determination of the azimuth quadrupole with 2D angular autocorrelations, which accurately distinguish ``flow'' (quadrupole) from …
By the sample generated by the AMPT with string melting model, we compare the azimuthal distributions of multiplicity, total transverse rapidity, and mean transverse rapidity. It is demonstrated that the azimuthal distribution of mean transverse rapidity is a good probe of the radial kinetic expansion. The anisotropic part of the distribution characterizes the anisotropic nature of the radial expansion, and isotropic part is combinations of thermal motion and isotropic radial expansion.
Previous measurements of a quadrupole component of azimuth correlations denoted by symbol $v_2$ have been interpreted to represent elliptic flow, a hydrodynamic phenomenon conjectured to play a major role in noncentral nucleus-nucleus collisions. $v_2$ measurements provide the main support for conclusions that a ``perfect liquid'' is formed in heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC). However, conventional $v_2$ methods based on one-dimensional (1D) azimuth correlations give inconsistent results and may include a jet contribution. In some cases the data trends appear …
The Balitskii-Fadin-Kuraev-Lipatov (BFKL) multi-Pomeron model of Levin and Rezaeian, with extension to the gluon saturation region, is applied to long-range pseudorapidity correlations on relative azimuth for low momentum final-state hadrons produced in $\sqrt{s}$ = 200~GeV and 7~TeV p+p collisions. The multi-Pomeron exchange probabilities in the model were estimated by fitting the minimum-bias p+p multiplicity frequency distributions. The multi-Pomeron model prediction for the amplitude of the minimum-bias average quadrupole correlation, proportional to $\cos 2(ϕ_1 - ϕ_2)$, is consistent with…
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.
The forward-backward (FB) multiplicity correlations in two windows separated in rapidity and azimuth are analyzed in the framework of the model with independent identical emitters (strings). Along with the short-range contribution, originating from the correlation between particles produced by a single string, the long-range contribution, originating from the fluctuation in the number of strings, is taken into account. The connection of the FB multiplicity correlation coefficient with the two-particle correlation function and the di-hadron correlation analysis is traced. It's also shown that t…
I discuss novel QCD phenomena recently observed in p+p, p+A and A+A collisions, that result from the non-linear dynamics of small-x gluons. I focus on di-hadron correlation measurements, as opposed to single-hadron observables often too inclusive to distinguish possible new effects from established mechanisms. Specifically, I discuss angular correlations of forward di-hadrons in d+Au collisions and long-range rapidity correlations in high-multiplicity p+p and Au+Au collisions.
Forward di-jet production in d+Au collisions at RHIC provides sensitivity to Bjorken-x between 0.001 and 0.02 for the nuclear gluon density . The STAR experiment at RHIC has continuous azimuthal coverage with electromagnetic calorimeters for pseudo-rapidity from -1 to 4. We have measured forward+mid-rapidity $π^{0}-π^{0}$ and $π^{0}-h$ azimuthal correlations and forward+forward rapidity $π^{0}-π^{0}$ azimuthal correlations. Both analyses use the Forward Meson Spectrometer (FMS) triggered data in RHIC 2008 run p+p and d+Au collisions at $\sqrt{s_{NN}}$=200 GeV. The end-cap electromagnetic calor…
The forward-backward (FB) charged particle multiplicity correlations between windows separated in rapidity and azimuth are analyzed using a model that treats strings as independent identical emitters. Both the short-range (SR) contribution, originating from the correlation between multiplicities produced from a single source, and the long-range (LR) contribution, originating from the fluctuation in the number of sources, are taken into account. The dependencies of the FB correlation coefficient, $b$, on the windows' rapidity and azimuthal acceptance and the gaps between these windows are studi…
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…
According to the flow narrative commonly applied to high-energy nuclear collisions a 1D cylindrical-quadrupole component of 2D angular correlations conventionally denoted by quantity $v_2$ is interpreted to represent elliptic flow: azimuth modulation of transverse or radial flow in noncentral nucleus-nucleus (A-A) collisions. The nonjet (NJ) quadrupole component exhibits various properties inconsistent with a flow or hydro interpretation, including the observation that NJ-quadrupole centrality variation in $A$-$A$ collisions has no relation to strongly-varying jet modification ("jet quenching"…
Background: A component of azimuth correlations from high-energy heavy ion collisions varying as $\cos(2ϕ)$ and denoted by symbol $v_2$ is conventionally interpreted to represent "elliptic flow," a hydrodynamic manifestation of the initial-state åoverlap geometry. Several numerical methods are used to estimate $v_2$, resulting in various combinations of "flow" and "nonflow" that reveal systematic biases in the $v_2$ estimates. QCD jets contribute strongly to azimuth correlations and specifically to the $\cos(2ϕ)$ component. Purpose: We question the extent of jet-related ("nonflow") bias in and…
The nuclear modification factor $R_{AA}$ for $π_0$ production in Au+Au collisions at $\sqrt{s}=200$ AGeV is calculated, and studied at high transverse momenta $p_T$. The soft thermalized nuclear medium is described within the framework of relativistic ideal three-dimensional hydrodynamics. The energy loss of partonic jets is evaluated in the context of gluon bremsstrahlung in the thermalized partonic matter. We provide a systematic analysis of the azimuthal asymmetry of $π_0$ suppression at high $p_T$ in central and non-central collisions, at mid and forward rapidity. The determination of $R_{…
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…
According to the flow narrative commonly applied to high-energy nuclear collisions a cylindrical-quadrupole component of 1D azimuth angular correlations is conventionally denoted by quantity $v_2$ and interpreted to represent elliptic flow. Jet angular correlations may also contribute to $v_2$ data as "nonflow" depending on the method used to calculate $v_2$, but 2D graphical methods are available to insure accurate separation. The nonjet (NJ) quadrupole has various properties inconsistent with a flow interpretation, including the observation that NJ quadrupole centrality variation in A-A coll…
Within A Multi-Phase Transport model, we investigate decorrelation of event planes over pseudorapidity and its effect on azimuthal anisotropy measurements in relativistic heavy-ion collisions. The decorrelation increases with increasing η gap between particles used to reconstruct the event planes. The third harmonic event planes are found even anticorrelated between forward and backward rapidities, the source of which may root in the opposite orientation of the collision geometry triangularities. The decorrelation may call into question the anisotropic flow measurements with pseudorapidity gap…
We examine dijet production at large rapidity intervals at Tevatron energies, by using the theory of Lipatov and collaborators which resums the leading powers of the rapidity interval. We analyze the growth of the Mueller-Navelet $K$-factor in this context and find it to be negligible. However, we do find a considerable enhancement of jet production at large transverse momenta. In addition, we show that the correlation in transverse momentum and azimuthal angle of the tagging jets fades away as the rapidity interval is increased.
In this talk we review the models describing the hard diffractive production of jets or more generally high-mass states in presence of rapidity gaps in hadron-hadron and lepton-hadron collisions. By rapidity gaps we mean regions on the lego plot in (pseudo)-rapidity and azimuthal angle where no hadrons are produced, between the jet(s) and an elastically scattered hadron (single hard diffraction) or between two jets (double hard diffraction).
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 dihadron azimuthal correlation produced nearly back-to-back in unpolarized hadron collisions, arising from the product of two Collins fragmentation functions. Using the latest Collins fragmentation functions extracted from the global analysis of available experimental data, we make predictions for the azimuthal correlation of two-pion production in $pp$ collisions at RHIC energies. We find that the correlation is sizable in the mid-rapidity region for moderate jet transverse momentum.
In the paper we discuss the angular correlation present in hadron-hadron collisions at large rapidity difference ($\bas\,y_{12}\,\gg\,1$). We find that in the CGC/saturation approach the largest contribution stems from the density variation mechanism. Our principal results are that the odd Fourier harmonics($v_{2n+1}$), decrease substantially as function of $y_{12}$, while the even harmonics ($v_{2n}$ ), increase considerably with a growth of $y_{12}$.
We discuss, in the framework of perturbative QCD at next to leading order, two related observables which are usually considered to provide tests of the BFKL dynamics : jet-jet correlations at Tevatron energies and forward particle-jet correlations at HERA. In the first case we study the rapidity gap dependence of the azimuthal correlations and find slightly too strong correlations at large gap. In the second case we discuss the cross section as well as the azimuthal correlations over a rapidity gap range of 5 units. We find that the requirement of a forward particle imposes strong kinematical …
The production of jet pairs with small transverse momentum and large relative rapidity in high energy hadron-hadron collisions is studied. The rise of the parton-level cross section with increasing rapidity gap is a fundamental prediction of the BFKL `perturbative pomeron' equation of Quantum Chromodynamics. However, at fixed collider energy it is difficult to disentangle this effect from variations in the cross section due to the parton distributions. It is proposed to study instead the distribution in the azimuthal angle difference of the jets as a function of the rapidity gap. The flattenin…
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 propose a new method to study transverse flow effects in relativistic nuclear collisions by Fourier analysis of the azimuthal distribution on an event-by-event basis in relatively narrow rapidity windows. The distributions of Fourier coefficients provide direct information on the magnitude and type of flow. Directivity and two dimensional sphericity tensor, widely used to analyze flow, emerge naturally in our approach, since they correspond to the distributions of the first and second harmonic coefficients, respectively. The role of finite particle fluctuations and particle correlations is …
Dihadron azimuth correlations can provide combinatoric access to jet structure in nuclear collisions. To isolate true jet yields a background must be subtracted, including a constant offset and a contribution from "elliptic flow" (azimuth quadrupole measured by $v^2_2$). The principle of "zero yield at minimum" (ZYAM) has been introduced to determine the constant offset. Independent measurements determine $v_2^2$. This analysis demonstrates that the ZYAM concept is invalid (offset typically overestimated) and $v_2^2$ is also overestimated by conventional measurements. Jet yields are thus subst…
In this paper we calculate the contribution to rapidity and angular correlations of the first Pomeron loop diagram in the dense partonic environment. This diagram is expected to give the largest contribution to the density variation mechanism of the angular correlations. We show that this diagrams leads to sizable contributions to the rapidity correlation functions of the order of $σ_{in} /\Lb πR^2\Rb$ where $σ_{in}$ is the inelastic cross section and $R$ is the size of the typical dipole inside the proton saturation scale. Therefore, the correlations do not depend on the saturation scale. We …
Analysis and interpretation of spectrum and correlation data from high-energy nuclear collisions is currently controversial because two opposing physics narratives derive contradictory implications from the same data---one narrative claiming collision dynamics is dominated by dijet production and projectile-nucleon fragmentation, the other claiming collision dynamics is dominated by a dense, flowing QCD medium. Opposing interpretations seem to be supported by alternative data models, and current model-comparison schemes are unable to distinguish between them. There is clearly need for a convin…
We extend the k_\perp-factorization formalism for exclusive photoproduction of vector mesons to the production of electroweak Z^0 bosons. Predictions for the gamma p \to Z^0 p and p p \to p p Z^0 reactions are given using an unintegrated gluon distribution tested against deep inelastic data. We present distributions in the Z^0 rapidity, transverse momentum of Z^0 as well as in relative azimuthal angle between outgoing protons. The contributions of different flavours are discussed. Absorption effects lower the cross section by a factor of 1.5-2, depending on the Z-boson rapidity. We also discus…
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…
Event geometry and initial state correlations have been invoked as possible explanations of long range azimuthal correlations observed in high multiplicity p+p and p+Pb collisions. We study the rapidity dependence of initial state momentum correlations and event-by-event geometry in $\sqrt{s}=5.02~\rm{TeV}$ p+Pb collisions within the 3+1D IP-Glasma model~\cite{Schenke:2016ksl}, where the longitudinal structure is governed by JIMWLK rapidity evolution of the incoming nuclear gluon distributions. We find that the event geometry is correlated across large rapidity intervals whereas initial state …
An established phenomenology and theoretical interpretation of $p$-$p$ collision data at lower collision energies should provide a reference for $p$-$p$ and other collision systems at higher energies, against which claims of novel physics may be tested. The description of $p$-$p$ collisions at the relativistic heavy ion collider (RHIC) has remained incomplete even as claims for collectivity and other novelties in data from smaller systems at the large hadron collider (LHC) have emerged recently. In this study we report the charge-multiplicity dependence of two-dimensional (2D) angular correlat…
Radial flow can be directly extracted from the azimuthal distribution of mean transverse rapidity. We apply the event-plane method and the two-particle correlation method to estimate the anisotropic Fourier coefficient of the azimuthal distribution of mean transverse rapidity. Using the event sample generated by a multiphase transport model with string melting, we show that both methods are effective. For the two-particle correlation method to be reliable, the mean number of particles in an azimuthal bin must be above a certain threshold. Using these two methods, anisotropic radial flow can be…
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 investigate the contributions from the so-called elliptic gluon Wigner distributions to the rapidity and azimuthal correlations of particles produced in high energy $pA$ collisions by applying the double parton scattering mechanism. We compute the `elliptic flow' parameter $v_2$ as a function of the transverse momentum and rapidity, and find qualitative agreement with experimental observations. This shall encourage further developments with more rigorous studies of the elliptic gluon distributions and their applications in hard scattering processes in $pp$ and $pA$ collisions.
Two-dimensional angular correlation data from the STAR experiment at RHIC and from the LHC experiments provide critical information about dynamical processes in relativistic heavy-ion collisions. The principal correlation structures of interest are a broad jet-related peak at small relative azimuth ($ϕ$) extending to large relative pseudorapidity ($η$), the dijet ridge at large relative azimuth, and an independent double ridge on $ϕ$ represented by a quadrupole function. The broad peak at small relative azimuth has been attributed, in large part, to initial-state fluctuations and hydrodynamic …
A phenomenological analysis is presented of recent two-particle angular correlation data on relative pseudorapidity ($η$) and azimuth reported by the Compact Muon Solenoid (CMS) Collaboration for $\sqrt{s}$ = 7 TeV proton-proton collisions. The data are described with an empirical jet-like model developed for similar angular correlation measurements obtained from heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC). The same-side (small relative azimuth), $η$-extended correlation structure, referred to as the {\em ridge}, is compared with three phenomenological correlation struct…
For high-pT forward processes at the Large Hadron Collider (LHC), QCD logarithmic corrections in the hard transverse momentum and in the large rapidity interval may both be quantitatively significant. The theoretical framework to resum consistently both kinds of logarithmic corrections to higher orders in perturbation theory is based on QCD high-energy factorization. We present numerical Monte Carlo applications of this method to final-state observables associated with production of one forward and one central jet. By computing jet correlations in rapidity and azimuth, we analyze the role of c…
We investigate the azimuthal anisotropy $v_2$ of particle production in nucleus-nucleus collisions in the maximum entropy approach. This necessitates two new phenomenological input parameters $δ$ and $λ_2$ compared with integrated multiplicity distributions. The parameter $δ$ describes the deformation of a flux tube and can be theoretically calculated in a bag model with a bag constant which depends on the density of surrounding flux tubes. The parameter $λ_2$ defines the anisotropy of the particle distribution in momentum space and can be connected to $δ$ via the uncertainty relation. In this…
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…
The elliptic flow coefficient ($v_{2}$) of $ϕ$ mesons at mid-rapidity as a function of transverse momentum ($p_{T}$) is measured for Au+Au collisions at centre of mass energy ($\sqrt{s_{NN}}$) 27 and 54.4 GeV. The $v_{2}$ measurement is done using event plane from Time Projection Chamber (TPC, $|η|$ $<$1.0) and Event Plane Detectors (EPD, 2.1$<$$|η|$$<$5.1) for 54.4 and 27 GeV, respectively. A high precision test of the number of constituent quark scaling of $ϕ$ meson $v_{2}$ (by including measurements for other hadrons) has been shown. The results are compared to transport model (AMPT) calcul…
The azimuthal asymmetry of minijet system produced at the early stage of nucleon-nucleon and nuclear collisions in a central rapidity window is studied. We show that in pp collisions the minijet transverse energy production in a central rapidity window is essentially unbalanced in azimuth due to asymmetric contributions in which only one minijet hits the acceptance window. We further study the angular pattern of transverse energy flow generated by semihard degrees of freedom at the early stage of high energy nuclear collisions and its dependence on the number of semihard collisions in the mode…
The two-particle short-range correlation functions in rapidity, azimuthal angle and transverse momentum, following from the decay of statistical clusters are evaluated and discussed.
We estimate the amount of collective "elliptic flow" expected at mid-rapidity in proton-proton (p-p) collisions at the CERN Large Hadron Collider (LHC), assuming that any possible azimuthal anisotropy of the produced hadrons with respect to the plane of the reaction follows the same overlap-eccentricity and particle-density scalings as found in high-energy heavy ion collisions. Using a Glauber eikonal model, we compute the p-p eccentricities, transverse areas and particle-multiplicities for various phenomenological parametrisations of the proton spatial density. For realistic proton transverse…
We introduce a new measurable quantity, $R_{Δϕ}$, for studies of the rapidity and transverse momentum dependence of dijet azimuthal decorrelations in hadron-hadron collisions. In pQCD, $R_{Δϕ}$ is computed as a ratio of three-jet and dijet cross sections in which the parton distribution functions cancel to a large extent. At the leading order, $R_{Δϕ}$ is proportional to $α_s$, and the transverse momentum dependence of can therefore be exploited to determine $α_s$. We compute the NLO pQCD theory predictions and non-perturbative corrections for $R_{Δϕ}$ at the LHC and the Tevatron and investiga…
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…
Within the AMPT Monte Carlo model, hot spots in the initial transverse parton density are shown to lead to harmonic flows which all contribute to dihadron azimuthal correlation. The net back-to-back dihadron correlation after subtraction of harmonic flows still has a double-peak that is independent of the initial geometric triangularity at a fixed impact-parameter and unique to the structure of jet-induced Mach cone and expanding hot spots dragged by radial flow. The longitudinal structure of hot spots also leads to a near-side ridge in dihadron correlation with a large rapidity gap. By succes…
Two dimensional low-$p_T$ dihadron correlations in azimuthal angle $ϕ$ and pseudo-rapidity $η$ in high-energy heavy-ion collisions are investigated within both the HIJING Monte Carlo model and an event-by-event (3+1)D ideal hydrodynamic model. Without final-state interaction and collective expansion, dihadron correlations from HIJING simulations have a typical structure from minijets that contains a near-side two-dimensional peak and an away-side ridge along the $η$-direction. In contrast, event-by-event (3+1)D ideal hydrodynamic simulations with fluctuating initial conditions from the HIJING+…
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…
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…
