Ridge formation in near-side correlation in heavy-ion collisions is studied in the framework of a phenomenological model, called Correlated Emission Model (CEM). Successive soft emissions due to jet-medium interaction lead to the enhancement of thermal partons which follow the local flow directions. The correlation between the flow direction and the semihard parton direction is the major factor that causes the ridge formation to depend on the trigger direction relative to the reaction plane. With the use of a few parameters we have been able to reproduce the data on the ridge yields as functions of the trigger azimuthal angle for different centralities. An inside-outside asymmetry function is proposed to further probe the characteristics of the azimuthal correlation function. Insights are provided for the understanding of some detailed aspects of the centrality dependence.
Azimuthal anisotropy is studied by taking into account the ridges created by semi-hard scattering, which is sensitive to the initial spatial configuration in non-central heavy-ion collisions. No rapid thermalization is required. Although hydrodynamics is not used in this study, the validity of hydrodynamical expansion is not excluded at later time after equilibration is achieved. Phenomenological properties of the bulk and ridge behaviors are used as inputs to determine the elliptic flow of pion and proton at low p_T. At intermediate p_T the recombination of shower partons with thermal partons…
The azimuthal angular dependence of the nuclear modification factor R_{AA}(p_T, phi,N_{part}) recently obtained by PHENIX is related at low p_T to the trigger phi dependence of the ridge yield as measured by STAR in a framework in which the azimuthal anisotropy is driven by semihard scattering near the surface. Careful consideration of the initial geometry leads to the determination of a surface segment in which the production of semihard partons are responsible for the phi dependence of the inclusive distribution on the one hand, and for the angular correlation in ridge phenomenology on the o…
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 …
Correlation studies exhibit a ridge-like feature in rapidity and azimuthal angle, with and without a jet trigger. We ask whether the feature in untriggered correlations can be a consequence of transverse flow and viscous diffusion.
Nuclear collisions exhibit long-range rapidity correlations not present in proton-proton collisions. Because the correlation structure is wide in relative pseudorapidity and narrow in relative azimuthal angle, it is known as the ridge. Similar ridge structures are observed in correlations of particles associated with a jet trigger (the hard ridge) as well as correlations without a trigger (the soft ridge). Earlier we argued that the soft ridge arises when particles formed in an early Glasma stage later manifest transverse flow. We extend this study to address new soft ridge measurements. We th…
The origin of the trigger-angle dependence of the ridge structure in two-hadron long-range correlations, as observed at RHIC, is discussed as due to an interplay between the elliptic flow caused by the initial state global geometry and flow produced by fluctuations.
Relativistic Heavy Ion Collider experiments exhibit correlations peaked in relative azimuthal angle and extended in rapidity. Called the ridge, this peak occurs both with and without a jet trigger. We argue that the untriggered ridge arises when particles formed by flux tubes in an early glasma stage later manifest transverse flow. Combining a blast wave model of flow fixed by single-particle spectra with a simple description of the glasma, we find excellent agreement with current data.
We present new results on 2-particle azimuthal ($Δϕ$) correlation relative to event plane and 3-particle pseudorapidity ($Δη$) correlation at mid-rapidity in Au+Au collisions at $\sqrt{{\it s}_{NN}}$ = 200 GeV, measured by the STAR experiment. While jet-like correlation is symmetric, ridge is found to be asymmetric when trigger particle azimuth is between in- and out-of-plane. The charge ordering properties between associated and trigger particles are exploited to separate jet-like and ridge contributions in 3-particle $Δη$-$Δη$ correlations. We found that like-sign triplets are dominated by r…
Peripheral one-tube model has shown to be a nice tool for dynamically understanding several aspects of ridge structures in long-range two-particle correlations, observed experimentally and obtained also in our model calculations using NexSPheRIO code. Here, we study an extension of the model, to initial configurations with several peripheral tubes distributed randomly in azimuth. We show that the two-particle correlation is almost independent of the number of tubes, although the flow distribution becomes indeed strongly event dependent. In our picture, the ridge structures are causally connect…
We review the models suggested, to date, as an explanation for the so called "ridge" phenomenon, an elongation in rapidity of 2-particle correlations seen at RHIC and LHC energies. We argue that these models can be divided into two phenomenologically distinct classes: "Hotspot+flow" driven correlations, where initial state correlations created by structures local in configuration space are collimated by transverse flow, and models where the azimuthal correlation is created through local partonic interactions in a high gluon density initial state. We further argue that the key to distinguish th…
Correlation measurements indicate that excess two particle correlations extend over causally disconnected rapidity ranges. Although, this enhancement is broad in relative rapidity $η=η_1 - η_2$, it is focused in a narrow region in relative azimuthal angle $ϕ=ϕ_1 - ϕ_2$. The resulting structure looks like a ridge centered at $η= ϕ=0$. Similar ridge structures are observed in correlations of particles associated with a jet trigger (the hard ridge) and in correlations without a trigger (the soft ridge). The long range rapidity behavior requires that the correlation originates in the earliest stag…
Hadron correlations in jets, ridges and opposite dijets at all $p_T$ above 2 GeV/c are discussed. Since abundant data are available from RHIC at intermediate $p_T$, a reliable hadronization scheme at that $p_T$ range is necessary in order to relate the semihard partonic processes to the observables. The recombination model is therefore first reviewed for that purpose. Final-state interaction is shown to be important for the Cronin effect, large B/M ratio and forward production. The effect of semihard partons on the medium is then discussed with particular emphasis on the formation of ridge wit…
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…
Pseudorapidity and azimuthal three-particle correlations are studied based on a correlated-cluster model of multiparticle production. The model provides a common framework for correlations in proton-proton and heavy-ion collisions allowing easy comparison with the measurements. It is shown that azimuthal cluster correlations are definitely required in order to understand three-particle correlations in the near-side ridge effect. This is similar to the explanation of the ridge phenomenon found in our previous analysis of two-particle correlations and generalizes the model to higher-order correl…
Two-dimensional correlation functions in $Δη-Δϕ$ for charged hadrons emitted in heavy-ion collisions are calculated in event-by-event hydrodynamics. With the Glauber model for the initial density distributions in the transverse plane and elongated density profiles in the longitudinal direction, the flow patterns in the azimuthal angle of the two-dimensional correlation function are properly reproduced. We show that the additional fall-off of the same-side ridge in the longitudinal direction can be explained as an effect of local charge conservation at a late stage of the evolution. This additi…
Azimuthal anisotropy in heavy-ion collisions is studied by taking into account the ridges generated by semi-hard scattering of intermediate-momentum partons, which can be sensitive to the initial spatial configuration of the medium in non-central collisions. In a simple treatment of the problem where the recombination of only thermal partons is considered, analytical formulas can be derived that yield results in accord with the data on v_2 for p_T <1-2 GeV/c. Centrality dependence is described by a geometrical factor. Ridge phenomenology is used to determine the initial slopes of v_2 at low p_…
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 argue that "ridge" in 2-particle correlation function associated with hard trigger at RHIC heavy ion collisions is naturally explained by an interrelation of jet quenching and hydrodynamical transverse flow. The excess particles forming the ridge are produced by QCD bremsstrahlung along the beam (and thus have wide rapidity distribution) and then boosted by transverse flow. Nontrivial correlation between directions of the jet and the radial flow is provided by jet quenching: our straightforward and basically parameter-independent calculation reproduces the angular shape, width and other pro…
We discuss the physics of the ridge -- azimuthally collimated long range rapidity correlations -- in high multiplicity proton-proton and proton-nucleus collisions. We outline some of the theoretical discussions in the literature that address the systematics of these ridge correlations.
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…
We point out that Bose enhancement in a hadronic wave function generically leads to correlations between produced particles. We show explicitly, by calculating the projectile density matrix in the Color Glass Condensate approach to high-energy hadronic collisions, that the Bose enhancement of gluons in the projectile leads to azimuthal collimation of long range rapidity correlations of the produced particles, the so-called ridge correlations.
An event generator is constructed on the basis of a model of multiple scattering of partons so that the trajectory of a parton traversing a dense and expanding medium can be tracked. The parameters in the code are adjusted to fit the Δϕazimuthal distribution on the far side when the trigger momentum is in the non-perturbative region, p_T(trigger)<4 GeV/c. The dip-bump structure for 1<p_T(assoc)<2.5 GeV/c is reproduced by averaging over the exit tracks of deflected jets. An essential characteristic of the model, called Markovian Parton Scattering (MPS) model, is that the scattering angle is ran…
An interpretation of the ridge phenomenon found in pp collisions at 7 TeV is given in terms of enhancement of soft partons due to energy loss of semihard jets. A description of ridge formation in nuclear collisions can directly be extended to pp collisions, since hydrodynamics is not used, and azimuthal anisotropy is generated by semihard scattering. Both the p_T and multiplicity dependencies are well reproduced. Some suggestions are made about other observables.
We study untriggered di-hadron correlations in Pb+Pb at 2.76 TeV, based on an event-by-event simulation of a hydrodynamic expansion starting from flux tube initial conditions. The correlation function shows interesting structures as a function of the pseudorapidity difference $Δη$ and the azimuthal angle difference $Δϕ$, in particular comparing different centralities. We can clearly identify a peak-like nearside structure associated with very low momentum components of jets for peripheral collisions, which disappears towards central collisions. On the other hand, a very broad ridge structure f…
In this paper, we investigate the influence of coherent pion emission on long-range azimuthal correlations in relativistic proton-proton collisions. We study the pion momentum distribution for a coherent source with both transverse and Bjorken longitudinal expansions, and calculate the two-particle correlation function $C(Δη,Δϕ)$. A "ridge" structure is observed in the correlation function $C(Δη,Δϕ)$ of the coherent pion emission, whether the coherent source is expanding or static. The onset of this long-range azimuthal correlation can be traced back to the asymmetric initial transverse profil…
Using the CGC formalism, we calculate the two-gluon rapidity correlations of strong colour fields in $pp$, $pA$ and $AA$ collisions, respectively. If one trigger gluon is fixed at central rapidity, a ridge-like correlation pattern is obtained in symmetry $pp$ and $AA$ collisions, and a huge bump-like correlation pattern is presented in asymmetry $pA$ collisions. It is demonstrated that the ridge-like correlation patterns are caused by the stronger correlation with the gluon of colour source. The transverse momentum and incident energy dependence of the ridge-like correlation pattern is also sy…
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.
Dihadron correlations with a high-pt trigger particle are analyzed by STAR relative to the event plane in Au+Au collisions at 200 GeV (arXiv:1010.0690v1). The elliptic and quadrangular flow anisotropies are subtracted. The remaining dihadron correlation signals are found to be composed of a near-side peak, which is separated into jet-like and "ridge"-like components, and an away-side correlation structure. The ridge-like structure is found to decrease with the trigger particle azimuthal angle relative to the event plane from in-plane to out-of-plane. The away-side structure is found to evolve …
One of the most important experimental results for proton-proton scattering at the LHC is the observation of a so-called "ridge" structure in the two particle correlation function versus the pseudorapidity difference $Δη$ and the azimuthal angle difference $Δϕ$. One finds a strong correlation around $Δϕ=0$, extended over many units in $Δη$. We show that a hydrodynamical expansion based on flux tube initial conditions leads in a natural way to the observed structure. To get this result, we have to perform an event-by-event calculation, because the effect is due to statistical fluctuations of th…
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…
We demonstrate that in the framework of the event-by-event hydrodynamics followed by statistical hadronization, the proper charge conservation in the mechanism of hadron production provides the crucial non-flow component and leads to agreement with the two-dimensional two-particle correlation data in relative azimuthal angle and pseudorapidity at soft transverse momenta (p_T<2GeV). The fall-off of the same-side ridge in relative pseudorapidity follows from the fact that a pair of particles with balanced charges is emitted from the same fluid element, whose collective velocity collimates the mo…
We show that the long-range rapidity correlations between the produced charged-hadron pairs from two BFKL parton showers generate considerable azimuthal angle correlations. These correlations have no 1/N_c suppression. The effect of gluon saturation on these correlations are discussed and we show that it is important. We show that a pronounced ridge-like structure emerges by going from the BFKL to the saturation region. We show that the ridge structure at high-energy proton-proton and nucleus-nucleus collisions has the same origin and its main feature can be understood due to initial-state eff…
The 2D azimuth & rapidity structure of the two-particle correlations in relativistic A+A collisions is altered significantly by the presence of sharp inhomogeneities in superdense matter formed in such processes. The causality constraints enforce one to associate the long-range longitudinal correlations observed in a narrow angular interval, the so-called (soft) ridge, with peculiarities of the initial conditions of collision process. This study's objective is to analyze whether multiform initial tubular structures, undergoing the subsequent hydrodynamic evolution and gradual decoupling, can f…
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…
In this paper, we give an account of the peripheral-tube model, which has been developed to give an intuitive and dynamical description of the so-called ridge effect in two-particle correlations in high-energy nuclear collisions. Starting from a realistic event-by-event fluctuating hydrodynamical model calculation, we first show the emergence of ridge + shoulders in the so-called two-particle long-range correlations, reproducing the data. In contrast to the commonly used geometric picture of the origin of the anisotropic flow, we can explain such a structure dynamically in terms of the presenc…
Dihadron azimuthal angle correlations relative to the reaction plane have been investigated in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV using a multi-phase transport model (AMPT). Such reaction plane azimuthal angle dependent correlations can shed light on path-length effect of energy loss of high transverse momentum particles propagating through the hot dense medium. The correlations vary with the trigger particle azimuthal angle with respect to the reaction plane direction, $ϕ_{s}=ϕ_{T}-Ψ_{EP}$, which is consistent with the experimental observation by the STAR collaboration. The dihad…
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 …
In the momentum kick model, a near-side jet emerges near the surface, kicks medium partons, loses energy, and fragments into the trigger particle and fragmentation products. The kicked medium partons subsequently materialize as the observed ridge particles, which carry direct information on the magnitude of the momentum kick and the initial parton momentum distribution at the moment of jet-(medium parton) collisions. The initial parton momentum distribution extracted from the STAR ridge data for central AuAu collisions at \sqrt{s_{NN}}=200 GeV has a thermal-like transverse momentum distributio…
We report the first three-particle coincidence measurement in pseudorapidity ($Δη$) between a high transverse momentum ($p_{\perp}$) trigger particle and two lower $p_{\perp}$ associated particles within azimuth $\mid$$Δϕ$$\mid$$<$0.7 in $\sqrt{{\it s}_{NN}}$ = 200 GeV $d$+Au and Au+Au collisions. Charge ordering properties are exploited to separate the jet-like component and the ridge (long-range $Δη$ correlation). The results indicate that the particles from the ridge are uncorrelated in $Δη$ not only with the trigger particle but also between themselves event-by-event. In addition, the prod…
We analyze PHENIX near-side ridge data for central Au+Au collisions at \sqrt{s_{NN}}=200 GeV with the momentum kick model, in which a near-side jet emerges near the surface, kicks medium partons, loses energy, and fragments into the trigger particle and fragmentation products. The kicked medium partons subsequently materialize as the observed ridge particles, which carry direct information on the early parton momentum distribution and the magnitude of the momentum kick. We find that the PHENIX ridge data can be described well by the momentum kick model and the extracted early partons momentum …
The STAR Collaboration reported measurements of di-hadron azimuthal correlation in medium-central Au+Au collisions at 200 A$\,$GeV, where the data are presented as a function of the trigger particle's azimuthal angle relative to the event plane $ϕ_s $. In particular, it is observed that the away-side correlation evolves from single- to double-peak structure with increasing $ϕ_s$. In this work, we present the calculated correlations as functions of both $ϕ_s$ and particle transverse momentum $p_T $, using the hydrodynamic code NeXSPheRIO. The results are found to be in reasonable agreement with…
STAR measurements of dihadron correlations with high-pt trigger partcles in Au+Au collisions at 200 GeV are presented with subtraction of v2, v3, and v4 backgrounds. The vn azimuthal anisotropies were measured by the two-particle cumulant method with η gap to reduce nonflow. The dihadron correlations relative to the v2 as well as the v3 harmonic planes are also presented. Implications of the results are discussed.
We obtain prompt di-photon cross-section in proton-nucleus collisions in Hamiltonian light-cone approach within a hybrid approximation, treating the projectile proton in the parton model and the target nucleus in the Color-Glass-Condensate approach. We study in details the di-photon correlations in quark-nucleus and proton-nucleus collisions at RHIC and the LHC. We show that the single fragmentation di-photon produces the away side correlations peak, and the double fragmentation component of prompt di-photon is responsible for the near-side peak, and the long-range in rapidity near-side azimut…
The novel phenomena observed in particle angular correlations are reviewed. They include the double-peak away-side azimuthal correlations in relativistic heavy-ion collisions and the long-range pseudorapidity near-side (ridge) correlations in heavy-ion as well as in proton-induced collisions. The collision system and energy dependence of these phenomena are examined, wherever possible and most abundantly for the ridge correlations. Their possible theoretical interpretations and what might be learned about the properties of the collision systems from theoretical comparisons are discussed. Prosp…
Using the AMPT model for relativistic heavy ion collisions, we have studied the di-hadron azimuthal angular correlations triggered by emitted jets in Au+Au collisions at center of mass energy $\sqrt{s_{NN}}=200$ GeV and impact parameter $b=8$ fm. A double-peak structure for the associated particles at the away side of trigger particles is obtained after subtracting background correlations due to the elliptic flow. Both the near-side peak and the away-side double peaks in the azimuthal angular correlations are, however, significantly suppressed (enhanced) in events of small (large) triangular f…
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+…
In an earlier paper we developed a Parton Bubble Model (PBM) for RHIC/LHC, based on a substructure of a ring of localized bubbles which initially contain 3-4 partons of almost entirely gluons. A Glasma Flux Tube Model (GFTM) which formed longitudinal flux tubes in the transverse plane of two colliding sheets of Color Glass Condensate (CGC) which pass through one another had been developed. These sheets create boost invariant flux tubes of longitudinal color electric and magnetic fields. A blast wave gives the tubes near the surface transverse flow in the same way it gave flow to the bubbles in…
We extend the CGC approach to calculation of the double inclusive gluon production by including high-density effect in the CGC wave function of the projectile (proton). Our main result is that these effects lead to the appearance of odd harmonics in the two-particle correlation C(k,p). We find that in the high momentum limit, |k|,|p|>>Q_s, this results in a positive c_1{2}. Additionally when the magnitudes of the two momenta are approximately equal, |k|/|p| ~ 1, the density effects also generate a positive third harmonic c_3{2}, which translates into a non-vanishing v_3 when the momenta of the…
Two-particle correlations in relative rapidity and azimuth are studied for the p-Pb collisions at the LHC energy of 5.02 TeV in the framework of event-by-event 3+1-dimensional viscous hydrodynamics. It is found that for the highest-multiplicity events the observed ridge structures appear in a natural way, suggesting that collective flow may be an important element in the evolution of the system. We also discuss the role of the charge balancing and the transverse-momentum conservation.
Azimuthal correlations of charged hadrons with direct-photon ($γ_{dir}$) and neutral-pion ($π^{0}$) trigger particles are analyzed in central Au+Au and minimum-bias $p+p$ collisions at $\sqrt{s_{_{NN}}} = 200$ GeV in the STAR experiment. The charged-hadron per-trigger yields at mid-rapidity from central Au+Au collisions are compared with $p+p$ collisions to quantify the suppression in Au+Au collisions. The suppression of the away-side associated-particle yields per $γ_{dir}$ trigger is independent of the transverse momentum of the trigger particle ($p_{T}^{\mathrm{trig}}$), whereas the suppres…
