Range Rapidity Correlations Research Articles

Origins of collectivity in small systems

We review recent developments in the theoretical description and understanding of multi-particle correlation measurements in collisions of small projectiles (p/d/3He) with heavy nuclei (Au, Pb) as well as proton+proton collisions. We focus on whether the physical processes responsible for the observed long range rapidity correlations and their azimuthal structure are the same in small systems as in heavy ion collisions. In the latter they are interpreted as generated by the initial spatial geometry being transformed into momentum correlations by strong final state interactions. However, explicit calculations show that also initial state momentum correlations are present and could contribute to observables in small systems. If strong final state interactions are present in small systems, recent developments show that results are sensitive to the shape of the proton and its fluctuations.

Bose-Einstein correlations andv2nandv2n−1in hadron and nucleus collisions

We show that Bose-Einstein correlations of identical particles in hadron and nucleus high energy collisions, lead to long range rapidity correlations in the azimuthal angle. These correlations are inherent features of the CGC/saturation approach, however, their origin is more general than this approach. In framework of the proposed technique both even and odd $v_n$ occur naturally, independent of the type of target and projectile. We are of the opinion that it is premature to conclude that the appearance of azimuthal correlations are due to the hydrodynamical behaviour of the quark-gluon plasma.

Perturbative QCD and beyond: Azimuthal angle correlations in deuteron-deuteron scattering from Bose-Einstein correlations

In this paper, we found within the framework of perturbative QCD, that in deuteron-deuteron scattering the Bose-Einstein correlations due to two parton showers production, induce azimuthal angle correlations, with three correlation lengths: the size of the deuteron ($R_D$), the proton radius ($R_N$), and the size of the BFKL Pomeron which, is closely related to the saturation momentum ($R_c \sim 1/Q_s$). These correlations are independent of the values of rapidities of the produced gluons (long range rapidity correlations), for large rapidities ($\bas |y_1 - y_2| \geq 1$), and have no symmetry with respect to $\phi \to \pi - \phi$ ($ \vec{p}_{T1} \to - \vec{p}_{T1}$). Therefore, they give rise to $v_n$ for all values of $n$, not only even values. The contributions with the correlation length $R_D$ and $R_N$ crucially depend on the non-perturbative contributions, and to obtain estimates of their values, requiries a lot of modeling, while the correlations with $R_c \sim 1/Q_s$ have a perturbative QCD origin, and can be estimated in the ColorGlass Condensate (CGC) approach.

The Ridge and Di-hadron Correlations from the BES at RHIC

Di-hadron correlations are a key observable in heavy-ion collisions, and play a critical role in establishing the equation of state for hot and dense nuclear matter. In this analysis, the first set of results of 2D di-hadron correlations (Δϕ, Δη) for Au+Au collisions with center-of-mass energies sNN=7.7,11.5,14.5,19.6,27, and 39 GeV from the STAR experiment is presented. Anisotropy coefficients of second and third orders (ν2,3{2}) from long range rapidity correlations of di-hadrons are obtained, and when scaled by multiplicity, ν32 shows a non-monotonic behavior as a function of energy.

Photon-jet ridge at RHIC and the LHC

We investigate long range rapidity correlations of pairs of prompt photon and jet in the Color Glass Condensate (CGC) framework in proton-proton and proton-nucleus collisions at RHIC and the LHC. We show that photon-jet correlations exhibit long-range azimuthal collimation at near-side for low transverse momenta of the produced photon and jet in high-multiplicity events. These ridge-like features are strikingly similar to the observed ridge effect for di-hadron correlations at RHIC and the LHC. We show that correlations in the relative rapidity and the relative azimuthal angle between pairs of prompt photon and jet strongly depend on the gluon saturation dynamics at small-x kinematics and such measurements can help to understand the true origin of the observed di-hadron ridge in p+A collisions, and address whether the ridge is a universal phenomenon for all two particle correlations at high energy and high multiplicity events. We also investigate if there is a ridge-like structure for photon-hadron pair correlations at RHIC and the LHC. We found that the hadronization of jet has non-trivial effects on the photon-jet correlations.

CGC/saturation approach for high energy soft interactions:v2in proton-proton collisions

In this paper we continue our program to construct a model for high energy soft interactions, based on the CGC/saturation approach. We demonstrate that in our model which describes diffractive physics as well as multi-particle production at high energy, the density variation mechanism leads to the value of $v_2$ which is about $60\% \div 70\%$ of the measured $v_2$. Bearing in mind that in CGC/saturation approach there are two other mechanisms present: Bose enhancement in the wave function and local anisotropy, we believe that the azimuthal long range rapidity correlations in proton-proton collisions stem from the CGC/saturation physics, and not from quark-gluon plasma production.

Energy dependence of the ridge in high multiplicity proton-proton collisions

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 that the azimuthal structure of these recent ATLAS ridge measurements strongly constrain hydrodynamic interpretations of such correlations in high multiplicity p+p collisions.

Initial State Correlations and the Ridge

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.

CGC/saturation approach for soft interactions at high energy: long range rapidity correlations

In this paper we continue our program to build a model for high energy soft interactions, that is based on the CGC/saturation approach.The main result of this paper is that we have discovered a mechanism that leads to large long range rapidity correlations, and results in large values of the correlation function $R\Lb y_1,y_2\Rb \,\geq \,1$, which is independent of $y_1$ and $ y_2$. Such behaviour of the correlation function, provides strong support for the idea, that at high energies the system of partons that is produced, is not only dense, but also has strong attractive forces acting between the partons.

Bose enhancement and the ridge

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.

Entanglement entropy and entropy production in the color glass condensate framework

We compute the entanglement entropy of soft gluons in the wave function of a fast moving hadron and discuss its basic properties. We also derive the expression for entropy production in a high energy hadronic collision within the Color Glass formalism. We show that long range rapidity correlations give negative contribution to the production entropy. We calculate the (naturally defined) temperature of the produced system of particles, and show that it is proportional to the average transverse momentum of the produced particles.

Eccentric protons? Sensitivity of flow to system size and shape in p+p, p+Pb, and Pb+Pb collisions.

We determine the transverse system size of the initial nonequilibrium Glasma state and of the hydrodynamically evolving fireball as a function of produced charged particles in p+p, p+Pb, and Pb+Pb collisions at the Large Hadron Collider. Our results show features similar to those of recent measurements of Hanbury Brown-Twiss (HBT) radii by the ALICE Collaboration. Azimuthal anisotropy coefficients vn generated by combining the early time Glasma dynamics with viscous fluid dynamics in Pb+Pb collisions are in excellent agreement with experimental data for a wide range of centralities. In particular, event-by-event distributions of the vn values agree with the experimental data out to fairly peripheral centrality bins. In striking contrast, our results for p+Pb collisions significantly underestimate the magnitude and do not reproduce the centrality dependence of data for v2 and v3 coefficients. We argue that the measured vn data and HBT radii strongly constrain the shapes of initial parton distributions across system sizes that would be compatible with a flow interpretation in p+Pb collisions. Alternately, additional sources of correlations may be required to describe the systematics of long-range rapidity correlations in p+p and p+Pb collisions.

Long range correlations in high multiplicity hadron collisions: Building bridges with ridges

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.

Explanation of systematics of CMSp+Pbhigh multiplicity dihadron data atsNN=5.02 TeV

In a recent article (arXiv:1210.3890), we showed that high multiplicity di-hadron proton- proton (p+p) data from the CMS experiment are in excellent agreement with computations in the Color Glass Condensate (CGC) Effective Field Theory (EFT). This agreement of the theory with several hundred data points provides a non-trivial description of both nearside ("ridge") and away-side azimuthal collimations of long range rapidity correlations in p+p collisions. Our prediction in arXiv:1210.3890 for proton-lead (p+Pb) collisions is consistent with results from the recent CMS p+Pb run at $\sqrt{s}_{\rm NN} = 5.02$ TeV for the largest track multiplicity $N_{\rm track}\sim 40$ we considered. The CMS p+Pb data shows the following striking features: i) a strong dependence of the ridge yield on $N_{\rm track}$, with a significantly larger signal than in p+p for the same $N_{\rm track}$, ii) a stronger $p_T$ dependence than in p+p for large $N_{\rm track}$, and iii) a nearside collimation for large $N_{\rm track}$ comparable to the awayside for the lower $p_T = p_{T}^{\rm trig.}=p_{T}^{\rm assoc.}$ di-hadron windows. We show here that these systematic features of the CMS p+Pb di-hadron data are all described by the CGC (with parameters fixed by the p+p data) when we extend our prediction in arXiv:1210.3890 to rarer high multiplicity events. We also predict the azimuthally collimated yield for yet unpublished windows in the $p_{T}^{\rm trig.}$ and $p_{T}^{\rm assoc.}$ matrix.

Azimuthal Collimation of Long Range Rapidity Correlations by Strong Color Fields in High Multiplicity Hadron-Hadron Collisions

The azimuthal collimation of dihadrons with large rapidity separations in high multiplicity p+p collisions at the LHC is described in the color glass condensate (CGC) effective theory [A. Dumitru, K. Dusling, F. Gelis, J. Jalilian-Marian, T. Lappi, and R. Venugopalan, Phys. Lett. B 697, 21 (2011).] by N(c)(2) suppressed multiladder QCD diagrams that are enhanced α(S)(-8) due to gluon saturation in hadron wave functions. We show that quantitative computations in the CGC framework are in good agreement with data from the CMS experiment on per trigger dihadron yields and predict further systematics of these yields with varying trigger p(T) and charged hadron multiplicity. Radial flow generated by rescattering is strongly limited by the structure of the p+p dihadron correlations. In contrast, radial flow explains the systematics of identical measurements in heavy ion collisions.

Hidden asymmetry and long range rapidity correlations

Interpretation of long-range rapidity correlations in terms of the fluctuating rapidity density distribution of the system created in high-energy collisions is proposed. When applied to recent data of the STAR Collaboration, it shows a substantial asymmetric component in the shape of this system in central Au–Au collisions, implying that boost invariance is violated on the event-by-event basis even at central rapidity. This effect may seriously influence the hydrodynamic expansion of the system.

Centrality and energy dependence of rapidity correlation patterns in relativistic heavy ion collisions

The centrality and energy dependence of rapidity correlation patterns are studied in Au+Au collisions by using AMPT with string melting, RQMD and UrQMD models. The behaviors of the short-range correlation (SRC) and the long-range correlation (LRC) are presented clearly by two spatial-position dependent correlation patterns. For centrality dependence, UrQMD and RQMD give similar results as those in AMPT, i.e., in most central collisions, the correlation structure is flatter and the correlation range is larger, which indicates a long range rapidity correlation. A long range rapidity correlation showing up in RQMD and UrQMD implies that parton interaction is not the only source of long range rapidity correlations. For energy dependence, AMPT with string melting and RQMD show quite different results. The correlation patterns in RQMD at low collision energies and those in AMPT at high collision energies have similar structures, i.e. a convex curve, while the correlation patterns in RQMD at high collision energies and those in AMPT at low collision energies show flat structures, having no position dependence. Long range rapidity correlation presents itself at high energy and disappears at low energy in RQMD, which also indicates that long range rapidity correlations may come from some trivial effects, rather than the parton interactions.

Two-Hadron Correlations in the Color Glass Condensate Formalism

Two-hadron correlations are a sensitive probe of the dynamics of gluon saturation and the Color Glass Condensate formalism where the degrees of freedom are Wilson lines of the gluon field. It is shown that unlike structure functions in DIS and single hadron production in proton-nucleus collisions, higher point functions of Wilson lines appear in two-hadron production cross section. We derive equations for the energy ($x$) evolution of these higher point functions using the JIMWLK Hamiltonian and show that dipole approximation, employed in the literature to fit the di-hadron data measured by the STAR collaboration in the forward rapidity region, breaks down. This necessitates an investigation of the full hierarchy of the JIMWLK evolution equations for these higher point functions and their solutions. This can then be used to make a quantitative analysis of the di-hadron correlations in the forward rapidity region in deuteron-gold collisions at RHIC and in the long range rapidity correlations observed in proton-proton collisions at the LHC.

Multiplicity distributions and long range rapidity correlations

The physics of the initial conditions of heavy ion collisions is dominated by the nonlinear gluonic interactions of QCD. These lead to the concepts of parton saturation and the Color Glass Condensate (CGC). We discuss recent progress in calculating multigluon correlations in this framework, prompted by the observation that these correlations are in fact easier to compute in a dense system (nucleus–nucleus) than a dilute one (proton–proton).

Long range correlations, event simulation and parton percolation

We study the RHIC data on long range rapidity correlations, comparing their main trends with different string model simulations. Particular attention is paid to color percolation model and its similarities with color glass condensate. As both approaches corresponds, at high density, to a similar physical picture, both of them give rise to a similar behavior on the energy and the centrality of the main observables. Color percolation explains the transition from low density to high density.