Long-range Rapidity Correlations Research Articles

Closing in on critical net-baryon fluctuations at LHC energies: Cumulants up to third order in Pb–Pb collisions

Fluctuation measurements are important sources of information on the mechanism of particle production at LHC energies. This article reports the first experimental results on third-order cumulants of the net-proton distributions in Pb–Pb collisions at a center-of-mass energy sNN=5.02 TeV recorded by the ALICE detector. The results on the second-order cumulants of net-proton distributions at sNN=2.76 and 5.02 TeV are also discussed in view of effects due to the global and local baryon number conservation. The results demonstrate the presence of long-range rapidity correlations between protons and antiprotons. Such correlations originate from the early phase of the collision. The experimental results are compared with HIJING and EPOS model calculations, and the dependence of the fluctuation measurements on the phase-space coverage is examined in the context of lattice quantum chromodynamics (LQCD) and hadron resonance gas (HRG) model estimations. The measured third-order cumulants are consistent with zero within experimental uncertainties of about 4% and are described well by LQCD and HRG predictions.

Long-Range Correlations between Observables in a Model with Translational Invariance in Rapidity

We estimate the impact of the fixation of the total number of sources (quark–gluon strings) on the long-range rapidity correlations between different observables. In our approach this condition models the fixation of the collision centrality class, what is the usual practice in modern collider experiments, like Relativistic Heavy Ion Collider (RHIC), Large Hadron Collider (LHC) and so on. The estimates are obtained under the assumption of the translational invariance in rapidity, which is usually assumed in mid-rapidity region at high energies. Based on these assumptions, we are developing a technique for the analytical calculation of various average values of extensive and intense variables at high string densities on the transverse lattice, taking into account the effects of string fusion, leading to the formation of string clusters. Using this technique we calculate the asymptotes of the correlations coefficients both between the multiplicities and between the multiplicity and the event-mean transverse momentum of particles in two separated rapidity intervals. As a result, we found that fixing the total number of strings has a significant effect on the behavior of both types of correlations, especially in the case of a uniform distribution of strings in the transverse plane.

Calculation of Long-Range Rapidity Correlations in the Model with String Fusion on a Transverse Lattice

By the model with the fusion of quark-gluon strings on a transverse lattice the correlations between observables from separated rapidity intervals in high-energy hadronic interactions are considered. The asymptotes of the long-range rapidity correlation coefficients between the multiplicities (n–n) and between the event-mean transverse momentum and the multiplicity of charged particles (pt–n) in these observation windows at large string density were explicitly calculated with the additional condition fixing the total number of initial strings. It is shown that this condition, which imitates in our model the fixation of the collision centrality class, has a significant impact on the behavior of the n–n and pt–n correlation coefficients for both homogeneous and inhomogeneous distribution of strings in the transverse plane.

Correlations between multiplicities and transverse momenta in nucleus-nucleus collisions from model with cluster of fused color strings

The long-range rapidity correlations between the multiplicities (n-n) and the transverse momentum and the multiplicity (pT-n) of charged particles are analyzed in the framework of the simple string inspired model with two types of sources. The sources of the first type correspond to the initial strings formed in a hadronic collision. The sources of the second type imitate the appearance of the emitters of a new kind resulting from interaction (fusion) of the initial strings. The model enabled to describe effectively the influence of the string fusion effects on the strength both the n-n and the pT-n correlations. Modification of the model to the analogue of the “core-corona” mechanism allows to take into account event selection criteria based on centrality and perform a comparison with existing experimental data on correlation measurements in nucleus-nucleus collisions at LHC energies. It is shown that string fusion effects in the model with the core-corona mechanism lead to the change of a sign of the pT-n correlation coefficient with a decrease of a centrality interval width.

Short- and long-range rapidity correlations in the model with a lattice in transverse plane

In the framework of the quark-gluon string model we consider the various fluctuation and correlation observables used in the analysis of the multiparticle production in hadronic interactions at high energy. We express these observables through the fundamental string characteristics and analyze their resulting properties: the dependence on the width of observation window(s), the range of the correlation in rapidity, the intensive or strongly intensive behavior. To take into account the influence of a string fusion processes on the string characteristics and on the behavior of the observables. we use the version of string model with a lattice (grid) in the impact parameter plane. In particular we show that the observable between multiplicities in two acceptance windows separated in rapidity, which is a strongly intensive in the case with independent identical strings, loses this property, when we take into account the string fusion and the formation of strings of a few different types takes place in a collision.

Cumulant expansion in gluon saturation and five- and six-gluon azimuthal correlations

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 expansion of the gluon correlators that is valid in the gluon saturation limit. We show that the cumulant expansion of the gluon correlators that is used for counting the number of diagrams to be calculated does not follow the standard cumulant expansion. We also explain how these findings can be used in obtaining experimentally relevant observables such as flow coefficients calculated from correlations as well as ratios of the correlation functions of different orders.

Long-range rapidity correlations between mean transverse momenta

The forward-backward correlation strength between event-mean transverse momenta of particles produced in separated rapidity intervals in high energy hadronic collisions is analyzed in the simple model with the string fusion on a transverse lattice. The coefficient of long-range rapidity p t - p t correlation is obtained using the negative binomial distribution for the number of strings, which is closer to reality than the poissonian one. The results demonstrate good agreement with the asymptotes of the correlation coefficient analytically calculated earlier at large string density. It is observed that at LHC energy the p t - p t correlation coefficient reveals the drop for most central collisions. The model calculations show that the physical reason for this decrease is the attenuation of color field fluctuations due to the string fusion at large string density, whereas at RHIC energy the string density is not enough to provide a decline of the correlation coefficient for most central collisions.

Heavy-flavour production in high-energy d-Au and p-Pb collisions

Soft-hadron measurements in high-energy collisions of small systems like p-Pb and d-Au show peculiar qualitative features (long-range rapidity correlations, flattening of the $p_T$-spectra with increasing hadron mass and centrality, non-vanishing Fourier harmonics in the azimuthal particle distributions) suggestive of the formation of a strongly-interacting medium displaying a collective behaviour, with a hydrodynamic flow as a response to the pressure gradients in the initial conditions. Hard observables (high-$p_T$ jet and hadron spectra) on the other hand, within the current large systematic uncertainties, appear only midly modified with the respect to the benchmark case of minimum-bias p-p collisions. What should one expect for heavy-flavour particles, initially produced in hard processes but tending, in the nucleus-nucleus case, to approach kinetic equilibrium with the rest of the medium? This is the issue we address in the present study, showing how the current experimental findings are compatible with a picture in which the formation of a hot medium even in proton-nucleus collisions modifies the propagation and hadronization of heavy-flavour particles.

Multiparticle long-range rapidity correlations from fluctuation of the fireball longitudinal shape

We calculate the genuine long-range multi-particle rapidity correlation functions, $C_{n}(y_1,...,y_n)$ for $n=3,4,5,6$, originating from fluctuations of the fireball longitudinal shape. In these correlation functions any contribution from the short-range two-particle correlations, and in general up to $(n-1)$-particle in $C_n$, is suppressed. The information about the fluctuating fireball shape in rapidity is encoded in the cumulants of coefficients of the orthogonal polynomial expansion of particle distributions in rapidity.

Long-range rapidity correlations between mean transverse momenta in the model with string fusion

The long-range correlation between mean-event transverse momenta, being robust against the volume fluctuations and the details of the centrality determination, enables to obtain the signatures of string fusion at the initial stage of hadronic interaction in relativistic heavy ion collisions. The dependence of the correlation strength between mean-event transverse momenta on the collision centrality and initial energy is analyzed in a simple model with quark-gluon string fusion on the transverse lattice. It is shown that above RHIC energy the dependence reveals the decline of the correlation coefficient for most central collisions, reflecting the attenuation of color field fluctuations due to the string fusion at large string density. It is also found that contrary to the correlation between transverse momenta of single particles the strength of the correlation between mean-event transverse momenta of particles in two separated rapidity intervals is not decreasing with the total number of produced strings, remaining significant even in the case of Pb-Pb collisions, in which the total number of strings can reach several thousand.

Novel collective phenomena in high-energy proton–proton and proton–nucleus collisions

The observation of long-range rapidity correlations among particles in high-multiplicity p–p and p–Pb collisions has created new opportunities for investigating novel high-density QCD phenomena in small colliding systems. We review experimental results related to the study of collective phenomena in small systems at RHIC and the LHC along with the related developments in theory and phenomenology. Perspectives on possible future directions for research are discussed with the aim of exploring emergent QCD phenomena.

Influence of the quark–gluon string fusion mechanism on long-range rapidity correlations and fluctuations

Multiparticle production in soft hadronic interactions can be successfully described in the framework of the color-string approach, which will probably be derived from the first principles of chromodynamics in the future. A fundamental property of this approach is the translation invariance of the rapidity spectrum of charged particles produced by one source at high energies. This symmetry results in the appearance of long-range rapidity correlations through event-by-event fluctuations of the number and/or type of strings. We describe the behavior of correlations between multiplicities (n–n) and between the transverse momentum and multiplicities (pt–n) of charged particles with the mechanism of forming sources of two types taken into account. We obtain an exact analytic expression for the (n–n)-correlation coefficient. Because no exact solution can be obtained for the (pt–n)-correlation coefficient, we propose an effective approximation that significantly simplifies numerical computations. We verify all these results by direct simulation using the Monte Carlo method. We also investigate how the fusion mechanism influences the behavior of strongly intensive variables characterizing the multiplicity fluctuations in two rapidity windows.

Triple-gluon and quadruple-gluon azimuthal correlations from glasma and higher-dimensional ridges

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 the long-range rapidity correlations ("ridges") and $v_n$ moments of the azimuthal distribution of detected hadrons. The glasma description reproduces the systematics of the data on both p-p and p-Pb ridges. As an alternative, relativistic hydrodynamics has also been applied to these small systems quite successfully. With the triple- and quadruple-gluon azimuthal correlations, this work aims to set the stage by going beyond the double-gluon azimuthal correlations in order to settle unambiguously the origin of "collectivity" in p-p and p-Pb collisions. We derive the triple- and quadruple-gluon azimuthal correlation functions in terms of unintegrated gluon distributions at arbitrary rapidities and azimuthal angles of the produced gluons. Then, unintegrated gluon distributions from the running coupling Balitsky-Kovchegov evolution equation are used to calculate the triple- and quadruple-gluon correlations for various parameters of gluon momenta, initial scale for small-$x$ evolution and beam energy.

LONG-RANGE RAPIDITY CORRELATIONS IN HEAVY-LIGHT ION COLLISIONS

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 correlations, and (iv) near-side azimuthal correlations which are long-range in rapidity. The geometric correlations (i) are due to the fact that nucleons are correlated by simply being confined within the same nucleus and may lead to long-range rapidity correlations for the produced particles without strong azimuthal angle dependence. Somewhat surprisingly, long-range rapidity correlations (iii) and (iv) have exactly the same amplitudes along with azimuthal and rapidity shapes: one centered around Δϕ = π with the other one centered around Δϕ = 0 (here Δϕ is the azimuthal angle between the two produced gluons). We thus observe that the early-time CGC dynamics in nucleus-nucleus collisions generates azimuthal non-flow correlations which are qualitatively different from jet correlations by being long-range in rapidity. If strong enough, they have the potential of mimicking the elliptic (and higher-order even-harmonic) flow in the di-hadron correlators: one may need to take them into account in the experimental determination of the flow observables.

Long-range rapidity correlations in high energy AA collisions in Monte Carlo model with string fusion

The magnitude of long-range correlations between observables in two separated rapidity windows, proposed as a signature of the string fusion and percolation phenomenon, is studied in the framework of non-Glauber Monte Carlo string-parton model, based on the picture of elementary collisions of color dipoles. The predictions, obtained with and without string fusion, demonstrate effects of color string fusion on the observables in Pb-Pb collisions at the LHC: decrease of n-n correlation coeffcient with centrality and negative pt-n correlations, if a suffciently effective centrality estimator is applied. In general case it is shown that the values of n-n and pt-n correlation coeffcients strongly depend on the method of collision centrality fixation. In contrast, the predictions obtained for pt-pt correlation have almost no effect of centrality determination method and the corresponding experimental data would produce the strong limitation on the transverse radius of a string.

Long-range rapidity correlations in soft interactions at high energies

In this paper we take the next step (following the successful description of inclusive hadron production) in describing the structure of the bias events without the aid of Monte Carlo codes. Two new results are presented: (i) a method for calculating the two particle correlation functions in the BFKL pomeron calculus in zero transverse dimension; and (ii) an estimation of the values of these correlations in a model of soft interactions. Comparison with the multiplicity data at the LHC is given.

Modeling of exclusive parton distributions and long-range rapidity correlations in proton-proton collisions at the LHC energies

Soft pp interactions are considered in the framework of the phenomenological model with color strings formation. Under the assumption, that the elementary collision is realized as interaction of two color dipoles, the total inelastic cross section and the multiplicity of the charged particles are estimated and used for the parameters fixing. The special attention is given to the modelling of exclusive parton distributions taking into account the energy conservation and fixing the mass center that is necessary for the description of correlations, corresponding Monte Carlo procedures are developed for an arbitrary number of partons in a hadron. The string fusion algorithm in a cross-section plane is developed taking into account the finite rapidity width of strings. In this framework the influence of string fusion effects on long-range correlations of charged particles are estimated. The proposed algorithms are planned to be used for studying of heavy ion collisions.

High-density QCD and the new LHC data

We present some of the features shown by RHIC and LHC data concerning high density, emphasizing the differences and similarities between the big bang and the little big bang. We briefly discuss multiplicity rapidity distributions, geometric scaling, saturation momentum of gluons, harmonic moments, and longrange rapidity correlations.

Comparison of the color glass condensate to dihadron correlations in proton-proton and proton-nucleus collisions

We perform a detailed comparison of long-range rapidity correlations in the color glass condensate framework to high multiplicity dihadron 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 nontrivial 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 $\ensuremath{\Delta}\ensuremath{\phi}\ensuremath{\sim}0$, is sensitive to the shape of unintegrated gluon distributions in the hadrons that are renormalization group evolved in rapidity from the beam rapidities to those of the measured hadrons. We present estimates for the collimated dihadron yield expected in central deuteron-gold collisions at the Relativistic Heavy Ion Collider.

Long-range rapidity correlations in heavy–light ion collisions

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 correlations, and (iv) near-side azimuthal correlations which are long-range in rapidity. The geometric correlations (i) are due to the fact that nucleons are correlated by simply being confined within the same nucleus and may lead to long-range rapidity correlations for the produced particles without strong azimuthal angle dependence. Somewhat surprisingly, long-range rapidity correlations (iii) and (iv) have exactly the same amplitudes along with azimuthal and rapidity shapes: one centered around Δ ϕ = π with the other one centered around Δ ϕ = 0 (here Δ ϕ is the azimuthal angle between the two produced gluons). We thus observe that the early-time CGC dynamics in nucleus–nucleus collisions generates azimuthal non-flow correlations which are qualitatively different from jet correlations by being long-range in rapidity. If strong enough, they have the potential of mimicking the elliptic (and higher-order even-harmonic) flow in the di-hadron correlators: one may need to take them into account in the experimental determination of the flow observables.