Two-particle Rapidity Correlations Research Articles

Study of forward–backward correlation and multiplicity fluctuations of pions produced in p–p collisions at recent LHC energies

The two-particle rapidity correlation among the pions produced in p–p collisions at recent LHC energies 2.76, 5.02, 7 and 13 TeV are studied in this paper by using the analysis of events generated by UrQMD-3.4, AMPT-2.26 and PYTHIA-8.3. Our investigation for bin-to-bin fluctuation using the variance of forward–backward asymmetry parameter in the forward–backward pseudo-rapidity windows is done through the simulated data. In addition to that, energy-wise variation of correlation strength (β), the probability distribution of roughness parameter () and number density fluctuation parameter (d ik ) are also incorporated in this investigation. Also, we have tried to study the same for the data of different impact parameters generated using the UrQMD model, and the comparison is made with its minimum biased events data-set. The analysis signifies, that the signature of dynamical fluctuation is not so prominent but increases a bit with the increase in energy. An increase in the correlation strength with the increase in energy signifies the contribution of long-range correlation is more in comparison to the short-range one. However, there is no such accountable effect of various impact parameters seen in the present study.

Thermal noise in non-boost-invariant dissipative hydrodynamics

We study the effects of hydrodynamic fluctuations in non-boost-invariant longitudinal expansion of matter formed in relativistic heavy ion collisions. We formulate the theory of thermal noise within second-order viscous hydrodynamics treating noise as a perturbation on top of the non-boost-invariant flow. We develop a numerical simulation model to treat the (1+1)-dimension hydrodynamic evolution. The code is tested to reproduce the analytic results for the Riemann solver for expansion of matter in vacuum. For viscous hydrodynamic expansion, the initial energy density distribution are obtained by reproducing the measured charged hadron rapidity distribution at the RHIC energies. We show that the longitudinal rapidity correlations arising from space-time dependent thermal noise and from an induced thermal perturbation have distinct structures. In general, the rapidity correlations are found to be dominated by temperature fluctuations at small rapidity separation and velocity fluctuations at large rapidities. We demonstrate that thermal noise produce ridge-like two-particle rapidity correlations which persist at moderately large rapidities. The magnitude and pattern of the correlations are quite sensitive to various second-order dissipative formalisms and to the underlying equations of state, especially at large rapidities. The short-range part of the rapidity correlation is found to be somewhat enhanced as compared to that in boost-invariant flow of matter.

Thermal noise in a boost-invariant matter expansion in relativistic heavy-ion collisions

We formulate a general theory of thermal fluctuations within causal second-order viscous hydrodynamic evolution of matter formed in relativistic heavy-ion collisions. The fluctuation is treated perturbatively on top of a boost-invariant longitudinal expansion. Numerical simulation of thermal noise is performed for a lattice QCD equation of state and for various second-order dissipative evolution equations. Phenomenological effects of thermal fluctuations on the two-particle rapidity correlations are studied.

Evidence of forward–backward multiplicity correlation at SPS energy

In this paper, a detailed study of two-particle rapidity correlation has been presented by measuring the dynamical fluctuation variable [Formula: see text] in forward and backward pseudo-rapidity window of shower particles produced in the relativistic heavy ion collision, [Formula: see text]O–AgBr interactions at 60[Formula: see text]AGeV and [Formula: see text]S–AgBr interactions at 200[Formula: see text]AGeV. Variations of [Formula: see text] with rapidity gap between forward and backward zones and with the width of each zone have been studied. For both cases, [Formula: see text] increase with increasing either width of the zone or gap between the zones. Our findings show the presence of strong long-range correlation. Comparison of experimental results with MC-RAND events confirms the present correlation to be dynamical in nature. We have also compared our results with FRITIOF and UrQMD events. Such events also show the presence of correlation, but found to fail to reproduce the experimental results both quantitatively and qualitatively. Strength of correlation is dependent on the centrality of collision for experimental events, it decreases with centrality.

Constraints on rapidity-dependent initial conditions from charged-particle pseudorapidity densities and two-particle correlations

We study the initial three-dimensional spatial configuration of the quark-gluon plasma produced in relativistic heavy-ion collisions using centrality and rapidity-dependent measurements of charged particle pseudorapidity densities and two-particle correlations. A cumulant-generating function is used to parametrize the rapidity dependence of local entropy deposition and extend arbitrary boost-invariant initial conditions to nonzero beam rapidities. The model is compared to p+Pb and Pb+Pb single-particle distributions and systematically optimized using Bayesian parameter estimation to extract high-probability initial condition parameters. The optimized initial conditions are then compared to a number of experimental observables including two-particle rapidity correlations, the rapidity dependence of anisotropic flow, and event-plane decorrelations.

Saturation scale fluctuations and multiparticle rapidity correlations

We study the effect of intrinsic fluctuations of the proton saturation momentum scale on event-by-event rapidity distributions. Saturation scale fluctuations generate an asymmetry in the single particle rapidity distribution in each event resulting in genuine n-particle correlations having a component linear in the rapidities of the produced particles, $y_1\cdots y_n$. We introduce a color domain model that naturally explains the centrality dependence of the two-particle rapidity correlations recently measured by ATLAS while constraining the probability distribution of saturation scale fluctuations in the proton. Predictions for n = 4, 6 and 8 particle correlations find that the four and eight-particle cumulant change sign at an intermediate multiplicity, a signature which could be tested experimentally.

Two-particle rapidity correlations between relativistic particles in central collisions of $$^{197}$$ 197 Au nuclei in emulsion at 11.6 A GeV/c

It is shown that in central collisions of $^{197}$Au nuclei with heavy emulsion nuclei at 11.6 $A$GeV/c two-particles pseudorapidity correlations for produced particles in terms of correlation functions demonstate predominantly long-range behaviour in contrast to nucleon-nucleon interactions. The experimental data are compared with calculations based on the FRITIOF-M model and the model of independent emission of particles.

Probing proton fluctuations with asymmetric rapidity correlations

Intrinsic fluctuations of the proton saturation momentum generate asymmetric rapidity distributions on an event-by-event basis. We argue that the asymmetric component, $\ensuremath{\langle}{a}_{1}^{2}\ensuremath{\rangle}$, of the orthogonal polynomial decomposition of the two-particle rapidity correlation function is a sensitive probe to this distribution of fluctuations. We present a simple model connecting the experimentally measured $\ensuremath{\langle}{a}_{1}^{2}\ensuremath{\rangle}$ to the variance, $\ensuremath{\sigma}$, of the distribution of the logarithm of the proton saturation scale. We find that $\ensuremath{\sigma}\ensuremath{\approx}0.5--1$ describes the asymmetric component of the rapidity correlations recently measured by the ATLAS Collaboration.

Forward–backward multiplicity correlation in high-energy nucleus–nucleus interactions at a few AGeV/c

We have presented a systematic study of two-particle rapidity correlations in terms of investigating the dynamical fluctuation observable in the forward–backward pseudo-rapidity windows by analyzing the experimental data of interactions at 4.5 AGeV/c, interactions at 4.1 AGeV/c, and interactions at 4.5 AGeV/c. The experimental results have been compared with the results obtained from the analysis of event sample simulated (MC-RAND) by generating random numbers and also with the analysis of events generated by the UrQMD and AMPT model. Our study confirms the presence of strong short-range correlations among the produced particles in the forward and the backward pseudo-rapidity region. The analysis of the simple Monte Carlo-simulated (MC-RAND) events signifies that the observed correlations are not due to mere statistics only; explanation of such correlations can be attributed to the presence of dynamical fluctuations during the production of charged pions. Comparisons of the experimental results with the results obtained from analyzing the UrQMD data sample indicate that the UrQMD model cannot reproduce the experimental findings. The AMPT model also cannot explain the experimental results satisfactorily. Comparisons of our experimental results with the results obtained from the analysis of higher energy emulsion data and with the results of the RHIC data have also been presented.

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.

Longitudinal fluctuations of the fireball density in heavy-ion collisions

We show that fluctuations of the fireball shape in the longitudinal direction generate nontrivial rapidity correlations that depend not only on the rapidity difference, ${y}_{1}\ensuremath{-}{y}_{2}$, but also on the rapidity sum, ${y}_{1}+{y}_{2}$. This is explicitly demonstrated in a simple wounded nucleon model, and the general case is also discussed. It is argued that rapidity fluctuations are large compared to normal statistical fluctuations. We show how to extract different components of the fluctuating fireball shape from the measured two-particle rapidity correlation function. The experimental possibility of studying the longitudinal initial conditions in heavy-ion and proton-proton collisions is emphasized.

Long range two-particle rapidity correlations in [formula omitted] collisions from high energy QCD evolution

Long range rapidity correlations in A + A collisions are sensitive to strong color field dynamics at early times after the collision. These can be computed in a factorization formalism (Gelis, Lappi and Venugopalan (2009) [1]) which expresses the n-gluon inclusive spectrum at arbitrary rapidity separations in terms of the multi-parton correlations in the nuclear wavefunctions. This formalism includes all radiative and rescattering contributions, to leading accuracy in α s Δ Y , where Δ Y is the rapidity separation between either one of the measured gluons and a projectile, or between the measured gluons themselves. In this paper, we use a mean field approximation for the evolution of the nuclear wavefunctions to obtain a compact result for inclusive two gluon correlations in terms of the unintegrated gluon distributions in the nuclear projectiles. The unintegrated gluon distributions satisfy the Balitsky–Kovchegov equation, which we solve with running coupling and with initial conditions constrained by existing data on electron–nucleus collisions. Our results are valid for arbitrary rapidity separations between measured gluons having transverse momenta p ⊥ , q ⊥ ≳ Q s , where Q s is the saturation scale in the nuclear wavefunctions. We compare our results to data on long range rapidity correlations observed in the near-side ridge at RHIC and make predictions for similar long range rapidity correlations at the LHC.

Independent π −-meson production in pp interactions

It is shown that experimental data on the multiparticle production of negatively charged pions in proton-proton interactions at $$\sqrt s \leqslant 30 GeV$$ do not involve significant indications of the existence of anycorrela tions between negatively charged pions, apart from those that are associated with momentum conservation and with interference. The multiplicity distributions in rapidity intervals, forward-backward correlations, and two-particle rapidity and transverse-momentum correlations do not contradict the independent production of negatively charged pions. No constraints on the multiplicity distributions of product particles follow from their independent production.

Two-particle rapidity correlations from the Bose-Einstein effect in central28Si+Au collisions at14.6AGeV/cand intermittency

In previous work, the E802 Collaboration at the BNL-AGS used negative binomial distribution (NBD) fits to charged particle multiplicity distributions from central collisions of 16O+Cu at 14.6A GeV/c to derive the two-particle short-range rapidity correlation length and strength. These turned out to be much shorter and weaker than the values for hadron collisions, which led to a simple and elegant explanation of intermittency. In the present work, a direct measurement of the two-particle correlation of identified pions in the E802/E859 magnetic spectrometer is performed in the interval 1.5<~y<~2.0 for central 28Si+Au collisions, both in terms of Qinv=|q→|2−q02, where q=p2−p1=(q→,q0), and also in terms of |η2−η1| and |y2−y1|, where p,η, and y are the four-momentum, pseudorapidity, and rapidity of the pions. It is demonstrated that the two-pion correlation in rapidity (and pseudorapidity) is entirely due to the Bose-Einstein interference. The directly measured correlation length in both η and y is ξ=0.19±0.03 for two π−, with strength R(0,0)∼1%, in agreement with the previous E802 indirect measurements derived from the NBD analysis of intermittency.Received 19 February 1997DOI:https://doi.org/10.1103/PhysRevC.56.1544©1997 American Physical Society

Two-particle rapidity correlations in C+Ta interactions at 4.2A GeV/c.

Two-particle rapidity correlations for pp, p${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$ pairs in C+Ta interactions at 4.2 GeV/c per nucleon are presented. The experimental data are obtained with a 2 m propane bubble chamber exposed on the JINR, Dubna, synchrophasotron. It is found that the strength of the correlations does not depend on particle combination, but strongly depends on the rapidity and collision centrality. The quark-gluon-string model describes these features of the correlations well, but needs to be tuned in the target fragmentation region. Since the quark-gluon-string model simulates the nucleus-nucleus collisions by the superposition of hadron-hadron collisions, we conclude that there is no evidence of a collective behavior in our data. This conclusion is additionally supported by the intermittency analysis. \textcopyright{} 1996 The American Physical Society.

Multiplicity distributions from central collisions of 16O+Cu at 14.6A GeV/c and intermittency.

The E-802 Collaboration at the BNL-AGS has measured charged particle multiplicity distributions from central (ZCAL) collisions of {sup 16}O+Cu at 14.6{ital A} GeV/{ital c} as a function of the pseudorapidity interval {delta}{eta}{ge}0.1 in the range 1.2{le}{eta}{le}2.2. The fluctuations of these distributions as a function of the pseudorapidity interval have been studied by the method of normalized factorial moments and also by directly fitting the measurements to negative binomial distributions (NBD). Excellent fits to NBD were obtained in all {delta}{eta} bins, allowing, for the first time, a systematic formulation of the subject of intermittency in terms of distributions to complement the description based on normalized factorial moments. In agreement with all previous measurements of NBD fits to multiplicity distributions in hadron and lepton reactions, the {ital k} parameter of the NBD fit for central {sup 16}O+Cu collisions is found to exhibit an apparently linear increase with the {delta}{eta} interval, albeit with a much steeper slope than for other reactions, and a nonzero intercept, {ital k}(0){ne}0. The evolution of the NBD parameter {ital k}({delta}{eta}) is used to determine the two-particle short-range rapidity correlation length for central {sup 16}O+Cu collisions, {xi}=0.18{plus_minus}0.05, which is much shorter than the value {xi}{similar_to}1--3 for hadron collisions, butmore » this is a quantitative rather than a qualitative difference. These results lead to a simple and elegant explanation of the intermittency formalism, without resort to fractals, for all reactions, which demystifies intermittency---for {sup 16}O+Cu central collisions, intermittency is nothing more than the apparent statistical independence of the multiplicity in small pseudorapidity bins, {delta}{eta}{similar_to}0.2, due to the surprisingly short two-particle rapidity correlation length.« less

Inclusive rapidity correlations of π− mesons inpp interactions

The simple single-parameter approximation of one-particle semi-inclusive rapidity distributions of negative particles (π− mesons) inpp interactions at various multiplicities over the investigated range of primary momenta 6.6.–400 GeV/c is presented. Assuming the lack of any kind of correlations in semi-inclusive events, a good description of experimental data on two-particle inclusive rapidity correlations (pseudocorrelations) is obtained. Data on forward-backward, right-left correlations and multiplicity distributions in rapidity intervals and intervals separated by empty gaps do not contradict independent π− production either.

Production of charged hadrons by positive muons on deuterium and xenon at 490 GeV

Results on the production of charged hadrons in muon-deuteron and muon-xenon interactions are presented. The data were taken with the E665 spectrometer, which was exposed to the 490 GeV muon beam of the Tevatron at Fermilab. The use of a streamer chamber as vertex detector provides nearly 4π acceptance for charged particles. The μD data are compared with the μXe data in terms of multiplicity distributions, average multiplicities, forward-backward multiplicity correlations, rapidity and transverse momentum distributions and of two-particle rapidity correlations of charged hadrons. The data cover a range of invariant hadronic massesW from 8 to 30 GeV.

Correlation measurements in high-multiplicity events.

Requirements for correlation measurements in high-multiplicity events are discussed. Attention is focused on detection of so-called hot spots, two-particle rapidity correlations, two-particle momentum correlations (for quantum interferometry), and higher-order correlations. The signal-to-noise ratio may become large in the high-multiplicity limit, allowing meaningful single-event measurements, only if the correlations are due to collective behavior.

Rapidity correlations in ultra-relativistic nuclear collisions

I present an analysis of two-particle rapidity correlations in O+Em and S+Em collisions at 200 GeV/nucleon, using a technique that gives maximal information without reusing data. The correlations are anomalously large, signalling large-scale deconfinement (involving ten charged pions on average). The shape of the correlation function is not well determined, and should be remeasured with higher statistics.