Search for Long-Range Correlations in Relativistic Heavy-Ion Collisions at SPS Energies

Long range correlations are searched for by analyzing the experimental data on 16O-AgBr and 32S-AgBr collisions at 200A GeV/c and the results are compared with the predictions of a multi phase transport (AMPT) model. The findings reveal that the observed forward-backward (F-B) multiplicity correlations are mainly of short-range in nature. The range of F-B correlations are observed to extend with increasing projectile mass. The observed extended range of F-B correlations might be due to overall multiplicity fluctuations arising because of nuclear geometry. The findings are not sufficient for making any definite conclusions regarding the presence of long-range correlations.


Introduction:
One of the main goals of studying nucleus-nucleus collisions at relativistic energies is to study the properties of strongly interacting matter under extreme conditions of initial energy density and temperature, where formation of quark-gluon plasma(QGP) is envisaged to take place [1,2,3]. Correlations among the relativistic charged particles produced in different pseudorapidity,η bins are considered as a powerful tool for understanding the underlying mechanism of multiparticle production in hadron-hadron(hh), hadron-nucleus(hA) and nucleus-nucleus(A-A) collisions [4,5,6]. Both short-and long-range correlations have been observed in hadronic and heavy-ion collisions at SPS and RHIC energies [5,6,7,8,9,10]. These observed correlations have been interpreted in terms of the concept of clustering [11], that is, the particle production takes place via the formation of some intermediate states, referred to as 'clusters' which finally decay isotropically in their centre-of-mass(c.m.) frame to real hadrons. Useful information regarding the properties of clusters, for example, size of clusters, number of clusters produced on event-by-event(ebe) basis and the 'width', the extent of phase space occupied, and so forth, can be extracted by studying the two particle angular correlations [3,12,13]. It has been suggested [4,5,14,15] that inclusive two particle correlations have two components: the short range correlations (SRC) and the long range correlations(LRC). The SRC have been observed to remain confined to a region, η ∼ ±1 unit around mid rapidity, while the LRC, which arise due to ebe fluctuations of overall particle multiplicity, extend to a rather longer range [14,15,16] (> 2 units of η ). LRC have been observed at relatively higher incident energies [6,14,15,16,17,18], while the magnitude of LRC, in the case of hh collisions, has been reported to increase with increasing beam energies as the non-singly diffractive inelastic cross-section increases significantly with incident energy for hh collisions at √ s > 100 GeV [19]. These effects have been successfully explained in terms of multiparton interactions [18]. For AA collisions, the multiparton interactions are expected to give rise to LRC, which would extend to rather longer range as compared to those observed in hh collision at the same incident energy [6,15,20,21]. The color glass condensate picture of particle productions and the multiple scattering model also predict presence of LRC in AA collisions [6,8,15,20,22,23].
After the availability of the data from relativistic heavy ion collider(RHIC) and then from large hadron collider(LHC), interest in the studies involving particle correlations has considerably increased. It is because of the idea that modifications of the cluster characteristics and (or) shortening in the correlation length in the pseudorapidity space, if observed particularly at these energies may be taken as a signal of transition to quark-gluon plasma formation [4,15,24].
A number of attempts have been made by theoretical and experimental physicists [5,6,13,25,26,27,28,29,30,31,32,33,34,35] to study forward-backward (F-B) correlations at RHIC and LHC energies. It is, however, essential to identify some baseline contributions to the experimentally observed correlations which do not depend on new physics, for example, formation of some exotic states like DCC or QGP. It is, therefore, considered worthwhile to carry out a systematic study of F-B correlations at lower energies, BNL, and SPS because of the fact that only a few attempts have been made to study F-B correlations at these energies [9,14,15,16,36].
Such studies would help understand systematically the underlying physics at energies from SPS to RHIC, like dependence of correlation strength and correlation length on beam energy and system size. Once such dependence is understood, modification in the cluster characteristics or shortening of correlation length may be looked into to search for QGP formation.

Formalism:
F-B correlations are generally investigated by examining the following type of linear dependence of mean charged particle multiplicity in the backward(B) hemisphere, < n b > on the multiplicity of the particles emitted in the forward (F) hemisphere, n f : where a is intercept and b represents the slope. For symmetric F and B regions, b is often termed as the correlation strength and is expressed in terms of expectation value [6,15,28,37]: where D f f and D bf denote the forward-forward and backward-forward dispersions, respectively. experiments performed by EMU01 collaboration [38]. The other relevant details of the data, like, criteria for selection of events, classification of tracks, selection of AgBr group of events, and so forth, may be found elsewhere [4,38,39,40].
The emission angle, θ of the relativistic charged particle with respect to beam axis were measured by the coordinate method. The values of x, y, z coordinates at the vertex and at two points one on shower and the other on beam tracks were measured and the pseudorapidity variable, η was calculated using the relation, η = −lntan(θ/2). It should be emphasized that the conventional emulsion technique has two main advantages over the other detectors: (i) its 4π solid angle coverage and (ii) emulsion data are free from biases due to full phase space coverage. In the case of other detectors, only a fraction of charged particles are recorded due to the limited acceptance cone. This not only reduces the charged particle multiplicity but may also distort some of the events characteristics, such as particle density fluctuations [4,41]. In order to compare the findings of the present work with a multi phase transport model,AMPT [42], two samples of events corresponding to 16 [43,44]. The values of impact parameter for each data set is so set that the mean multiplicities of relativistic charged particles becomes nearly equal to those obtained for the experimental data sets.
The AMPT model is a mixed model based on both hadronic and partonic phases [44].
There are four subprocesses in this model [44,45]; phase space initialization, the parton-parton interactions, the conversion from partonic to the hadronic matter and the late hadronic interactions. The initialization takes the HIJING model [46] as event generator which included minijet production and soft string excitation.
The hadronization process is described by Quark Coalescence Model [44] in which two nearest partons combine to become a meson and three nearest partons combine to form a baryon. Finally the rescattering and resonance decay of partons are described by ART (a relativistic transport) model [48].
Pseudorapidity distribution of relativistic charged particles for the experimental and AMPT event samples at the two incident energies considered are displayed in Figure 1. It is interesting to note in the figure that the distributions corresponding to experimental and AMPT events acquire almost similar shapes.  Table 1. Values of b for various data sets are also calculated using (2) and are listed in Table 1 [9,15]. It may also be noted from the figure that although AMPT predicts the similar trends of variations of b with η w for both the data sets yet it is evidently clear that AMPT predicted values are somewhat smaller as compared to those observed for the experimental data in the entire range of η w considered.

Results and discussion
Furthermore, it is also clear from Figure 5 that the values of b for any given η w are nearly the same for both the data sets. This suggests that the values of b are independent of the mass of the colliding nuclei. It should be mentioned here that, in the saturation region, that is, the region,(η w > 1.5), values of b, for the experimental data have been reported [15] to decrease with increasing projectile energy. Such a decrease in the values of b has been observed due to the increase in the ratio < n f > / < n s > even in the limited phase space [15]; < n f > denotes the average number of charged particles in the F region and while < n s > is the mean charged particle multiplicity in the considered phase space.
In order to examine the presence of LRC, if any, contribution from SRC is to be eliminated. For this purpose F-B correlations are studied by adopting the method which has frequently been used, particularly at RHIC and LHC energies [5,6,25,27,28,29,30,31,32,34]. According to this method, η windows of small but equal widths, η w are placed in F and B regions in such a way that they are separated by equal distances(in η units), η gap with respect to centre of sym- to be due to formation of resonance or clusters in the central rapidity region, the decay products of which would be emitted in both F and B regions [11,14,16,17].
This observation is not sufficient to consider it as an indication of the presence of some LRC but it does suggest that the range of F-B correlations extends with increasing mass of the projectile. The range of F-B correlations has also been observed to increase with increasing beam energy in 16 O-AgBr collisions in the energy range from 14.5A to 200A GeV/c [15]. It has been argued [34] that the extended range of F-B correlations may be explained from simple statistical considerations of uncorrelated production of charged particles. Correlations in this range, if observed at higher beam energy or with heavier projectile, arise due to overall multiplicity fluctuations [6,14,16,17,34]; such fluctuations in AA collisions may show-up because of fluctuations in nuclear geometry [34]. It has also been pointed out [34] that before drawing up any conclusions regarding the presence of dynamical LRC, it should be confirmed that the observed F-B correlations are not arising due to overall multiplicity fluctuations by studying the multiplicity distributions and F-B correlations simultaneously in the same experiment.

Summary
On the basis of the findings of the present work, the following conclusions may be arrived at: 1. The observed F-B correlations are mainly of short-range in nature. However, the range of F-B correlations are observed to increase with increasing projectile mass and beam energy. This extended range of correlations at higher beam energy or larger projectile mass may be due to overall multiplicity fluctuations arising because of nuclear geometry.

The study of F-B correlations dependences on the pseudorapidity bin-width
and position indicates that the correlation strength b remains independent of the projectile mass.
3. The Monte Carlo model, AMPT is observed to reproduce the data nicely.
AMPT Expt.  Figure 6: Dependence of correlation strength, b on separation gap between two symmetric pseudorapidity windows, η gap for various data sets.