THE NUCLEAR EFFECT ANALYSIS IN RELATIVISTIC HEAVY ION COLLISIONS AT BNL ENERGIES

In this article, an attempt has been made to understand the behavior of the secondary charged particles multiplicity distributions produced during the heavy ion collisions at ultra-relativistic energies by using the Hurst exponent of the two dimensional (2D) factorial moments, Fq. For this purpose the experimental data have been analyzed by using the “Hurst exponent” in the original intermittency formula by considering different values of Hurst exponent (H = 1.0, 1.5, 2.0, 2.5). The investigations reveal the power law behavior, exhibited in self-affine or nuclear effect analysis, better than that in self-similar analysis. Finally, the described works were found very much significant and also it was within good agreement with some other works.


INTRODUCTION
The primary objective of particle physics is to discover the fundamental forces and symmetries, and the elementary particles in Nature. A hierarchy of constituents of matter has been observed: macroscopic matter consists of molecules and atoms, the atoms consist of nucleons which in turn are formed of quarks, anti-quarks and gluons (partons). These results have been obtained by 1125 NUCLEAR EFFECT ANALYSIS IN RELATIVISTIC HEAVY ION COLLISIONS scattering experiments at higher and higher energies, as required to achieve information on smaller and smaller objects. At the moment the hierarchy ends at quarks: no substructure has been observed for them, so they are regarded as point like particles. Isolated single free quarks have never been observed, and therefore it is conjectured that quarks are confined together with other quarks to form hadrons.
The study of multiplicity correlations and fluctuations of produced charged particles in high energy ion collisions has been well known for few decades. This has never been more apparent than in recent years where these measurements helped to mark the discovery of new state of matter, so called Quark-Gluon Plasma (QGP) [1][2][3][4][5]. Various types of correlations and fluctuations present in heavy ion collisions at relativistic energies can provide us with valuable knowledge regarding the microscopic interactions inside the high density medium. In particular, the non-perturbative aspects of the strong interaction are difficult to study experimentally and probing the hot and dense QGP is one of the few avenues we have available. (i) In one dimension (1D) phase space of pseudorapidity, the rise of ln < F q > with the increasing phase space partition number M is much weaker for A-A collisions than for h-h collisions and the heavier the colliding nuclei are, the weaker is the rising of ln < F q > .
(ii) In 2D or 3D, the ln < F q > vs. lnM plot for A-A collisions is bending upwards strongly, much stronger than for h-h collisions and the heavier the colliding nuclei are, the stronger is the upward bending of ln < F q > vs. ln M plot.
Here, we illustrate various steps needed to obtain a reliable measurement of the "Hurst exponent" so called Hq moments. This includes the evaluation of both statistical and systematic errors, followed by a short study of the truncation in the tail of the charged-particle multiplicity distribution. The outcomes were compared to the numerous analytical QCD predictions which exist up to the Next to Next to Leading Logarithm Approximation (NNLLA) based on the study of various Monte Carlo models.

EXPERIMENTAL DETAILS
The experiment data has been collected in the present work by FUJI type nuclear emulsion stacks, those were irradiated horizontally with a beam of 28 Si nuclei (like projectile) and hit the heterogeneous mixture of nuclear emulsion (fixed target) at 14.6A GeV at Alternating Gradient Synchrophasotron (AGS) of Brookhaven National Laboratory (BNL), NewYork, USA. The scanning of the exposed emulsion stacks was performed with the help of Leica DM2500M microscope with a 10 objective and 10 ocular lens provided with semi-automatic scanning stages. The method of line scanning was used to collect the inelastic 28 Si-Em interactions. The interactions collected from line scanning were scrutinized under an optical microscope (Semi-Automatic Computerized, Leica DM6000M) with a total magnification of 10 * 100 using 10 eyepiece and 100 oil immersion objective. The measuring system associated with it has 1 μm resolution along X and Y axes and 0.5 μm resolution along the Z-axis. The detailed discussion about the present experiment can be found in our earlier publications [9][10][11][12][13].

MATHEMATICALLY TOOLS
It has been found that the above two apparently contradictory observations are due to the superposition effect of the contribution from the large number of elementary collisions in a nuclear collision process.
To characterize the phase space partition in 2D, a quantity known as "Hurst exponent" [14][15] The scale factors of M η and M ϕ are connected to each other by the relation: where N is the integer part and 0   1 represents the fractional part.

RESULTS AND DISCUSSIONS
In the present work, we used  = -2  max  +2 and  = 0-2. The M η was varied from 2-30.
Further, to reduce the effect of non flat particle density distributions, the cumulative variables X η and X ϕ were used to make it in the corresponding regions 0-1. By using the above partition scheme, the values of ln < F 2 > were calculated with the help of general adaptation of Intermittency / scaled factorial moments F q (M).

M. AYAZ AHMAD
The behavior of ln < F 2 > vs. ln M have been shown in Fig. 1(a-d) for the collisions of 28 Si with emulsion nuclei at an energy 409 GeV for different values of exponent H. From this figure it has been observed that there is strong upward curve bend in Fig. 1 (a). However, when H increases, the upward bending is found weakened in Fig. 1(b-d).

Figure 1(a-d):
The dependence of ln < F 2 > on ln M at energy  409GeV. We observe that the two dimensional second order factorial moment exhibits an upward bending as a function of partition of space, which is in turn means the superposition of contributions from the elementary collisions in the nucleus-nucleus collisions. This upward bending could, however, be removed by choosing proper partition along the longitudinal and perpendicular directions, that is, the right value of Hurst exponent "H". Moreover, it has been observed that heavier the colliding are, the strong the upward bending is. It is consistence with the fact that the number of elementary collisions is more for heavier nuclei.

CONCLUSION AND FINAL REMARKS
It is worth mentioning that if QGP is formed, then there will be no elementary collisions. This in turn will lead to vanishing of the superposition effect due to the contribution of elementary collisions in nucleus-nucleus (A-A) collisions. Under such conditions, the upward bending in the two dimensional second factorial moment plots is not likely to be seen. Hence the study of the nuclear effect in nucleus-nucleus (A-A) collisions could be used as another indirect test of QGP formation.