Study of Charge azimuthal Correlations at 200 GeV in Au + Au Collisions
Vivek Batra
Physics and Astronomy Department, WayneStateUniversity
Introduction
During the summer of 2003, I worked at the Physics Department of Wayne State University. I worked under the guidance and supervision of Professor Pruneau. My project was on “Net Charge Correlation”. The motivation of this project is to understand the correlation between positive-positive, negative-negative and positive-negative particles produced in Au-Au collisions at energies in the range of 300 MeV to 2 GeV per nucleon. The beam energy of the gold nuclei before the collision is 100 GeV per nucleon.
Experiment
Computing is an indispensable tool in handling and analyzing such large amounts of data. During the first three weeks, I learned C++ and wrote many simple programs (finding prime numbers, computing factorial of a number, solution of a quadratic equation, etc.).I familiarized myself with Linux operating system and Root environment.
The next part of the project was to understand the code that generates the correlation histograms. The basis of the experiment is to first find the reaction plane and then determine the correlation relative to it. We divide the reaction plane into 12 sectors. Next, we determine the number of positive and negative species produced in each sector. Using methods of Statistical Physics, we can find the correlation coefficient (ν dynamic) of particles produced in one sector versus another sector. We also looked at positive-positive, negative-negative and positive-negative correlations exclusively. This required a minor modification in the code. We plotted the correlation coefficient versus the multiplicity in the first set of histograms.
In order to compare the correlation coefficients for a central collision, I extracted the contents of the central collision (ninth bin) from each of the twelve histograms (1-
1, 1-2... 1-12) and plotted them on to one histogram. One of the macros I wrote, rebinned each of the twelve histograms by a factor of two, got the contents of the fifth bin and displayed them on to a new histogram. This helped us to compare correlation as a direct function of sector permutations. An almost sinusoidal behavior was observed in the histogram. I wrote a macro that plotted peripheral to central collisions on the same histogram. Another interesting modification that we did was to change the energy range to 1-2 GeV for data analysis. This helped us to see correlation among jets i.e. particles with high energy moving in the same direction.
We also changed the pseudo rapidity (η) range from -0.75η <0.75 to -0.75η <0 to find the reaction plane. The shape of the histogram remained almost the same. At the end of the project, I did some analytical calculations to subtract the flow background from the histograms and see the effect of particle correlations exclusively.
Interpretation of Results
A zero correlation means that the events are uncorrelated. Such a distribution is called Poissonian. If the particles are correlated or mutually dependent, then the distribution is referred to as super-Poissonian (not necessarily). Sub-Poissonian distribution implies that the events are anti-correlated. If we are looking at coefficient of correlation for positive-positive particles exclusively, it is important to note that the data is not normalized.
The histogram that we obtain is symmetrical about the sixth and seventh bin. That is, we obtain similar coefficients of correlation in the fifth and eight bin, fourth and ninth bin and so on. But a noteworthy point is that this observation is not true for the first and twelfth bin. The coefficient for the first bin is remarkably higher than the last bin. This can be explained by high particle-particle interactions in the first sector.
Results
The following histogram is a plot of correlation of positive particles in sector 1 with negative particles in sectors 1,2… 12. The energy of the particles is 1-2 GeV and the pseudo rapidity range is -0.75 <η < 0.The circle is for the most central collision and the cross for the most peripheral collision. Square and full square indicate intermediate collision.
The next three histograms plot normalized correlation for sector permutations, namely (1, 1), (1, 4), and (1, 7) as a function of centrality of the collision.
(1, 1)
(1, 4)
(1, 7)
The next histogram is a plot of correlation of positive particles in sector 4 with positive particles in sectors 1, 2… 12.
The next three histograms plot normalized correlation for sector permutations, namely (4, 1), (4, 4), and (4, 7) as a function of centrality of the collision.
(4, 1)
(4, 4)
(4, 7)
The next histogram is a plot of correlation of negative particles in sector 4 with negative particles in sectors 1, 2… 12.
The next three histograms plot normalized correlation for sector permutations, namely (4, 1), (4, 4), and (4, 7) as a function of centrality of the collision.
(4, 1)
(4, 4)
(4, 7)
Conclusion
This project helped me understand the basics of programming and computing. I got wonderful insight on how to use probability and statistics in doing correlation analysis. I tried to understand the reasons behind the symmetry of the almost sinusoidal histograms that I obtained. I saw the contribution of flow in the histograms and how to subtract it in order to obtain particle-particle correlations exclusively.