Abstract
Recently, a complex network based method of visibility graph has been applied to confirm the scale-freeness and presence of fractal properties in the process of multiplicity fluctuation. Analysis of data obtained from experiments on hadron-nucleus and nucleus-nucleus interactions results in values of Power of Scale-Freeness of Visibility Graph (PSVG) parameter extracted from the visibility graphs. Here, the relativistic nucleus-nucleus interaction data have been analysed to detect azimuthal anisotropy by extending the visibility graph method and extracting the average clustering coefficient, one of the important topological parameters, from the graph. Azimuthal-distributions corresponding to different pseudorapidity regions around the central pseudorapidity value are analysed utilising the parameter. Here we attempt to correlate the conventional physical significance of this coefficient with respect to complex network systems, with some basic notions of particle production phenomenology, like clustering and correlation. Earlier methods for detecting anisotropy in azimuthal distribution were mostly based on the analysis of statistical fluctuation. In this work, we have attempted to find deterministic information on the anisotropy in azimuthal distribution by means of precise determination of topological parameter from a complex network perspective.
Highlights
Many authors have probed the azimuthal anisotropy of the produced particles in ultrarelativistic heavy-ion collisions as a function of transverse momentum and it has been used as one of the major observables to study the collective properties of nuclear matter [Ex. [1]]
Experimental data from 32S-AgBr at 200A GeV interaction has been analysed using the complex network based visibility graph method and the Power of Scale-Freeness of Visibility Graph (PSVG) values obtained thereof have been compared for all the overlapping η-regions centered around cr, and it has been shown that the multiplicity fluctuation in high-energy interaction is self-similar and scale-free [30]
Bilandzic et al have discussed that azimuthal anisotropic distribution might be the underlying cause of collective anisotropic flow of the produced particles in ultrarelativistic heavy-ion collisions [3]
Summary
Many authors have probed the azimuthal anisotropy of the produced particles in ultrarelativistic heavy-ion collisions as a function of transverse momentum and it has been used as one of the major observables to study the collective properties of nuclear matter [Ex. [1]]. The initial coordinate space anisotropy of the overlapping zone of the colliding nuclei, in which the produced nuclear matter thermalization transforms via reciprocal interactions into the final state anisotropy in the momentum space. This area has been a field of immense interest in the recent past. If one uses just the orthogonality properties of trigonometric functions, the Fourier series can produce some nonvanishing flow harmonics which can not confirm whether the azimuthal anisotropic distribution in momentum space has originated from a collective anisotropic flow or from some other fully unrelated physical process capable of yielding event-by-event anisotropies (as, for example, minijets) [3].
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