Probing resonance states in high-energy interaction: a novel approach using complex network technique based on symmetry scaling

Traditionally invariant-mass/transverse-momentum methods were being used to probe various resonance-states in high-energy-collision. Here, we have done scaling analysis by implementing complex-network-based-method (a chaos-based-approach) of visibility-graph to analyze different resonance-states. In the process we use scaling-exponent [power of scale-freeness-of-visibility-graph (PSVG)] calculated from the aforementioned graph. The method is applied to analyze the fractal behavior of pseudo-rapidity-space of the produced dimuons from the events produced in p–p collision at 7 and 8 TeV from CMS collaboration for different ranges of invariant mass of the dimuons. It is found that the fluctuation-pattern of the pseudorapidity-spaces with different ranges of invariant mass has inherent scale-freeness and shows high degree of self-similarity and fractal nature. Moreover, the experiment reveals that the scaling pattern, degree-of-scale-freeness and fractal na ture of the fluctuation differ with different pseodorapidity-space having different ranges of invariant-mass. This change in scaling behavior is reflected in the values of (PSVG) extracted from the corresponding pseudorapidity-space. These different degree of changes in the simple yet rigorous parameter (PSVG) may be indicative of the formation of various resonance-like states(producing di-leptons) and other unusual phenomena. We propose that this method may detect the resonance states in various high energy interactions without using conventional methods of invariant-mass/transverse-momentum techniques and also may detect some unusual phenomena like formation of clusters or structures of cascades etc. This paper reports an application of this method to probe resonance states in p–p collision data at 7 and 8 TeV from CMS by analyzing pseudorapidity-space of the produced dimuons without analyzing their invariant-mass-spectrum.