P-adic coverage method in fractal analysis of showers |
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Authors: | T G Dedovich M V Tokarev |
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Institution: | 1.Joint Institute for Nuclear Research,Dubna,Russia |
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Abstract: | Self-similarity in multiple processes at high energies is considered. It is assumed that a parton cascade transforms into
a hadron shower with a fractal structure. The box counting (BC) method used to calculate the fractal dimension is analyzed.
The parton shower with permissible 1/3 parts of pseudorapidity space, which corresponds to a triadic Cantor set, was used
as a test fractal. It was found that there is an optimal set of bins (a parameter of the BC method) that allows one to find
the fractal dimension with maximal accuracy. The optimal set of bins is shown to depend on the fractal generation law. The
P-adic coverage (PaC) method is proposed and used in the fractal analysis. This method makes it possible to determine the
fractal dimension of a shower as accurately as possible, the number of fractal levels and partons at each branching point
during the parton shower evolution, the type of cascade (either random or regular), and its structure. It is shown to be applicable
to an analysis of the regular and random N-ary cascades with permissible 1/k parts of the space studied. |
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