Vertex Counting: Statistical Distribution of Vertices in Large Sets of Tree Diagrams

Details Vertex Counting: Statistical Distribution of Vertices in Large Sets of Tree Diagrams Vertex Counting: Statistical Distribution of Vertices in Large Sets of Tree Diagrams

2002-09-13

arxiv.org/abs/hep-ph/0209155v1

Eur.Phys.J.C27:291-296,2003

Physics

High Energy Physics

High Energy Physics - Phenomenology

17 pages, 6 figures

Scientific paper

10.1140/epjc/s2002-01102-6

We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and we compute the mean and variance of this distribution for several theories. We show the distribution's `fine structure', arising from topological sum rules, can be obtained.

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