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Renormalization Invariants and Quark Flavor Mixings
A set of renormalization invariants is constructed using approximate,
two-flavor, analytic solutions for RGEs. These invariants exhibit explicitly
the correlation between quark flavor mixings and mass ratios in the context of
the SM, DHM and MSSM of electroweak interaction. The well known empirical
relations , can
thus be understood as the result of renormalization evolution toward the
infrared point. The validity of this approximation is evaluated by comparing
the numerical solutions with the analytical approach. It is found that the
scale dependence of these quantities for general three flavoring mixing follows
closely these invariants up to the GUT scale.Comment: 23 pages, 7 figure
Laplacian spectral characterization of some double starlike trees
A tree is called double starlike if it has exactly two vertices of degree
greater than two. Let denote the double starlike tree obtained by
attaching pendant vertices to one pendant vertex of the path and
pendant vertices to the other pendant vertex of . In this paper, we prove
that is determined by its Laplacian spectrum
- β¦