209,540 research outputs found

    Renormalization Invariants and Quark Flavor Mixings

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    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 θ23∝ms/mb\theta_{23}\propto m_s /m_b , θ13∝md/mb\theta_{13}\propto m_d /m_b 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

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    A tree is called double starlike if it has exactly two vertices of degree greater than two. Let H(p,n,q)H(p,n,q) denote the double starlike tree obtained by attaching pp pendant vertices to one pendant vertex of the path PnP_n and qq pendant vertices to the other pendant vertex of PnP_n. In this paper, we prove that H(p,n,q)H(p,n,q) is determined by its Laplacian spectrum
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