32,595 research outputs found

    Phenomenology of A Supersymmetric Model for Fermion Mass Hierarchy

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    Some phenomenological aspects of a supersymmetric model for fermion mass hierarchy proposed previously are discussed. It is required that the lepton universality violation is near to its current experimental bound. The lepton number violation decay modes τ→2eμ\tau \to 2e\mu and 3μ3\mu maybe observable in the near future. The Majorana mass of electron-neutrino is predicted to be about 0.1 eV. The fine-tuning problem is discussed.Comment: 13 pages, latex, two figures, substantially revise

    Supersymmetry for Flavors

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    An understanding of the lepton masses within the framework of SUSY is presented. A family symmetry is introduced. Sneutrino VEV breaks this symmetry. The tau mass is due to the Higgs VEV, and muon mass purely from the sneutrino VEV. A viable model is constructed, which predicts (1-10) MeV tau-neutrino.Comment: 5 pages, latex, no figure. Talk at the workshop on Frontier of Theoretical Physics, Beijing, Nov., 199

    Packing Topological Minors Half-Integrally

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    The packing problem and the covering problem are two of the most general questions in graph theory. The Erd\H{o}s-P\'{o}sa property characterizes the cases when the optimal solutions of these two problems are bounded by functions of each other. Robertson and Seymour proved that when packing and covering HH-minors for any fixed graph HH, the planarity of HH is equivalent with the Erd\H{o}s-P\'{o}sa property. Thomas conjectured that the planarity is no longer required if the solution of the packing problem is allowed to be half-integral. In this paper, we prove that this half-integral version of Erd\H{o}s-P\'{o}sa property holds with respect to the topological minor containment, which easily implies Thomas' conjecture. Indeed, we prove an even stronger statement in which those subdivisions are rooted at any choice of prescribed subsets of vertices. Precisely, we prove that for every graph HH, there exists a function ff such that for every graph GG, every sequence (Rv:v∈V(H))(R_v: v \in V(H)) of subsets of V(G)V(G) and every integer kk, either there exist kk subgraphs G1,G2,...,GkG_1,G_2,...,G_k of GG such that every vertex of GG belongs to at most two of G1,...,GkG_1,...,G_k and each GiG_i is isomorphic to a subdivision of HH whose branch vertex corresponding to vv belongs to RvR_v for each v∈V(H)v \in V(H), or there exists a set Z⊆V(G)Z \subseteq V(G) with size at most f(k)f(k) intersecting all subgraphs of GG isomorphic to a subdivision of HH whose branch vertex corresponding to vv belongs to RvR_v for each v∈V(H)v \in V(H). Applications of this theorem include generalizations of algorithmic meta-theorems and structure theorems for HH-topological minor free (or HH-minor free) graphs to graphs that do not half-integrally pack many HH-topological minors (or HH-minors)
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