Two Higgs Doublet Model in a Noncommutative Geometry on the Discrete Space M_4×Z_4 : Particles and Fields

概要

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The two Higgs doublet model with the symmetry of SU(3)_c×SU(2)_L×U(1)_Y is reconstructed in a new scheme of a noncommutative differential geometry (NCG) on the discrete space M_4×Z_4, which is a product space of Minkowski space and four point space. The characteristic point of this new scheme is to take the fermion field to be a vector in a 24-dimensional space which contains all leptons and quarks. Corresponding to this specification, all gauge and Higgs boson fields are represented in 24×24 matrix forms. We incorporate the Higgs boson fields h and h^^^〜=τ^2h*τ^2 which contain two Higgs doublet h_1 and h_2 trans forming as (2,1) and (2,-1) under SU(2)_L×U(1), respectively. h and h^^^〜 are properly placed on the discrete space Z_4. Owing to the new algebraic rules adopted in this article, we can obtain the necessary potential and interacting terms between these Higgs bosons, which are responsible for giving masses to the particles included. Up and down quarks have different masses through the vacuum expectation value of h_2 and h_1 respectively.
理論物理学刊行会の論文
1997-03-25