Mininal SU(5) Grand Unified Theory Based on Generalized Covariant Derivatives with Gauge and Higgs Fields

概要

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The minimal SU(5) grand unified theory is reformulated in a new scheme of field theory endowed with generalized covariant derivatives for the fermion fields. The covariant derivatives, which take values in both the internal Lie algebra su(5) and the vector space of Dirac matrices, include degrees of freedom of both the gauge fields and the 5-plet and 24-plet Higgs fields. Commutators of the covariant derivatives define field strengths for the gauge and Higgs fields. The bosonic part of the Lagrangian is determined by quadratic invariants of the field strengths. All coefficients of the Higgs potential are paramitrized as second order rational functions of parameters in the covariant derivatives. Hierarchically different mass scales, the electroweak scale and the grand unified scale, are nertly incorporated in the covariant derivatives in terms of parameters related to the Higgs fields and of vacuum parameters being independent of any interactions. The Georgi-Glasyow symmetry is proved to spontaneously break down into the Weinberg-Salam symmetry for a choice of the sign of the Higgs coupling constant that prohibits colored Higgs bosons from mediating rapid proton decay.
理論物理学刊行会の論文
1996-03-25