The Improved Bounce Solution of SU(2)-Higgs Model

We further develop the reduced action formalism of the SU(2)-Higgs model originally given by Aoyama et.al.. Our new ansatz for the sphaleron solution makes it possible to apply this formalism to all range of the Higgs self coupling constant. Based on the formalism, we construct a bounce solution oscillating around the sphaleron.Comment: Plain TeX, 12 pages plus 3 figures available upon request, TMUP-HEL-930

Dynamical realization of democratic Yukawa matrices and alignment of A-terms

We study realization of the democratic form of Yukawa matrices by infrared fixed points. We investigate renormalization-group flows of Yukawa couplings in models with a single Yukawa matrix for three families, and up and down-sector Yukawa matrices. It is found that each model has its certain pattern of renormalization-group flows of Yukawa matrices. We apply them to the charged lepton sector and quark sector, and show that realistic results for the second and third families are obtained with natural initial conditions, e.g. $(V_{MNS})_{23} \sim 2/\sqrt{6}$, $m_s/m_b \sim V_{cb} \sim m_{\mu}/m_\tau$ and $m_c/m_t \sim (m_s/m_b)^{3/2}$. We also study corresponding A-terms. The A-terms approach toward the universal form with no physical CP-violating phase. Thus, constraints due to various neutral flavor changing processes except for $\mu \to e \gamma$ are found to be satisfied by this dynamics. In order to suppress the electric dipole moments as well as $\mu \to e \gamma$ sufficiently, more alignment of the A-terms with some reason is required.Comment: 25 pages, late

Visiting Old, Learn New (Logic, Algebraic system, Language and Related Areas in Computer Science)

This is a summary of our results [Y. Kobayashi, K. Shirayanagi, M. Tsukada and S.-E. Takahasi, A complete classification of three-dimensional algebras over ℂ and ℝ（温故知新） Asian-European J. Math. 14 (2021).]