Relation between quark masses and weak mixings

Abstract

Simple transformation formulas between fermion matrices and observables, and numerical values of quark matrices, are obtained on a particular weak basis with one quark matrix diagonal and the other with vanishing elements 1-1, 1-3 and 3-1, and with only the element 2-2 complex. When we choose $M_u$ diagonal, then $M_d$ shows intriguing numerical properties which suggest a four parameter description of it, which implies $V_{us}\simeq \sqrt{m_d/m_s}$, $V_{cb}\simeq (3/\sqrt{5})(m_s/m_b)$ and $V_{ub}\simeq (1/\sqrt{5})(\sqrt{m_d{m}_s}/m_b)$. Few comments on mass-mixing relations are added.

8 pages LaTeX, no figures. Some misprints corrected and reference style changed

References in corpus (5)

• Updated Estimate of Running Quark Masses
• Triangular mass matrices of quarks and Cabibbo-Kobayashi-Maskawa mixing
• NNI-Form Quark Mass Matrix Expressed by the Observable Quantities
• The rephasing freedom and the NNI form of quark mass matrices
• Fermion Mass Matrices in term of the Cabibbo-Kobayashi-Maskawa Matrix and Mass Eigenvalues

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• Testing quark mass matrices with right-handed mixings
• Fermion masses and mixings in gauge theories
• Neutrinos Meet Supersymmetry: Quantum Aspects of of Neutrinophysics in Supersymmetric Theories