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Dual Revelations of Quark Mass Hierarchies

Ying Zhang

Abstract

To solve the mystery of flavor structure, we demonstrate two revelations emerging from the hierarchical masses of quarks: one for the mass matrix itself and one for the CKM mixing. These revelations naturally lead to a non-redundant, ordered, and family-unified quark flavor structure, which serves as a candidate to replace the unclear Yukawa interactions of the Standard Model.

Dual Revelations of Quark Mass Hierarchies

Abstract

To solve the mystery of flavor structure, we demonstrate two revelations emerging from the hierarchical masses of quarks: one for the mass matrix itself and one for the CKM mixing. These revelations naturally lead to a non-redundant, ordered, and family-unified quark flavor structure, which serves as a candidate to replace the unclear Yukawa interactions of the Standard Model.

Paper Structure

This paper contains 21 sections, 57 equations, 3 figures, 2 tables.

Table of Contents

  1. Motivation
  2. First Revelation: The Factorized Mass Matrix
  3. Redundant Right-Handed Transformations
  4. Hierarchical Mass Structure
  5. Leading-Order Structure
  6. Implication: The Yukawa Basis
  7. Second Revelation: Sub-Unitarity of Quark Mixing
  8. Unitarity of the CKM Matrix
  9. The Sub-Unitarity Structure
  10. Implications for Mixing Angles
  11. A Unified Flavor Structure
  12. Family Symmetry and Its Breaking
  13. Structure of the CKM Matrix
  14. Unification Through Sub-Unitarity
  15. The Flat Matrix as the Natural Pattern
  16. ...and 6 more sections

Figures (3)

  • Figure 1: Quark Mass Scale
  • Figure 2: The $SO(2)^q$ symmetry of mass pattern.
  • Figure 3: The CKM mixing fit. The dashed line shows the sub-unitarity limit.