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Mass and Flavor Mixing Schemes of Quarks and Leptons

Harald Fritzsch, Zhi-zhong Xing

TL;DR

Mass and Flavor Mixing Schemes of Quarks and Leptons surveys phenomenological approaches to fermion masses and flavor mixing, highlighting how strong hierarchies and proposed flavor symmetries shape realistic mass matrices. The authors discuss Hermitian and non-Hermitian textures for quarks, texture zeros, democracy breaking, and running effects to connect high-scale models to low-energy observables. In the lepton sector they analyze neutrino mass textures under solar and atmospheric oscillation data, seesaw-invariant textures, and four-neutrino schemes to accommodate LSND, with a focus on large leptonic mixing and potential CP violation. The work emphasizes that upcoming B factories and long-baseline neutrino experiments will test these textures and shed light on CP violation, mass generation, and possible flavor symmetries.

Abstract

We give an overview of recent progress in the study of fermion mass and flavor mixing phenomena. The hints exhibited by the quark and lepton mass spectra towards possible underlying flavor symmetries, from which realistic models of mass generation could be built, are emphasized. A variety of schemes of quark mass matrices at low and superhigh energy scales are described, and their consequences on flavor mixing and CP violation are discussed. Instructive patterns of lepton mass matrices, which can naturally lead to large flavor mixing angles, are explored to interpret current data on atmospheric and solar neutrino oscillations. We expect that B-meson factories and long-baseline neutrino experiments will soon shed more light on the dynamics of fermion masses, flavor mixing and CP violation.

Mass and Flavor Mixing Schemes of Quarks and Leptons

TL;DR

Mass and Flavor Mixing Schemes of Quarks and Leptons surveys phenomenological approaches to fermion masses and flavor mixing, highlighting how strong hierarchies and proposed flavor symmetries shape realistic mass matrices. The authors discuss Hermitian and non-Hermitian textures for quarks, texture zeros, democracy breaking, and running effects to connect high-scale models to low-energy observables. In the lepton sector they analyze neutrino mass textures under solar and atmospheric oscillation data, seesaw-invariant textures, and four-neutrino schemes to accommodate LSND, with a focus on large leptonic mixing and potential CP violation. The work emphasizes that upcoming B factories and long-baseline neutrino experiments will test these textures and shed light on CP violation, mass generation, and possible flavor symmetries.

Abstract

We give an overview of recent progress in the study of fermion mass and flavor mixing phenomena. The hints exhibited by the quark and lepton mass spectra towards possible underlying flavor symmetries, from which realistic models of mass generation could be built, are emphasized. A variety of schemes of quark mass matrices at low and superhigh energy scales are described, and their consequences on flavor mixing and CP violation are discussed. Instructive patterns of lepton mass matrices, which can naturally lead to large flavor mixing angles, are explored to interpret current data on atmospheric and solar neutrino oscillations. We expect that B-meson factories and long-baseline neutrino experiments will soon shed more light on the dynamics of fermion masses, flavor mixing and CP violation.

Paper Structure

This paper contains 27 sections, 185 equations, 10 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Overview of fermion mass spectra
  3. Charged lepton and quark masses
  4. Massive Dirac and Majorana neutrinos
  5. Flavor mixing and $CP$ violation
  6. Number of fermion mixing parameters
  7. Conditions for $CP$ violation
  8. Unitarity triangles of quark mixing
  9. Unitarity triangles of lepton mixing
  10. Classification of different parametrizations
  11. A unique description of flavor mixing
  12. Realistic schemes of quark mass matrices
  13. Generic Hermitian mass matrices
  14. Symmetry limits of quark masses
  15. A Hermitian scheme with four texture zeros
  16. ...and 12 more sections

Figures (10)

  • Figure 2.1: Possible neutrino mass spectra to accommodate current data on solar, atmospheric and LSND neutrino oscillations.
  • Figure 3.1: Unitarity triangles of the flavor mixing matrix in the complex plane. Each triangle is named in terms of the quark flavor that does not manifest in its three sides.
  • Figure 3.2: Unitarity triangles of the lepton flavor mixing matrix in the complex plane. Each triangle is named by the flavor index that does not manifest in its three sides.
  • Figure 3.3: The light-quark triangle (a) and the rescaled unitarity triangle (b) in the complex plane.
  • Figure 4.1: The light-quark triangle (LT) in the complex plane.
  • ...and 5 more figures