[Paper Review] Complementary Quark and Lepton Deviation from Mass-Degeneracy Hierarchies

É. M. Lipmanov|ArXiv.org|Jun 10, 2009

Neutrino Physics Research6 references3 citations

TL;DR

This paper proposes a framework to explain the observed mass and mixing hierarchies in quarks and leptons by analyzing deviations from mass-degeneracy (DMD) in the context of the electroweak theory. Using linear and quadratic DMD-hierarchy equations with complementary patterns between quarks and charged leptons, it derives dual relations between Dirac and Majorana particles, naturally reproducing approximate quark-neutrino mixing angle complementarity through a small emergent parameter.

ABSTRACT

Near magnitudes of Dirac particle mass-ratios, mixing hierarchy-quantities and electroweak charges against the background of highly successful flavor-universal one-generation EW theory is a puzzle in need of diverse inclusive research. In this paper I study the problem in proper terms of lepton and quark Deviation-from-Mass-Degeneracy (DMD) hierarchies at tree EW approximation. As primary are considered not discrete flavor symmetry but rather the deviations from mass-degeneracy-symmetry without inventing exact particular symmetry. Empirically suggested benchmark flavor patterns (zero approximation) and deviations from benchmarks caused by emergence of a small related to EW charges parameter are considered two sources of realistic flavor quantities. Physically interesting mass and mixing flavor quantities are obtained as solutions of linear and quadratic DMD-hierarchy equation-pairs with complementary patterns of quark and lepton DMD-hierarchies. Dual relations between DMD-quantities of quarks and charged leptons (Dirac particles), on the one hand, and neutrinos (likely Majorana particles), on the other hand, are inferences. Considered in the literature approximate quark-neutrino mixing angle complementarity appears naturally from the violation of benchmark patterns by the emergent small parameter.

Motivation & Objective

• To address the puzzle of flavor hierarchy in quarks and leptons beyond discrete flavor symmetries.
• To model mass and mixing patterns using deviations from mass-degeneracy rather than exact symmetries.
• To derive dual relations between Dirac (quarks, charged leptons) and Majorana (neutrinos) particles via DMD hierarchies.
• To explain the observed approximate quark-neutrino mixing angle complementarity as a consequence of small parameter emergence.
• To provide a phenomenologically motivated framework using empirically suggested benchmarks and perturbative deviations.

Proposed method

• Formulates Deviation-from-Mass-Degeneracy (DMD) hierarchies at tree-level electroweak approximation.
• Uses linear and quadratic DMD-hierarchy equation-pairs to model flavor quantities in quarks and charged leptons.
• Introduces a small parameter related to electroweak charges as the source of deviations from benchmark flavor patterns.
• Applies complementary patterns of DMD between quarks and charged leptons to derive dual relations with neutrinos.
• Employs empirically suggested zero-approximation flavor patterns as baseline for perturbative corrections.
• Derives physical mass and mixing quantities as solutions of the DMD equation-pairs without assuming exact flavor symmetry.

Experimental results

Research questions

• RQ1 How can the observed mass and mixing hierarchies in quarks and leptons be explained without relying on discrete flavor symmetries?
• RQ2 What is the origin of the approximate quark-neutrino mixing angle complementarity in the context of electroweak theory?
• RQ3 How do small deviations from mass-degeneracy lead to realistic flavor quantities in the quark and lepton sectors?
• RQ4 What dual relations exist between Dirac-type particles (quarks, charged leptons) and Majorana-type particles (neutrinos) in the DMD framework?
• RQ5 Can a single small parameter arising from electroweak charges explain the observed flavor hierarchy patterns?

Key findings

• The model reproduces the approximate quark-neutrino mixing angle complementarity naturally through the violation of benchmark flavor patterns by a small emergent parameter.
• Solutions to the linear and quadratic DMD-hierarchy equation-pairs yield physically interesting mass and mixing flavor quantities for quarks and charged leptons.
• Dual relations between quark/charged lepton DMD-hierarchies and neutrino DMD-hierarchies are inferred as a direct consequence of the framework.
• The approach successfully incorporates electroweak charges as a source of deviations from mass-degeneracy, leading to realistic flavor patterns.
• The framework avoids the need to postulate exact flavor symmetries, instead focusing on measurable deviations from degeneracy.
• The final model is consistent with the one-generation electroweak theory and provides a phenomenologically viable alternative to symmetry-based flavor models.