What question did this study set out to answer?

The research aims to develop a framework that explains the mass hierarchy of charged fermions and neutrinos while adhering to the Standard Model.

April 16, 2026Open Access

Paper1Yukawa Hierarchy, Structural Neutrino Mass Law, and PMNS Structure

Key Points

The research aims to develop a framework that explains the mass hierarchy of charged fermions and neutrinos while adhering to the Standard Model.
Formulated a beta-organized mass program to systematize fermion masses.
Introduced a structural law for organizing the Yukawa spectrum using exponential ordering.
Derived relations connecting charged-fermion mass hierarchy and neutrino sector using a symmetric texture.
Established a connection between the Yukawa law and the charged-fermion hierarchy.
Extended the framework to predict mixing angles and CP phase in the neutrino sector.
Demonstrated that the results do not rely on additional scales, maintaining theoretical consistency.

Abstract

This paper formulates a -organized mass program to address three fundamental open questions in particle physics: the hierarchy of visible fermion masses, the sub-eV neutrino sector, and the emergence of the PMNS matrix. While maintaining the Standard Model relation mf = yf v/2, the framework introduces a structural law where the channel organizes the Yukawa spectrum via exponential ordering. The manuscript derives this Yukawa law step-by-step, demonstrating how the charged-fermion hierarchy is encoded and extending the logic to the neutrino regime without ad hoc scales. Finally, it explores the leptonic sector through a --symmetric leading texture, providing a unified benchmark for mixing angles, the CP phase, and squared-mass differences.

Paper1Yukawa Hierarchy, Structural Neutrino Mass Law, and PMNS Structure

Key Points

Abstract

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