Neutrino Mass Origin and Flavored-QCD axion in an Extra-Dimension

TL;DR

This paper introduces a unified extra-dimensional flavor model that explains fermion mass hierarchies, solves the strong CP problem, and predicts a QCD axion mass around 2.5×10⁻⁹ eV, consistent with experimental data.

Contribution

It presents a novel extra-dimensional framework with modular form Yukawa couplings, addressing fermion hierarchies, neutrino masses, and the strong CP problem simultaneously.

Findings

Explains quark and lepton mass and mixing hierarchies.

Provides a mechanism for light neutrino mass generation.

Predicts a QCD axion mass of approximately 2.5×10⁻⁹ eV.

Abstract

We propose a unified flavor model with the Standard Model fields on two 3-branes within an extra-dimensional setup, incorporating $\Gamma_N\times U(1)_X$ symmetry with a modulus and scalar field responsible for symmetry breaking. When compactified to four dimensions, Yukawa couplings, initially expressed as modular forms with mass dimensions, are normalized to conform to canonical four-dimensional theory, with the Yukawa coefficients being complex numbers of unit absolute value. We show that this model naturally explains the mass and mixing hierarchies of quarks and leptons, solves the strong CP problem, provides a natural solution to the hierarchy problem, and can inherently satisfy no axionic domain-wall problem. The $U(1)_X$ mixed gravitational anomaly-free condition necessitates that electrically neutral mirror bulk fermions couple to the normal neutrino field on the 3-brane, consistent with the boundary condition. Consequently, we demonstrate a mechanism for generating light neutrino masses, similar to the Weinberg operator, by transmitting the information of $U(1)_X$ breakdown between the two 3-branes. The scale of $U(1)_X$ breaking is estimated from neutrino data to be around $10^{15}$ GeV, leading to a QCD axion mass of approximately $2.5\times10^{-9}$ eV. Through numerical analysis, we demonstrate that the model yields results consistent with current experimental data on quarks and leptons, and it also provides predictions for neutrinos.