# On explaining the observed pattern of quark and lepton masses

## TL;DR

This paper proposes a model replacing the Higgs sector with a gauge flavor dynamics, explaining quark and lepton masses, neutrino Majorana masses, and predicting new Higgs particles at the Fermi scale, with a high flavor scale around 10^{14} GeV.

## Contribution

It introduces a gauge flavor dynamics framework that accounts for fermion mass patterns and neutrino masses, predicting new Higgs states and flavor gauge boson masses.

## Key findings

- Predicted three sterile-neutrino Majorana masses at scale Λ.
- Derived small Dirac masses exponentially suppressed relative to Λ.
- Estimated flavor scale Λ around 10^{14} GeV.

## Abstract

Higgs sector of the Standard model (SM) is replaced by the gauge $SU(3)_f$ quantum flavor dynamics (QFD) with one parameter, the scale $\Lambda$. Anomaly freedom of QFD demands extension of the fermion sector of SM by three sterile right-handed neutrino fields. Poles of fermion propagators with chirality-changing self-energies $\Sigma(p^2)$ spontaneously generated by QFD at strong coupling define: (1) Three sterile-neutrino Majorana masses $M_{fR}$ of order $\Lambda$. (2) Three Dirac masses $m_f$, degenerate for $e_f, \nu_f, u_f, d_f$ in family $f$, exponentially small with respect to $\Lambda$. Goldstone theorem implies: All eight flavor gluons acquire masses of order $M_{fR}$. $W$ and $Z$ bosons acquire masses of order $\sum m_f$, the effective Fermi scale. Composite 'would-be' Nambu-Goldstone bosons have their 'genuine' partners, the composite Higgs particles: The SM-like Higgs $h$ and two new Higgses $h_3$ and $h_8$, all with masses at Fermi scale; three Higgses $\chi_i$ with masses at scale $\Lambda$. Large pole-mass splitting of charged leptons and quarks in $f$ is arguably due to full QED $\Sigma(p^2)$-dependent fermion-photon vertices enforced by Ward-Takahashi identities. The argument relies on illustrative computation of pole-mass splitting found non-analytic in fermion electric charges. Neutrinos are the Majorana particles with seesaw mass spectrum computed solely by QFD. Available data fix $\Lambda$ to, say, $\Lambda \sim 10^{14} \rm GeV$.