$SU(3)_{F}$ Gauge Family Model and New Symmetry Breaking Scale From FCNC Processes

TL;DR

This paper explores an $SU(3)_F$ gauge family symmetry model explaining neutrino masses and mixings, analyzing its symmetry breaking scale, gauge boson masses, and their effects on flavor-changing neutral currents, with results consistent with current experimental bounds.

Contribution

It introduces a detailed analysis of the $SU(3)_F$ gauge family symmetry model's symmetry breaking scale and gauge boson masses based on FCNC processes, providing new constraints and insights.

Findings

Symmetry breaking scale can be as low as 300 TeV.

Lightest gauge boson mass estimated around 100 TeV.

New physics contributions are well below current experimental bounds.

Abstract

Based on the $SU(3)_{F}$ gauge family symmetry model which was proposed to explain the observed mass and mixing pattern of neutrinos, we investigate the symmetry breaking, the mixing pattern in quark and lepton sectors, and the contribution of the new gauge bosons to some flavour changing neutral currents (FCNC) processes at low energy. With the current data of the mass differences in the neutral pseudo-scalar $P^{0}-\bar{P}^{0}$ systems, we find that the $SU(3)_{F}$ symmetry breaking scale can be as low as 300TeV and the mass of the lightest gauge boson be about $100$TeV. Other FCNC processes, such as the lepton flavour number violation process $\mu^{-}\rightarrow e^{-}e^{+}e^{-}$ and the semi-leptonic rare decay $K\rightarrow \pi \bar{\nu} \nu$, contain contributions via the new gauge bosons exchanging. With the constrains got from $P^0-\bar{P}^0$ system, we estimate that the contribution of the new physics is around $10^{-16}$, far below the current experimental bounds.