Flavor unity in SU(7): Low-mass magnetic monopole, doubly charged lepton, andQ=53,−43quarks

Abstract

A specific flavor unification is suggested in the SU(7) gauge group. This model can be trivially extended to O(14). A global symmetry $\ensuremath{\Gamma}$ forbids mixings of the $b$ ($Q=\ensuremath{-}\frac{1}{3}$) quark with the $d$ and $s$ quarks, and of the $t$ ($Q=\frac{2}{3}$) quark with the $u$ and $c$ quarks. Since the $b$ and $t$ quarks carry different $\ensuremath{\Gamma}$ quantum numbers, they do not belong to the same $\mathrm{SU}{(2)}_{L}$ doublet. A mechanism for the $\ensuremath{\Gamma}$-symmetry violation is suggested, which allows $c\ensuremath{-}t$ mixing without $b$-quark mixing. There are unconventionally charged light (masses \ensuremath{\lesssim} 300 GeV) fermions: a doubly charged lepton ${T}^{\ensuremath{-}\ensuremath{-}}$, a $Q=\ensuremath{-}\frac{4}{3}$ quark $x$, and a $Q=\frac{5}{3}$ quark $y$. The bare value of the Weinberg angle ${{sin}^{2}\ensuremath{\theta}}_{W}^{0}=\frac{3}{20}$ is renormalized to the low-energy value by introducing an intermediate mass scale ${M}_{1}$. A topologically stable magnetic monopole is light ($\mathrm{mass}\ensuremath{\approx}\frac{{M}_{1}}{\ensuremath{\alpha}}$) and hence there does not exist a conflict arising from the grand unified theories and the hot-big-bang cosmology.