The Minimal SU(5) Unification Model

Abstract

I present the most minimal realistic $SU(5)$ unification model to date and discuss its main predictions. The particle content of the model comprises $5_H$, $24_H$, $35_H$, ${\overline{5}_F}_i$, ${10_F}_i$, $15_F$, $\overline{15}_F$, and $24_V$, where subscripts $H$, $F$, and $V$ denote whether a given representation contains scalars, fermions, or gauge bosons, respectively, while $i=1,2,3$. The model employs all possible interaction terms, as allowed by the Lorentz group, the $SU(5)$ gauge symmetry, and the aforementioned particle content, to generate the Standard Model fermion masses through three different mechanisms. It also connects the neutrino mass generation mechanism to the experimentally observed mass disparity between the down-type quarks and charged leptons. The minimal structure of the model requires $24_H$ and $5_H$ not only to break $SU(5)$ and $SU(3) \times SU(2) \times U(1)$ gauge groups, respectively, but to accomplish one additional task each. The model furthermore predicts that neutrinos are strictly Majorana fields, that one neutrino is purely a massless particle, and that neutrino masses are of normal ordering. The current experimental bound on the $p \rightarrow \pi^0 e^+$ lifetime limit, in conjunction with the prediction of the model for the gauge mediated proton decays, implies that there are four new scalar multiplets at or below a $120$\,TeV mass scale if these multiplets are mass degenerate. If these multiplets are not mass degenerate, the quoted limit then applies, for all practical purposes, to the geometric mean of their masses. The scalar multiplets in question transform as $(1,3,0)$, $(8,1,0)$, $(\overline{3},3,-2/3)$, and $(\overline{6},2,1/6)$ under the Standard Model gauge group $SU(3) \times SU(2) \times U(1)$ with calculable couplings to the Standard Model fields.