Fermion mass generation inSO(10)with a unified Higgs sector

Abstract

An analysis of generating fermion masses via cubic couplings in SO(10) grand unification with a unified Higgs sector is given. The new framework utilizes a single pair of vector--spinor representation $144+\bar{144}$ to break the gauge symmetry all the way to $SU(3)_C \times U(1)_{em}$. Typically the matter--Higgs couplings in this framework are quartic and lead to naturally suppressed Yukawa couplings for the first two generations. Here we show that much larger third generation couplings naturally arise at the cubic level with additional matter in 10--plet and 45--plet representations of SO(10). Thus the physical third generation is a mixture of 16, 10 and 45--plet representations while the remaining components become superheavy and are removed from the low energy spectrum. In this scenario it is possible to understand the heaviness of the top in a natural way since the analysis generates a hierarchy in the Yukawa couplings so that $h_{\textnormal {t}}/h_{\textnormal {b}}>> 1$ where $h_{\textnormal {t}} (h_{\textnormal {b}})$ are the top (bottom) Yukawa couplings. It is then possible to realize values of $\tan\beta$ as low as 2, which also helps to stabilize the proton.