Yukawa couplings and quark and lepton masses in an $SO(10)$ model with a unified Higgs sector

Fermion mass generation for the third generation is considered within a unified Higgs model with a single pair of vector-spinor $144+\overline{144}$ of Higgs multiplets. Extending a previous work it is shown that much larger masses can arise for all the third generation fermions from mixing with 45 and 120 matter multiplets via the cubic couplings $16·45·\overline{144}$ and $16·120·144$ in addition to the quartic couplings. Further, it is found that values of $\tan \beta$ as low as 10 can allow for a $b-\tau -t$ unification consistent with the current data. The quartic and cubic couplings naturally lead to Dirac as well as Majorana neutrino masses necessary for the generation of a seesaw neutrino mass of the right size for the tau neutrino.

Figure 1

Right panel: The RG evolution of the Yukawa coupling $h_b(Q)$ for the bottom quark and $h_{\tau }(Q)$ for the $\tau$ lepton for $\alpha =1$, 0.85, 0.7 (see Table ) from the grand unification scale to the electroweak scale where $t$ labeling the x-axis is defined so that $t=\ln (Q(\mathrm{GeV})/16{\pi }^2$. For the analysis of the figure in the right panel we have chosen $h_t(M_G)=0.575$ and $h_b(M_G)$ and $h_{\tau }(M_G)$ are then determined from Table . Left panel: The RG evolution of the Yukawa coupling $h_b(M_G)$ and of $h_t(M_G)$ for values of $h_t(M_G)=1$, 0.8, 0.57 5 and for $h_b(M_G)=1/\gamma$, $.8/\gamma$, $.575/\gamma$ for the case $\alpha =.7$ from the grand unification scale to the electroweak scale where $\gamma =10.73$ as given in Table . The best fit to the $b$, $\tau$, $t$ masses given in Eq. (13) occurs for $\alpha =.7$, $h_t(M_G)=0.575$.