Bottom-tau unification by neutrinos in a nonsupersymmetric SU(5) model

Abstract

We show that Yukawa couplings of bottom quarks and tau leptons can be unified in a non-supersymmetric SU(5) model. We introduce an arbitrary number of right-handed neutrinos. Their masses and Yukawa couplings that satisfy the unification condition by renormalization group evolution are shown. In the case that the grand unification scale is $10^{15.5}$GeV and three right-handed neutrinos have the same mass, the upper bound on their mass is $\sim 10^{14.1}$GeV.

Figures (5)

• Figure 1: Gauge coupling running considering one standard deviation. The GUT scale is taken to be $10^{15.5}$GeV. Dotted lines show the SM case ($\alpha_1$ does not change).
• Figure 2: Solid curves show the initial conditions of neutrino Yukawa couplings at $\mu=M_N$ that realize $b-\tau$ unification. Dashed curves show upper bounds from perturbativity ($M_G=10^{15.5}$GeV). Vertical lines indicate crossing points.
• Figure 3: Running of $b$ and $\tau$ Yukawa couplings in the case $N_g=1$, $M_N=10^{11.1}$GeV, $M_G=10^{15.5}$GeV. $y_\nu(t_N)=1.58$ is calculated by Eq. (\ref{['eyntn']}). Dashed and dot-dashed lines show errors given in Ref. Xing:2011aa. Vertical lines are drawn at $\mu=M_G$.
• Figure 4: Running of $b$ and $\tau$ Yukawa couplings in the case $N_g=2$, $M_N=10^{13.3}$GeV. Other conditions are same as in Fig. \ref{['fbt1']}.
• Figure 5: Running of $b$ and $\tau$ Yukawa couplings in the case $N_g=3$, $M_N=10^{14.1}$GeV. Other conditions are same as in Fig. \ref{['fbt1']}.