Axion in the minimal SO(10) GUT

Abstract

The QCD axion is investigated within the minimal supersymmetric SO(10) grand unified theory, where the Yukawa sector involves Higgs multiplets ${\bf 10}$ and $\overline{\bf 126}$. The relative phase between the VEVs of $({\bf 10,1,3})\subset\overline{\bf 126}$ and $({\bf \overline{10},1,3})\subset{\bf 126}$ under ${\rm SU}(4)_C\times{\rm SU}(2)_L\times{\rm SU}(2)_R$ is identified with the axion. The Peccei-Quinn and $B-L$ symmetry breaking scales coincide through $|\langleΔ_R\rangle|=|\langle\overlineΔ_R\rangle|$. The scalar partner of the lightest right-handed neutrino plays the role of the inflaton, realizing hybrid inflation consistent with the observed CMB density fluctuations. After inflation, both fields acquire VEVs, and the domain-wall problem is resolved through the Lazarides-Shafi mechanism, which naturally restricts the model to three generations.

Figures (2)

• Figure 1: Hybrid-inflation waterfall schematic: Order parameter $r_D\equiv |\Delta_R|/M=|\overline{\Delta}_R|/M$ as a function of the inflaton ratio $\tilde{N}_1/\tilde{N}_{1c}$ in F-term hybrid inflation LindeDvali. For $\tilde{N}_1>\tilde{N}_{1c}$ (right of the dashed line) the waterfall fields are stabilized at the origin and $r_D=0$ (inflation phase). When $\tilde{N}_1$ reaches the critical value $\tilde{N}_{1c}$, $m_\Delta^2$ turns tachyonic and the system rolls to the symmetry-breaking phase. Time flows from right to left along the horizontal axis.
• Figure 2: Schematic potential landscapes for the waterfall sector in terms of $x\equiv |\Delta_R|/M$ and $y\equiv |\overline{\Delta}_R|/M$. Left:for $\tilde{N}_1>\tilde{N}_{1c}$ the minimum is at $x=y=0$, so the inflationary valley lies at $\Delta_R=\overline{\Delta}_R=0$ with vacuum energy $V_0=\kappa^2M^4$. Right: for $\tilde{N}_1>\tilde{N}_{1c}$ a valley opens along the F-flat constraint $xy=1$ (dashed), and D-flatness $x=y$ (dash-dot) selects the true vacuum at $(x,y)=(1,1)$ where $V=0$.