Geometry of the Ground State of Higgs Fields in Next-to-MSSM

Abstract

Decomposing the Higgs potential ${\mathcal{V}}_{higgs}$ of next - to - Minimal Supersymmetric Standard Model (n-MSSM) \ as the sum of three contributions like ${\mathcal{V}}_{ch}+{\mathcal{V}}_{kah}+{\mathcal{V}}_{expl}$ and assuming the two following things: $\left(a\right)$ ${\mathcal{V}}_{higgs}$ dominated by ${\mathcal{V}}_{ch}$ coming from the chiral sector of supersymmetry: ${\mathcal{V}}_{ch}={\left|\nu \right|}^2\mathcal{U}$ with $\left|\nu \right|$ large and $\frac{\mathrm{r}}{|\nu |}<<1$; and $\left(b\right)$ replacing the chiral down Higgs superfield doublet ${\left({\mathbf{H}}_d\right)}^i$ of n-MSSM by a chiral anti-doublet ${\left({\mathbf{\Phi }}_d\right)}_i$; we derive the explicit geometry of the Higgs fields in the ground state $|{\Sigma }_{higgs}⟩$ found to be given by two intersecting conifolds. We show as well that the property $\tan {\beta }_{susy}=1$ living at singularity $r=0$ is a supersymmetric signal; and deviation away reads in terms of the Kahler parameter $r$ and the ${\vartheta }_{{}_W}$- Weinberg angle as $\tan \beta \simeq 1+\frac{\mathrm{r}}{2|\nu |}{\sin }^2{\vartheta }_{{}_W}$. Other related issues are also studied.

Comments: LaTex, 80 pages, 3 figures