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: $\mathcal{ V}_{ ch}=\left \vert \mathrm{ \nu }\right \vert ^{ 2}\mathcal{ U}$ with $\left \vert \mathrm{ \nu }\right \vert $ large and $\frac{ \mathrm{ r}}{ \left \vert \mathrm{ \nu }\right \vert }<<1$; and $\left( b\right) $ replacing the chiral down Higgs superfield doublet $\left( \boldsymbol{ H}_{ d}\right) ^{ i}$ of n-MSSM by a chiral anti-doublet $\left( \boldsymbol{ \Phi}_{ d}\right) _{ i}$; we derive the explicit geometry of the Higgs fields in the ground state $\left \vert \Sigma _{ higgs}\right \rangle $ 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 $\tan \beta \simeq1+\frac{ \mathrm{ r}}{ 2\left \vert \mathrm{ \nu }\right \vert }\sin^{ 2}\vartheta _{ _{ W}}$. Other related issues are also studied.
Categories: hep-ph hep-th