Next-to-Minimal Supersymmetric Standard Model in the context of Mu problem

In particle physics, NMSSM is an acronym for Next-to-Minimal Supersymmetric Standard Model. It is a supersymmetric extension to the Standard Model that adds an additional singlet chiral superfield to the MSSM and can be used to dynamically generate the ${\displaystyle \mu }$ term, solving the ${\displaystyle \mu }$-problem. Articles about the NMSSM are available for review.

The Minimal Supersymmetric Standard Model does not explain why the ${\displaystyle \mu }$ parameter in the superpotential term ${\displaystyle \mu H_{u}H_{d}}$ is at the electroweak scale. The idea behind the Next-to-Minimal Supersymmetric Standard Model is to promote the ${\displaystyle \mu }$ term to a gauge singlet, chiral superfield ${\displaystyle S}$. Note that the scalar superpartner of the singlino ${\displaystyle S}$ is denoted by ${\displaystyle {\hat {S}}}$ and the spin-1/2 singlino superpartner by ${\displaystyle {\tilde {S}}}$ in the following. The superpotential for the NMSSM is given by