Next-to-Minimal Supersymmetric Standard Model

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Next-to-Minimal Supersymmetric Standard Model" – news · newspapers · books · scholar · JSTOR (December 2010) (Learn how and when to remove this message)

In particle physics, NMSSM is an acronym for Next-to-Minimal Supersymmetric Standard Model. ^{[1][2][3][4][5]} 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.^[6][7]

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

${\displaystyle W_{\text{NMSSM}}=W_{\text{Yuk}}+\lambda SH_{u}H_{d}+{\frac {\kappa }{3}}S^{3}}$

where ${\displaystyle W_{\text{Yuk}}}$ gives the Yukawa couplings for the Standard Model fermions. Since the superpotential has a mass dimension of 3, the couplings ${\displaystyle \lambda }$ and ${\displaystyle \kappa }$ are dimensionless; hence the ${\displaystyle \mu }$-problem of the MSSM is solved in the NMSSM, the superpotential of the NMSSM being scale-invariant. The role of the ${\displaystyle \lambda }$ term is to generate an effective ${\displaystyle \mu }$ term. This is done with the scalar component of the singlet ${\displaystyle {\hat {S}}}$ getting a vacuum-expectation value of ${\displaystyle \langle {\hat {S}}\rangle }$; that is, we have

${\displaystyle \mu _{\text{eff}}=\lambda \langle {\hat {S}}\rangle }$

Without the ${\displaystyle \kappa }$ term the superpotential would have a U(1)' symmetry, so-called Peccei–Quinn symmetry; see Peccei–Quinn theory. This additional symmetry would alter the phenomenology completely. The role of the ${\displaystyle \kappa }$ term is to break this U(1)' symmetry. The ${\displaystyle \kappa }$ term is introduced trilinearly such that ${\displaystyle \kappa }$ is dimensionless. However, there remains a discrete ${\displaystyle \mathbb {Z} _{3}}$ symmetry, which is moreover broken spontaneously.^[8] In principle this leads to the domain wall problem. Introducing additional but suppressed terms, the ${\displaystyle \mathbb {Z} _{3}}$ symmetry can be broken without changing phenomenology at the electroweak scale.^[9] It is assumed that the domain wall problem is circumvented in this way without any modifications except far beyond the electroweak scale.

Other models have been proposed which solve the ${\displaystyle \mu }$-problem of the MSSM. One idea is to keep the ${\displaystyle \kappa }$ term in the superpotential and take the U(1)' symmetry into account. Assuming this symmetry to be local, an additional, ${\displaystyle Z'}$ gauge boson is predicted in this model, called the UMSSM.^{[citation needed]}