NMSSM

The Next-to-Minimal Supersymmetric Standard Model (NMSSM) is an extension of the MSSM that adds a gauge-singlet chiral superfield S. It is motivated by the μ problem of the MSSM, where the supersymmetric μ parameter must be near the electroweak scale but is otherwise arbitrary. In the NMSSM, μ is generated dynamically as μ_eff = λ ⟨S⟩, tying it to the vacuum expectation value of the singlet and the electroweak scale.

The model is defined by a superpotential that typically includes the MSSM matter terms with the MSSM μ-term replaced by λ S H_u H_d plus a self-interaction κ S^3/3 in the Z3-symmetric version. After S acquires a vacuum expectation value, an effective μ-term is generated. The NMSSM expands the neutral fermion sector with a singlino, resulting in five neutralinos, and enlarges the Higgs sector.

The Higgs sector of the NMSSM contains three CP-even and two CP-odd neutral Higgs bosons (in the CP-conserving limit), in addition to the charged Higgses. The mixing with the singlet can give rise to lighter singlet-dominated states and altered couplings. Consequently, new decay modes may appear, such as a SM-like Higgs decaying into lighter pseudoscalars or other Higgs states.

Phenomenologically, the λ term can raise the tree-level mass of the SM-like Higgs, helping address aspects of the hierarchy problem. The NMSSM provides viable dark matter candidates, often with a singlino component, and offers distinctive collider signatures due to the extended Higgs and neutralino sectors. Variants include the scale-invariant NMSSM and models with explicit μ terms; a Z3 symmetry can introduce a domain-wall problem, typically resolved by small explicit breaking terms or higher-dimensional operators.