Mu problem

Template:Short description In theoretical physics, the μ problem is a problem of supersymmetric theories, concerned with understanding the parameters of the theory.

Background

The supersymmetric Higgs mass parameter Template:Mvar appears as the following term in the superpotential: Template:Mvar Template:Mvar_u Template:Mvar_d. It is necessary to provide a mass for the fermionic superpartners of the Higgs bosons, i.e. the higgsinos, and it enters as well the scalar potential of the Higgs bosons.

To ensure that Template:Mvar_u and Template:Mvar_d get a non-zero vacuum expectation value after electroweak symmetry breaking, Template:Mvar should be of the order of magnitude of the electroweak scale, many orders of magnitude smaller than the Planck scale (Template:Mvar_pl), which is the natural cutoff scale. This brings about a problem of naturalness: Why is that scale so much smaller than the cutoff scale? And why, if the Template:Mvar term in the superpotential has different physical origins, do the corresponding scale happen to fall so close to each other?

Before LHC, it was thought that the soft supersymmetry breaking terms should also be of the same order of magnitude as the electroweak scale. This was negated by the Higgs mass measurements and limits on supersymmetry models.

One proposed solution, known as the Giudice–Masiero mechanism, is that this term does not appear explicitly in the Lagrangian, because it violates some global symmetry, and can therefore be created only via spontaneous breaking of this symmetry. This is proposed to happen together with F-term supersymmetry breaking, with a spurious field X that parameterizes the hidden supersymmetry-breaking sector of the theory (meaning that Template:Mvar_X is the non-zero Template:Mvar-term).

Let us assume that the Kahler potential includes a term of the form $\frac{X}{M_{\mathsf{p}\mathsf{l}}}{H}_{\mathsf{u}}{H}_{\mathsf{d}}$ times some dimensionless coefficient, which is naturally of order one, and where M_pl is Planck mass. Then as supersymmetry breaks, Template:Mvar_X gets a non-zero vacuum expectation value ⟨Template:Mvar_X⟩ and the following effective term is added to the superpotential: $\frac{⟨F_{\mathsf{X}}⟩}{M_{\mathsf{p}\mathsf{l}}}{H}_{\mathsf{u}}{H}_{\mathsf{d}},$ which gives a measured $\mu =\frac{⟨F_{\mathsf{X}}⟩}{M_{\mathsf{p}\mathsf{l}}}.$ On the other hand, soft supersymmetry breaking terms are similarly created and also have a natural scale of $\frac{⟨F_{\mathsf{X}}⟩}{M_{\mathsf{p}\mathsf{l}}}.$

See also

• NMSSM (Next-to-Minimal Supersymmetric Standard Model)
• Minimal Supersymmetric Standard Model
• Doublet–triplet splitting problem
• Hierarchy problem
• Little hierarchy problem

External links

• Supersymmetric Models with extra singlets: a review; DJ Miller, University of Glasgow

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