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In theoretical physics, the `!μ problem`! is a problem of `F33f`_`[supersymmetric`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Supersymmetry]`_`f theories, concerned with understanding the parameters of the theory.

>>Contents

• `F0af`_`[Background`#background]`_`f

• `F0af`_`[See also`#see-also]`_`f

• `F0af`_`[References`#references]`_`f

• `F0af`_`[External links`#external-links]`_`f

-─

>>Background

The supersymmetric `F33f`_`[Higgs`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Peter_Higgs]`_`f mass parameter μ appears as the following term in the `F33f`_`[superpotential`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Superpotential]`_`f: μ Hu Hd. It is necessary to provide a mass for the fermionic `F33f`_`[superpartners`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Superpartner]`_`f of the Higgs bosons, i.e. the `F33f`_`[higgsinos`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Higgsino]`_`f, and it enters as well the scalar potential of the Higgs bosons.

To ensure that Hu and Hd get a non-zero `F33f`_`[vacuum expectation value`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Vacuum_expectation_value]`_`f after `F33f`_`[electroweak symmetry breaking`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Electroweak_symmetry_breaking]`_`f, μ should be of the order of magnitude of the `F33f`_`[electroweak scale`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Electroweak_scale]`_`f, many orders of magnitude smaller than the `F33f`_`[Planck scale`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Planck_scale]`_`f (Mpl), which is the natural `F33f`_`[cutoff`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Cutoff_(physics)]`_`f scale. This brings about a problem of naturalness: Why is that scale so much smaller than the cutoff scale? And why, if the μ term in the superpotential has different physical origins, do the corresponding scale happen to fall so close to each other?

Before `F33f`_`[LHC`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=LHC]`_`f, it was thought that the `F33f`_`[soft supersymmetry breaking`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Soft_supersymmetry_breaking]`_`f 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.`:cite-ref-1[`F5bf`_`[1`#cite-note-1]`_`f]

One proposed solution, known as the `F33f`_`[Giudice`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Gian_Francesco_Giudice]`_`f–Masiero mechanism,`:cite-ref-2[`F5bf`_`[2`#cite-note-2]`_`f] is that this term does not appear explicitly in the Lagrangian, because it violates some global symmetry, and can therefore be created only via `F33f`_`[spontaneous breaking`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Spontaneous_symmetry_breaking]`_`f of this symmetry. This is proposed to happen together with `F33f`_`[F-term`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=F-term]`_`f `F33f`_`[supersymmetry breaking`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Supersymmetry_breaking]`_`f, with a spurious field X that parameterizes the hidden supersymmetry-breaking sector of the theory (meaning that FX is the non-zero F-term).

Let us assume that the `F33f`_`[Kahler potential`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Kahler_potential]`_`f includes a term of the form X M p l H u H d {\\displaystyle \\ {\\frac {X}{\\ M_{\\mathsf {pl}}\\ }}\\ H_{\\mathsf {u}}\\ H_{\\mathsf {d}}\\ } times some dimensionless coefficient, which is naturally of order one, and where Mpl is `F33f`_`[Planck mass`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Planck_mass]`_`f. Then as supersymmetry breaks, FX gets a non-zero vacuum expectation value ⟨FX⟩ and the following effective term is added to the superpotential: ⟨ ⟨ F X ⟩ ⟩ M p l H u H d , {\\displaystyle \\ {\\frac {\\ \\langle F_{\\mathsf {X}}\\rangle \\ }{\\ M_{\\mathsf {pl}}\\ }}\\ H_{\\mathsf {u}}\\ H_{\\mathsf {d}}\\ ,} which gives a measured μ μ = ⟨ ⟨ F X ⟩ ⟩ M p l . {\\displaystyle \\ \\mu ={\\frac {\\ \\langle F_{\\mathsf {X}}\\rangle \\ }{\\ M_{\\mathsf {pl}}\\ }}\\ .} On the other hand, soft supersymmetry breaking terms are similarly created and also have a natural scale of ⟨ ⟨ F X ⟩ ⟩ M p l . {\\displaystyle \\ {\\frac {\\ \\langle F_{\\mathsf {X}}\\rangle \\ }{\\ M_{\\mathsf {pl}}\\ }}\\ .}

>>See also

• `F33f`_`[NMSSM`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=NMSSM]`_`f (Next-to-Minimal Supersymmetric Standard Model)

• `F33f`_`[Minimal Supersymmetric Standard Model`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Minimal_Supersymmetric_Standard_Model]`_`f

• `F33f`_`[Doublet–triplet splitting problem`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doublet–triplet_splitting_problem]`_`f

• `F33f`_`[Hierarchy problem`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hierarchy_problem]`_`f

• `F33f`_`[Little hierarchy problem`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Little_hierarchy_problem]`_`f

>>References

`:cite-note-1`!1.`! `F0af`_`[↑`#cite-ref-1]`_`f `:citereffowlie2014`aFowlie, Andrew (2014). "Is the CNMSSM more credible than the CMSSM?". `*The European Physical Journal C`*. `!74`! (10): 3105. `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:1407.7534. `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:2014EPJC...74.3105F. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1140/epjc/s10052-014-3105-y. `F33f`_`[S2CID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=S2CID_(identifier)]`_`f 119304794.

`:cite-note-2`!2.`! `F0af`_`[↑`#cite-ref-2]`_`f `:citerefgiudice-g-f-masiero-a-1988`aGiudice, G.F.; Masiero, A. (1988). "A natural solution to the mu problem in supergravity theories". `*Physics Letters B`*. `!206`! (3): 480–484. `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:1988PhLB..206..480G. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1016/0370-2693(88)91613-9.

>>External links

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

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