imported>Ca: {{not to be confused with|MU puzzle}}

2025-04-25T05:30:32Z

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{{Short description|Problem of supersymmetric theories}}
{{not to be confused with|MU puzzle}}
In theoretical physics, the '''{{math|μ}} problem''' is a problem of [[supersymmetry|supersymmetric]] theories, concerned with understanding the parameters of the theory.

== Background ==
The supersymmetric [[Peter Higgs|Higgs]] mass parameter {{mvar|μ}} appears as the following term in the [[superpotential]]: {{nowrap|{{mvar|μ}} {{mvar|H}}{{sub|u}} {{mvar|H}}{{sub|d}}}}. It is necessary to provide a mass for the fermionic [[superpartner]]s of the Higgs bosons, i.e. the [[higgsino]]s, and it enters as well the scalar potential of the Higgs bosons.

To ensure that {{mvar|H}}{{sub|u}} and {{mvar|H}}{{sub|d}} get a non-zero [[vacuum expectation value]] after [[electroweak symmetry breaking]], {{mvar|μ}} should be of the order of magnitude of the [[electroweak scale]], many orders of magnitude smaller than the [[Planck scale]] ({{mvar|M}}{{sub|pl}}), which is the natural [[Cutoff (physics)|cutoff]] scale. This brings about a problem of naturalness: Why is that scale so much smaller than the cutoff scale? And why, if the {{mvar|μ}} 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.<ref>{{cite journal |last1 = Fowlie |first1 = Andrew |year = 2014 |title = Is the CNMSSM more credible than the CMSSM? |journal=The European Physical Journal C |volume=74 |issue=10 |page = 3105 |arxiv=1407.7534 |s2cid=119304794 |doi=10.1140/epjc/s10052-014-3105-y|bibcode = 2014EPJC...74.3105F }}</ref>

One proposed solution, known as the [[Gian Francesco Giudice|Giudice]]–Masiero mechanism,<ref>{{cite journal |author1=Giudice, G.F. |author2=Masiero, A. |year= 1988 |title= A natural solution to the mu problem in supergravity theories |journal=Physics Letters B |volume= 206 |issue= 3 |pages=480–484 |doi= 10.1016/0370-2693(88)91613-9 |bibcode = 1988PhLB..206..480G }}</ref> 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 symmetry breaking|spontaneous breaking]] of this symmetry. This is proposed to happen together with [[F-term]] [[supersymmetry breaking]], with a spurious field {{math|X}} that parameterizes the hidden supersymmetry-breaking sector of the theory (meaning that {{mvar|F}}{{sub|X}} is the non-zero {{mvar|F}}-term).

Let us assume that the [[Kahler potential]] includes a term of the form <math>\ \frac{X}{\ M_\mathsf{pl}\ }\ H_\mathsf{u}\ H_\mathsf{d}\ </math> times some dimensionless coefficient, which is naturally of order one, and where M<sub>pl</sub> is [[Planck mass]]. Then as supersymmetry breaks, {{mvar|F}}{{sub|X}} gets a non-zero vacuum expectation value ⟨{{mvar|F}}{{sub|X}}⟩ and the following effective term is added to the superpotential: <math>\ \frac{\ \langle F_\mathsf{X} \rangle\ }{\ M_\mathsf{pl}\ }\ H_\mathsf{u}\ H_\mathsf{d}\ ,</math> which gives a measured <math>\ \mu = \frac{\ \langle F_\mathsf{X} \rangle\ }{\ M_\mathsf{pl}\ }\ .</math> On the other hand, soft supersymmetry breaking terms are similarly created and also have a natural scale of <math>\ \frac{\ \langle F_\mathsf{X} \rangle\ }{\ M_\mathsf{pl}\ }\ .</math>

== See also ==
* [[NMSSM]] (Next-to-Minimal Supersymmetric Standard Model)
* [[Minimal Supersymmetric Standard Model]]
* [[Doublet–triplet splitting problem]]
* [[Hierarchy problem]]
* [[Little hierarchy problem]]

== References ==
{{reflist|25em}}

== External links ==
* [https://web.archive.org/web/20070927021637/http://whepp9.iopb.res.in/talks/DJ_Miller.ppt Supersymmetric Models with extra singlets: a review; DJ Miller, University of Glasgow]

[[Category:Supersymmetric quantum field theory]]
[[Category:Physics beyond the Standard Model]]

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Mu problem - Revision history

imported>Ca: {{not to be confused with|MU puzzle}}