The supersymmetric
Higgs mass parameter appears as the following term in the
superpotential: . 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 and get a non-zero
vacuum expectation value after
electroweak symmetry breaking, should be of the order of magnitude of the
electroweak scale, many orders of magnitude smaller than the
Planck scale (), 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 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 that parameterizes the hidden supersymmetry-breaking sector of the theory (meaning that is the non-zero -term). Let us assume that the
Kahler potential includes a term of the form \ \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
Planck mass. Then as supersymmetry breaks, gets a non-zero vacuum expectation value ⟨⟩ and the following effective term is added to the superpotential: \ \frac{\ \langle F_\mathsf{X} \rangle\ }{\ M_\mathsf{pl}\ }\ H_\mathsf{u}\ H_\mathsf{d}\ , which gives a measured \ \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 \ \frac{\ \langle F_\mathsf{X} \rangle\ }{\ M_\mathsf{pl}\ }\ . == See also ==