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 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.
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 FX is the non-zero F-term).
times some dimensionless coefficient, which is naturally of order one, and where Mpl is Planck mass.
Then as supersymmetry breaks, FX gets a non-zero vacuum expectation value ⟨FX⟩ and the following effective term is added to the superpotential:
On the other hand, soft supersymmetry breaking terms are similarly created and also have a natural scale of