Mu problem

In theoretical physics, the μ problem is a problem of supersymmetric theories, concerning with understanding the parameters of the theory.

The supersymmetric Higgs mass parameter μ appears as the following term in the superpotential: μH_uH_d. It is responsible for the fact that both H_u and H_d gets a non-zero vacuum expectation value after electroweak symmetry breaking, so that all quarks and leptons can get masses. It should therefore be of the order of magnitude of the electroweak scale, many orders of magnitude smaller than that of the planck scale, which is the natural cutoff scale.

The soft supersymmetry breaking terms should also be of the same order of magnitude as the electroweak scale. This brings about a problem of naturalness: why are these scales so much smaller than the cutoff scale and yet happen to fall so close to each other?

In gravity-mediated supersymmetry a proposed solution is that this term does not appear explicitly in the Lagrangian, because it violates PQ symmetry, and can therefore be created only via spontaneous symmetry breaking of this symmetry, which happens together with supersymmetry breaking, if supersymmetry breaks via an F-term, with the spurious field X (meaning that F_X is the non-zero F-term), assuming that the Kahler potential includes terms of the form f(X)H_uH_d for some function f.