Year: 2019
Type: article
Abstract: The supersymmetry (SUSY)-preserving $\ensuremath{\mu}$ parameter in SUSY theories is naively expected to be of order the Planck scale while phenomenology requires it to be of order the weak scale. This is the famous SUSY $\ensuremath{\mu}$ problem. Its solution involves two steps: first forbid $\ensuremath{\mu}$, perhaps via some symmetry, and then regenerate it of order the scale of soft SUSY-breaking terms. However, present LHC limits suggest the soft breaking scale ${m}_{\text{soft}}$ lies in the multi-TeV regime while naturalness requires $\ensuremath{\mu}\ensuremath{\sim}{m}_{W,Z,h}\ensuremath{\sim}100\text{ }\text{ }\mathrm{GeV}$ so that a little hierarchy (LH) appears with $\ensuremath{\mu}\ensuremath{\ll}{m}_{\text{soft}}$. We review 20 previously devised solutions to the SUSY $\ensuremath{\mu}$ problem and reevaluate them in light of whether they are apt to support the LH. We organize the 20 solutions as follows: (1) solutions from supergravity/superstring constructions, (2) extended minimal supersymmetric Standard Model solutions, (3) solutions from an extra local $U(1{)}^{\ensuremath{'}}$ and (4) solutions involving Peccei-Quinn symmetry and axions. Early solutions invoked a global Peccei-Quinn symmetry to forbid the $\ensuremath{\mu}$ term while relating the $\ensuremath{\mu}$ solution to solving the strong $CP$ problem via the axion. We discuss the gravity-safety issue pertaining to global symmetries and the movement instead toward local gauge symmetries or $R$ symmetries, either continuous or discrete. At present, discrete $R$ symmetries of order $M$ (${\mathbb{Z}}_{M}^{R}$) which emerge as remnants of the Lorentz symmetry of compact dimensions seem favored. Even so, a wide variety of regenerative mechanisms are possible, some of which relate to other issues such as the strong $CP$ problem or the generation of neutrino masses. We also discuss the issue of the experimental verification or falsifiability of various solutions to the $\ensuremath{\mu}$ problem. Almost all solutions seem able to accommodate the LH.
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2916203228