A mixed F- and D-term uplift in supergravity evades the Planckian lower bound on the R-axion decay constant, allowing it to be the QCD axion and dark matter.
Symmetry Principles toward Solutions of $\mu$ Problem
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abstract
We stress that a natural solution of the $\mu$ problem requires two ingredients: a symmetry that would enforce $\mu = 0$ as well as the occurence of a small breaking parameter that generates a nonzero $\mu$. It is suggested that both the Peccei-Quinn symmetry and the spontaneously broken $R$ symmetry may be the sources of the needed $\mu$ term in the minimal supersymmetric standard model provided that they are spontaneously broken at a scale $10^{10}-10^{12}$ GeV. To solve the strong CP problem with a hidden sector confining group, both of these symmetries are needed in superstring models with an anomalous $U(1)_A$.
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An Intermediate Scale R-axion \& the QCD Axion
A mixed F- and D-term uplift in supergravity evades the Planckian lower bound on the R-axion decay constant, allowing it to be the QCD axion and dark matter.