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\section{\usemenu{slacpub7050::context::slacpub7050005}{Hidden Sector Scenarios}}\label{section::slacpub7050005}
Finally, let us consider a possible theoretical motivation for the light
Higgsinogaugino window. In hidden sector models, SUSY breaking is
transmitted to the visible sector by gravitational strength
interactions. With a renormalizable hidden sector, in which SUSY
breaking remains in the flat space limit, the dynamical scale,
$\Lambda$, of the hidden sector gauge group, and the hidden sector
scalar expectation values, $Z$, are of the order of the intrinsic SUSY
breaking scale, $M_S \sim \Lambda \sim Z \sim \sqrt{m_{3/2} M_p} \sim
10^{1011}$ GeV. This allows an expansion of the operators which couple
the visible and hidden sectors in powers of $M_p^{1}$. In the rigid
supersymmetric limit, the dimension two soft terms arise from $D$ term
operators of the form ${1 \over M_p^2} \int d^4 \theta ~Z^*Z \phi^*\phi$
and ${1 \over M_p^2} \int d^4 \theta ~Z^*Z H_1 H_2$ \cite{26}, where $Z$
are any hidden sector fields and $\phi$ is a visible sector field. With
$F_Z \sim M_S^2$, we then have $m_{\phi}^2 \sim m_{12}^2 \sim
m_{3/2}^2$. Note that these dimension two terms arise even without
hidden sector singlets. The dimension three gaugino masses arise from
the dependence of a visible sector gauge kinetic function on a hidden
sector singlet $S$, which does not transform under any gauge symmetry,
${1 \over M_p} \int d^2 \theta ~S W^{\alpha} W_{\alpha}~+\mbox{ h.c.}$
Visible sector $A$ terms arise from $D$ term operators ${1 \over M_p}
\int d^4 \theta ~S \phi_i^*\phi_i~+\mbox{ h.c.}$, where $F_{\phi_i}^* =
h_{ijk} \phi_j \phi_k$ results from the visible sector Yukawa couplings
$W = h_{ijk} \phi_i \phi_j \phi_k$.\footnote{It is interesting to note
that the resulting $A$ terms are real. Independent of their magnitude,
$A$ terms therefore do not contribute to the SUSY $CP$ problem with a
renormalizable hidden sector.} Likewise, the $\mu$ term arises from
operators of the form ${1 \over M_p} \int d^4 \theta ~S H_1 H_2~+ \mbox{
h.c.}$ \cite{26}.
If the hidden sector singlets have $F$ components $F_S \sim M_S^2$, then
all the dimensionful parameters of the MSSM can be ${\cal O}(m_{3/2})$.
However, it is possible that the hidden sector singlets participate in
the supersymmetry breaking only radiatively so that $F_S \sim {\cal
O}(\lambda/4 \pi)^2 M_S^2$, where $\lambda$ is a hidden sector singlet
Yukawa coupling. All the dimension three soft terms and $\mu$ are then
automatically suppressed by ${\cal O}(\lambda/ 4 \pi)^2$.\footnote{The
$\mu$ term can also arise from an $H_1 H_2$ dependence of a hidden
sector gauge kinetic function ${1 \over M_p^2} \int d^2 \theta~ H_1 H_2
(W^{\alpha} W_{\alpha}) \vert_{\mbox{\tiny hidden}}~+\mbox{ h.c.}$
\cite{27}. For a renormalizable hidden sector with $\langle
W^{\alpha} W_{\alpha} \rangle \sim \Lambda^3 \sim M_S^3$ the resulting
$\mu$ term is very small. However, a nonrenormalizable hidden sector
with $\langle W^{\alpha} W_{\alpha} \rangle \sim \Lambda^3 \sim M_S^2
M_p$ gives $\mu \sim m_{3/2}$. The scenario discussed by Farrar and
Masiero in which all the dimension three terms but $\mu$ essentially
vanish \cite{28} is therefore realizable with a
nonrenormalizable hidden sector without singlets and with scalar
expectation values much less than $M_p$. The magnitude of the $\mu$
term therefore distinguishes between the renormalizable and
nonrenormalizable hidden sector motivations for light gauginos.}
Inclusion of supergravity interactions does not modify this conclusion.
The smallness of the dimension three terms in such a scenario leads to
the approximate $U(1)_R$ discussed above. This approximate symmetry is
not imposed by hand but simply arises accidentally as a result of the
hidden sector outlined above. Notice that this motivation for the
window requires the gluino also to be light
\cite{28,29}. Models with radiatively coupled
singlets have in fact been constructed \cite{30} and until recently
were the only known renormalizable models of dynamical supersymmetry
breaking with singlets \cite{31}. We therefore conclude that a
renormalizable hidden sector with radiatively coupled singlets
automatically leads to models that can fall in the light
Higgsinogaugino window.
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