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\subsection{\usemenu{slac-pub-7237::context::slac-pub-7237-0-0-5-1}{Virtual Effects}}\label{subsection::slac-pub-7237-0-0-5-1}
Supersymmetric theories can be probed indirectly by virtual
effects on low energy, high precision, processes \cite{32}.
Among these are precision electroweak measurements,
electric dipole moments, and flavor changing neutral currents.
In the minimal model of gauge-mediation, supersymmetric
corrections to electroweak observables are unobservably
small since the charginos, left handed sleptons,
and squarks are too heavy.
Likewise, the effect on
$R_b = \Gamma(Z^0 \to b \bar{b})/ \Gamma(Z^0 \to {\rm had})$
is tiny since the Higgsinos and both stops are heavy.
Electric dipole moments can arise from the single $CP$-violating
phase in the soft terms, discussed in section \docLink{slac-pub-7237-0-0-2.tcx}[minimalsection]{2.1}.
The dominant contributions to the dipole moments of atoms
with paired or unpaired electrons, and the neutron,
come from one-loop chargino processes, just as
with high scale supersymmetry breaking.
The bounds on the phase are therefore comparable to those
in the standard MSSM,
${\rm Arg}(m_{\lambda} \mu (m_{12}^2)^*) \lsim 10^{-2}$
\cite{33,34}.
It is important to note that in some schemes for
generating the Higgs sector parameters $\mu$ and $m_{12}^2$,
the soft terms are $CP$ conserving \cite{3},
in which case electric dipole moments are unobservably small.
This is also true for the boundary condition $m_{12}^2(M)=0$
since
$(m_{\lambda} \mu (m_{12}^2)^*)$ vanishes in this case.
Contributions to flavor changing neutral currents can
come from two sources in supersymmetric theories.
The first is from flavor violation in the squark or
slepton sectors.
As discussed in section \docLink{slac-pub-7237-0-0-1.tcx}[UVinsensitive]{1.1} this source
for flavor violation is naturally small with gauge-mediated
supersymmetry breaking.
The second source is from second order electroweak virtual
processes which are sensitive to flavor violation in the
quark Yukawa couplings.
At present the most sensitive probe for contributions of this
type beyond those of the standard model is $b \to s \gamma$.
In a supersymmetric theory one-loop
$\chi^{\pm}-\tilde{t}$ and $H^{\pm}-t$ contributions
can compete with the standard model
$W^{\pm}-t$ one-loop effect.
The standard model effect is dominated by the transition
magnetic dipole operator which arises from the electromagnetic penguin,
and the tree level charged current operator, which contributes
under renormalization group evolution.
The dominant supersymmetric contributions
are through the transition dipole operator.
It is therefore convenient to parameterize the
supersymmetric contributions as
%the fractional change in the magnitude of the dipole
%operator relative to the standard model
\beq
R_7 \equiv { C^{\rm MSSM}_7(\mW) \over C^{\rm SM}_7(\mW) } -1
\eq
where $C_7(\mW)$ is the coefficient of the dipole
operator at a renormalization scale $\mW$, and
$ C^{\rm MSSM}_7(\mW)$ contains the entire MSSM contributions
(including the $W^{\pm}-t$ loop).
In the limit of
decoupling the supersymmetric states and heavy Higgs bosons
$R_7 =0$.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\jfig{sfig9n}{fig18.ps}
{The parameter
$R_7\equiv C^{\rm{MSSM}}_7(\mW)/C^{\rm{SM}}_7(\mW)-1$ as a function
of the lightest neutralino mass, $m_{\chi^0_1}$, for
$\tan\beta =2,3,20$, and $\Lambda=M$.
The solid lines are for $\mu >0$ and the dashed lines for $\mu <0$.
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The parameter $R_7$ is shown in Fig. \docLink{slac-pub-7237.tcx}[sfig9n]{18} as a function
of the lightest neutralino mass, $m_{\chi^0_1}$, for
both signs of $\mu$,
$\tan\beta =2,3,20$, and $\Lambda=M$ \cite{35}.
The $\chi_1^0$ mass is plotted in Fig. \docLink{slac-pub-7237.tcx}[sfig9n]{18}
as representative of the overall scale of the superpartner
masses.
The dominant contribution comes from the
$H^{\pm}-t$ loop which adds constructively to the
standard model $W^{\pm}-t$ loop.
The $\chi^{\pm}-\tilde{t}$ loop gives a
destructive contribution which is smaller in magnitude
because the stops are so heavy.
The ${\rm sgn}~\mu$ dependence of $R_7$ results from this small
destructive contribution mainly because the Higgsino
component of the lightest chargino is larger(smaller) for
${\rm sgn}~\mu = +(-)$ (cf. Eq. \docLink{slac-pub-7237-0-0-3.tcx}[winoshift]{19}).
The $\chi^{\pm}-\tilde{t}$ loop amounts to roughly a
$-$15(5)\% contribution compared with the $H^{\pm}-t$ loop for
${\rm sgn}~\mu=+(-)$.
The non-standard model contribution to $R_7$ decreases for small
$\tan \beta$ since $m_{H^{\pm}} \simeq \mA$ increases
in this region.
In order to relate $R_7$ to ${\rm Br}( b \to s \gamma)$
the dipole and tree level charged current operators must
be evolved down to the scale $m_b$.
Using the results of Ref. \cite{36}, which include
the leading QCD contributions to the anomalous dimension
matrix, we find
\beq
\frac{{\rm Br}^{\rm{MSSM}}(b\to s\gamma)}{{\rm Br}^{\rm{SM}}
(b\to s\gamma)} \simeq |1+0.45 ~R_7(\mW)|^2.
\eq
for $m_t^{\rm pole} = 175$ GeV.
For this top mass
${\rm Br}^{\rm SM}(b \to s \gamma) \simeq (3.25 \pm 0.5)\times 10^{-4}$
where the uncertainties are estimates of the theoretical
uncertainty coming mainly from $\alpha_s(m_b)$ and
renormalization scale
dependence \cite{37}.
Using the ``lower'' theoretical value and the 95\% CL
experimental
upper limit of ${\rm Br}(b \to s \gamma) < 4.2 \times 10^{-4}$
from the CLEO measurement \cite{38}, we find
$R_7 < 0.5$.\footnote{
This is somewhat more conservative than the bound
of $R_7 < 0.2$ suggested in Ref. \cite{39}.}
This bound assumes that the non-standard model effects
arise predominantly in the dipole operator, and are constructive
with the standard model contribution.
In the MGM
for $\mu > 0$,
$\tan \beta =3$, and $\Lambda=M$, this bound corresponds to
$m_{\na} \gsim 45$ GeV, or a charged Higgs mass of
$m_{H^{\pm}} \gsim 300$ GeV.
The present experimental limit does not severely constrain
the parameter space of the MGM.
This follows from the fact that the charged Higgs is very
heavy over most of the allowed parameter space.
Except for very large $\tan \beta$
$m_{H^{\pm}} \gsim |\mu|$, and imposing electroweak symmetry
breaking implies
$ 3 m_{\na} \lsim |\mu| \lsim 6 m_{\na}$,
as discussed
in sections \docLink{slac-pub-7237-0-0-3.tcx}[EWSB]{3.1} and \docLink{slac-pub-7237-0-0-3.tcx}[higgssection]{3.2.3}.
For example, with the parameters of Table 1
$m_{H^{\pm}} \simeq 5.4 m_{\na}$.
Note that since the stops are never light in the minimal
model there is no region of the parameter space for which the
$\ca - \tilde{t}$ loop can cancel the $H^{\pm} -t$ loop.
Precise measurements of ${\rm Br}(b \to s \gamma)$ at future
$B$-factories, and improved calculations of the anomalous
dimension matrix and finite contributions at the scale $m_b$, will
improve the uncertainty in $R_7$ to $\pm 0.1$ \cite{40}.
Within the MGM, even for $\tan \beta =2$ and $\mu > 0$,
a measurement of ${\rm Br}(b \to s \gamma)$ consistent with the standard
model would give a bound on
the charged Higgs mass of $m_{H^{\pm}} \gsim 1200 $ GeV,
or equivalently an indirect bound on the chargino mass of
$\ca$ mass of $m_{\ca} \gsim 350 $ GeV.
Such an indirect bound on the chargino mass
is more stringent than the direct bound that
could be obtained at the main injector
upgrade at the Tevatron \cite{30}, and significantly
better than the direct bound that will be available at LEP II.