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Dear Editor, 

we thank the referees for their comments. Below we respond to the
point of criticism raised by Referee A.

We have slightly modified our manuscript after detecting a mistake in
our numerical procedure, please find the corrected LaTeX file
attached. The changes affect some numbers appearing in the text. We
acknowledge the colleagues who helped us find our mistake.

Now we comment on the report of Referee A: 

 {\it`` Since
it is relatively well known that both quantities are enhanced if
tan(beta) (a parameter of SUSY models) is large, this
correlation is not surprising.''}

The correlation is not trivial because both quantities depend on
different SUSY parameters, $Br(B_s\to \mu^+\mu^-)\propto
\tan^6\beta/M_A^4$ and $\delta a_\mu \propto 
\tan\beta/M_{Chargino}^2$. Hence the correlation is only there, once
the mSUGRA GUT scale conditions are imposed and the running of the
various parameters down to the Electroweak scale is performed. All and
all $M_A$ and chargino mass are driven by $M_{1/2}$ in mSUGRA and are
constrained from Radiative Electroweak Symmetry Breaking (through the
higgsino $\mu$ parameter). These relations do not exist in the
unconstrained MSSM where all these parameters are independent.

Next we discuss the question raised by you in the post scriptum:

{\it ``How model dependent are your results? Does, for example,
allowing nonuniversal gaugino masses change everything?''}

The correlation between the two observables is still there once we
violate the gaugino universality. For example, if we assume that at
the GUT scale we have for the gluino mass [and for the inputs of our
Fig.1 and for $\tan\beta=50$] $M_{\tilde{g}}=0.5M_{1/2}$ then we
obtain $Br(B_s\to \mu^+\mu^-) \simeq 2\times 10^{-7}$ and $\delta
a_\mu \simeq 42\times 10^{-10}$ while for $M_{\tilde{g}}=2 M_{1/2}$ we
obtain $Br(B_s\to \mu^+\mu^-) \simeq 2\times 10^{-8}$ and $\delta
a_\mu \simeq 16 \times 10^{-10}$. Both observables scale with the
gluino mass. This can be understood from the form of the MSSM
renormalization group equations (RGE's). Large SUSY QCD corrections
enter through the gluino mass in the RGE's for the squarks and these
enter into the running of the soft SUSY breaking Higgs masses. This effect
will affect the definition of the $\mu$ parameter from the
minimization condition.  Heavy gluino universality violation leads to
a heavy squark spectrum and to a big $\mu$ value. Thus one of the
charginos is heavy and suppresses the $(g-2)_\mu$ value and the CP-odd
Higgs mass is also heavy and suppresses the $Br(B_s\to \mu^+\mu^-)$
for very heavy gluino.  The two observables go hand in hand even in
this case although their values enhanced (weaken) for small (large)
gluino mass vs $M_{1/2}$.

Finally, we would like to comment on the scientific relevance of our
findings, which has been questioned by Referee A. The experimental
anomaly in $g-2$ has attracted an enormous attention from the
theoretical side, this year. mSUGRA is the most popular {\it GUT
  scale} model studied in phenomenological analyses of supersymmetry.
It is now common practice to include the experimental constraint from
$g-2$ into analyses of the mSUGRA parameter space. Hence it is of
utmost importance to identify consistency checks of the mSUGRA
interpretation of the excess in $g-2$, as we did with the correlation
of $g-2$ and the decay $B_s\to \mu^+\mu^-$. This is particularly
relevant since the decay $B_s\to \mu^+\mu^-$ can be probed in the next
run of the Tevatron, which  has just begun. While it was known before
that certain precision observables are sensitive to supersymmetry, it
is a new and exciting observation that a simple correlation of two
low-energy precision observables probes {\it GUT scale} boundary
conditions.  In the future the experimental test of our correlation
between $Br(B_s\to \mu^+\mu^-)$ and the Higgs masses may show further
evidence in favor or against the mSUGRA model.

In view of the fact that Referee B is supporting the publication in
PRL and Referee A acknowledges the scientific validity of our
manuscript, we would like to ask you to accept the manuscript for
publication in PRL. We believe that your expertise on the subject
allows you to correctly judge our clarifying comments on Referee A's
criticism, so that it is presumably not necessary to consult a third
referee other than you.

Sincerely,

A.~Dedes, H.~K.~Dreiner, U.~Nierste

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