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:

“ 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} → μ^{+}μ^{−}) ∝ tan^{6} β/M_{A}^{4} and δa_{μ} ∝ tan β/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 μ 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:

“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 β = 50] Mg̃ = 0.5M_{1/2} then we obtain Br(B_{s} → μ^{+}μ^{−}) ≃ 2 × 10^{−7} and δa_{μ} ≃ 42 × 10^{−10} while for Mg̃ = 2M_{1/2} we obtain Br(B_{s} → μ^{+}μ^{−}) ≃ 2 × 10^{−8} and δa_{μ} ≃ 16 × 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 μ parameter from the minimization condition. Heavy gluino universality violation leads to a heavy squark spectrum and to a big μ value. Thus one of the charginos is heavy and suppresses the (g − 2)_{μ} value and the CP-odd Higgs mass is also heavy and suppresses the Br(B_{s} → μ^{+}μ^{−}) 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 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} → μ^{+}μ^{−}. This is particularly relevant since the decay B_{s} → μ^{+}μ^{−} 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 GUT scale boundary conditions. In the future the experimental test of our correlation between Br(B_{s} → μ^{+}μ^{−}) 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