Note written by A. Dedes^{1}

1 Physikalisches Institut, Universität Bonn, Nußallee 12, D-53115 Bonn, Germany

[Based on “Correlation of B_{s} → μ^{+}μ^{−} and (g−2)_{μ} in minimal supergravity,” A. Dedes, H. K. Dreiner and U. Nierste, arXiv:hep-ph/0108037.]

Another interesting probe of supersymmetry is the decay B_{s} → μ^{+}μ^{−}. The SM prediction is given by B(B_{s} → μ^{+}μ^{−}) = (3.7 ± 1.2) · 10^{−9}, with the uncertainty (±25%) dominated by f_{B_{s}}. The current experimental bound on the Branching ratio, (B), has been set during Run-I of the Tevatron, where CDF [1] determined B(B_{s} → μ^{+}μ^{−}) < 2.6×10^{−6} at 90% C.L. In addition to the experimental challenge, the almost three orders of magnitude gap between the current experimental bound and the SM prediction makes this mode an excellent laboratory for new physics. In contrast to observables which enter the unitarity triangle [2], in the MSSM, the branching ratio B(B_{s} → μ^{+}μ^{−}) grows like tan^{6} β [3, 4, 5, 6], with a possible several orders of magnitude enhancement. More interestingly, it has been very recently shown [7] that in the minimal supergravity scenario (mSUGRA) there is a strong correlation with the muon anomalous magnetic moment (g − 2)_{μ}. An interpretation of the recently measured excess in (g−2)_{μ} in terms of mSUGRA corrections implies a substantial supersymmetric enhancement of the branching ratio B(B_{s} → μ^{+}μ^{−}): if (g −2)_{μ} exceeds the Standard Model prediction by (δa_{μ})_{SUSY} = 4·10^{−9}, B(B_{s} → μ^{+}μ^{−}) is larger by a factor of 10–100 than in the Standard Model and within reach of Run-II of the Tevatron. The single event sensitivity of CDF at Run-IIa is estimated to be 1.0·10^{−8}, for an integrated luminosity of 2 fb^{−1} [8]. Thus if mSUGRA corrections enhance B(B_{s} → μ^{+}μ^{−}) to e.g. 5 · 10^{−7}, one will see 50 events in Run-IIa. Run-IIb may collect 10-20 fb^{−1} of integrated luminosity, which implies 250-500 events in this example.

Following Ref. [7], in Fig.1 we show the contours of B(B_{s} → μ^{+}μ^{−}) (solid) and (δa_{μ})_{SUSY} (dashed) in this plane, for tan β = 50, A_{0} = 0, μ > 0 and m_{t} = 175 GeV. The shaded region is excluded through the various theoretical and experimental contstraints. A sensitivity of B(B_{s} → μ^{+}μ^{−}) ^{>} ∼ 2 · 10^{−7} at CDF now corresponds to a sensitivity of M_{1/2} ^{<} ∼ 280 GeV and M_{0} ^{<} ∼ 400 GeV, respectively. While CDF is not able to see squark masses directly up to 0.7 TeV (corresponding to M_{1/2} = M_{0} ≃ 300 GeV,), it will nevertheless be able to prepare the ground for LHC by observing the B_{s} → μ^{+}μ^{−} mode. Even better, after 10 fb^{−1} CDF will probe M_{1/2} ^{<} ∼ 450 GeV and M_{0} ^{<} ∼ 600 GeV (for tan β = 50) which in mSUGRA corresponds to masses for the heaviest superpartners of 1 TeV. We conclude the discussion of Fig.1 with the prediction of the light Higgs boson mass M_{h} (dot-dashed line) for tan β = 50 in the mSUGRA scenario [9]. Any measurement of B(B_{s} → μ^{+}μ^{−}) by itself implies a useful upper bound on M_{h}. The simultaneous information of B(B_{s} → μ^{+}μ^{−}) and δa_{μ} fixes M_{h} in most regions of the (M_{1/2}, M_{0})-plane. A Higgs mass around 115.6 GeV results in 10^{−8} ^{<} ∼ B(B_{s} → μ^{+}μ^{−}) ^{<} ∼ 3 · 10^{−7} which would most likely be measured before the Higgs boson is discovered.

References

[1] F. Abe et al. [CDF Collaboration], Phys. Rev. D 57, 3811 (1998).

[2] A. Bartl, T. Gajdosik, E. Lunghi, A. Masiero, W. Porod, H. Stremnitzer and O. Vives, Phys. Rev. D 64, 076009 (2001) [arXiv:hep-ph/0103324].

[3] K. S. Babu and C. Kolda, Phys. Rev. Lett. 84, 228 (2000) [hep-ph/9909476]; C. Huang, W. Liao and Q. Yan, Phys. Rev. D 59 (1999) 011701 [hep-ph/9803460].

[4] P. H. Chankowski and L. Slawianowska, Phys. Rev. D 63, 054012 (2001) [hepph/0008046].

[5] C. Bobeth, T. Ewerth, F. Kruger and J. Urban, Phys. Rev. D 64, 074014 (2001) [arXiv:hep-ph/0104284].

[6] G. Isidori and A. Retico, JHEP 0111, 001 (2001) [arXiv:hep-ph/0110121].

[7] A. Dedes, H. K. Dreiner and U. Nierste, Phys. Rev. Lett. 87, 251804 (2001) arXiv:hep-ph/0108037.

[8] D. Atwood et al., B Physics at the Tevatron: Run-II and Beyond, FERMILAB-Pub-01/197 (preliminary).

[9] S. Ambrosanio, A. Dedes, S. Heinemeyer, S. Su and G. Weiglein, arXiv:hepph/0106255.

Figure 1: Contour plots of the B(B_{s} → μ^{+}μ^{−}) (solid) and on (δa_{μ})_{SUSY} (dashed) in the (M_{0}, M_{1/2})-plane for mSUGRA parameter values as shown. Contours of the light Higgs boson mass (dot-dash line) are also shown. From Ref. [7].