The decay of a neutral Bs meson into a muon pair is a very rare process whose rate in principle could be severely affected by new physics beyond the standard model. We now know it is not: given the rate measured by the LHCb experiment, any new contribution to the decay amplitude has to be smaller than the standard model one. There's a medical discussion going on and on about the interpretation of this result in the context of supersymmetry. Indeed, the statements describing the LHCb result as "a blow to supersymmetry" or "putting SUSY into hospital" are silly (if you think it's the most spectacular change of loyalties since Terminator 2, read on till the end ;-) But what is the true meaning of this result?
To answer this question at a quantitative level it pays to start with a model independent approach (and technical too, to filter the audience ;-) B-meson decays are low-energy processes which are properly described within a low-energy theory with heavy particles, like W/Z bosons or new physics, integrated out. That is to say, one can think of the Bs→μμ decay as caused by effective 4-fermion operators with 1 b-quark, 1 s-quark, and 2 muons:
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In terms of the coefficients of these operators, the Bs→μμ branching fraction relative to the SM one is given by
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LHCb says that this ratio should not be larger than 2 or smaller than 1/3. This leads to model-independent constraints on the mass scales suppressing the 4-fermion operators. And so, the lower bound on ML and MR is about 30 TeV, that is similar in size of the standard model contribution. The bound on the scalar and pseudoscalar operators is much stronger: MS,MP≳150,200 TeV.
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Consequently, the LHCb result can be interpreted as a constraint on new physics capable of generating the 4-fermion operators listed above. For example, a generic pseudoscalar with order 1 couplings and flavor violating couplings to quarks and leptons must be heavier than about 100 TeV. It may sound surprising that the LHC can probe physics above 100 TeV, even if indirectly. But this is in fact typical for B-physics: observables related to CP violation and mixing of B-mesons are sensitive to similar energy scales (see e.g Table I of this paper). Notice however that 100 TeV is not a hard bound on new pseudoscalars. If the new physics has a built-in mechanism suppressing the flavor violating couplings then even weak scale masses may be allowed.
Now, what happens in SUSY? The bitch always comes in package with an extended Higgs sector, and the exchange of the heavier cousins of the Higgs boson can generate the operators MS and MP. However, bounds on the heavy Higgs masses from Bs→μμ will always be much weaker than 100 TeV quoted above. Firstly, the Higgses couple to mass, thus the Yukawa couplings relevant for this decay are much smaller than one. Secondly, the Higgses have flavor conserving couplings at tree-level, and flavor violation is generated only at 1 loop.
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But then SUSY has many knobs and buttons. The one called tanβ -- the ratio of the vacuum values of the two Higgs fields -- is useful here because the Yukawa couplings of the heavy Higgses to down-type quarks and leptons happen to be proportional to tanβ. Some SUSY contributions to the branching fraction are proportional to the 6th power of tanβ. It is then possible to pump up tanβ such that the SUSY contribution to Bs→μμ exceeds the standard model one and becomes observable. For this reason, Bs→μμ was hailed as a probe of SUSY.
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To conclude, you should interpret the LHCb measurement of the Bs→μμ branching fraction as a strong bound on theories on new physics coupled to leptons and, in a flavor violating way, to quarks. In the context of SUSY, however, there are far better reasons to believe her dead (flavor and CP, little hierarchy problem, direct searches). So one should not view Bs→μμ as the SUSY killer, but as just another handful of earth upon the coffin ;-)
Some pictures borrowed from Mathieu Perrin-Terrin's talk.