Which SUSY models are affected by the recent LHCb result? The LHCb has recently published the observation of $B_s \rightarrow \mu^+ \mu^-$ with a branching ratio that agrees with the Standard Model (SM). There are many blog posts about it (See: Of Particular Significance). 
The result initiated a debate over its implication on Supersymmetry in general, which I don't want to discuss here. But it certainly affects some Supersymmetric models that may have a different prediction than that of the SM. 
My questions are,


*

*Which models in particular are affected (or variants of models)?
What is the MSSM status? The NMSSM?

*Does the result affect some of the parameter space of a particular model, or does it rule out an entire model/or variant of a model?

 A: In both the MSSM and SM, $ B^0_s\to\mu^+\mu^- $ is a rare, loop-induced decay. The contributions to this from the MSSM arise from flavor-changing current loops to convert one of the initial valence quarks to be the anti-quark of the other. This will then lead to a Yukawa vertex with a neutral Higgs boson, of which there are three. 
To be more clear, the $B^0_s$ meson is a bound state of the $b$ and $\bar{s}$ valence quarks, so those are the initial particles. One of the these quarks, e.g., the $b$ will go through a supersymmetric flavor-changing loop to turn it into an $s$ quark. Now the $s$ and $\bar{s}$ meet at a Yukawa vertex, so that the Higgs mediates the decay into muons. Here is a diagram to illustrate the process as I have described it:

Now, in the large $\tan\beta$ limit, the branching ratio for this decay is given in the MSSM as 
\begin{multline*}
  \mathcal{B}r\left(B^0_s\to\mu^+\mu^-\right) \simeq 3.5\times10^{-5}
     \left(\frac{\tau_{B_s}}{1.5\,\mathrm{ps}}\right) \left(\frac{f_{B_s}}{230\,\mathrm{MeV}}\right)^2 
     \left(\frac{\left|V_{ts}^\mathrm{eff}\right|}{0.040}\right)^2 \\
     \times \left(\frac{\tan\beta}{50}\right)^6 \left(\frac{m_t}{m_A}\right)^4 
     \frac{(16\pi^2)^2\epsilon_Y^2}{(1+(\epsilon_0 + \epsilon_Y y^2_t)\tan\beta)^2(1+\epsilon_0\tan\beta)^2} 
\end{multline*}
where $\tau_{B_s}$ is the mean lifetime, $f_{B_s}$ is the decay constant, and $V^\mathrm{eff}_{ts}$ is the eective CKM matrix element. The loop
factors $\epsilon_0$ and $\epsilon_Y$ are given in terms of the 3rd generation squark soft masses.
The important thing to see is that large corrections arise if $\tan\beta\gtrsim50$, and if $m_A\lesssim m_t \simeq 173\,\mathrm{GeV}$. Typically in the MSSM, $m_A \simeq m_H$, so that factor accounts for both additional propagators in the MSSM case.
Thus in low energy MSSM theories, it is fair to say that the $ \mathcal{B}r\left(B^0_s\to\mu^+\mu^-\right) $ measurement requires one to have small $\tan\beta$ and/or heavy Higgs bosons. In fact, this is already necessary given that $m_h$ has been measured to be $\sim126\,\mathrm{GeV}$, but that is another story.
References


*

*S. Akula, P. Nath, Phys. Rev. D 87, 115022 (2013) 

*A. J. Buras, P. H. Chankowski, J. Rosiek and L. Slawianowska, Phys. Lett. B 546, 96 (2002).

