Conclusions of a possible decay of the Higgs-boson into $t\bar{t}$ Recently in the CERN courier www.cerncourier.com it was reported on the decay of the new boson found at the LHC (shortly called Higgs-boson $H$ in the following)
into a $b\bar{b}$-pair. I wonder if also the decay of the Higgs-boson into a $t\bar{t}$-pair already was found.
So my  first question is: Was $H \rightarrow t\bar{t}$ already found ? If yes, that would have profound implications I guess.
My second question is: If this first question is true, would it mean that supersymmetry would be ruled out then, since according to supersymmetry quarks of the same generation should couple to 2 different Higgs-bosons 
(which would be no longer true if the answer of my 1.question would be yes)?
In fact, this is a re-edit of the question 
"Check on Supersymmetry by measuring the Higgs-coupling to heavy fermions."
 A: As for your first question, as @anna pointed out, $H\to t\bar{t}$ is not possible with the Standard Model Higgs: $m_H < 2m_{t\bar{t}}$. A Higgs decaying into $t\bar{t}$ must be neutral. It turns out that the Minimal Supersymmetric Model (MSSM) does provide two neutral Higgs, a pseudo-scalar Higgs and two charged Higgs. There is therefore a good incentive to investigate such models, which are part of a larger class called Two-Higgs Doublet Models (2HDM). So far, LHC has failed to discover any of those. 
As for your second question, you are making a subtle mistake. The neutral components of the two Higgs field developing non-zero vacuum expectation values, let's call them by $H_1^0$ and $H_2^0$ do indeed couple only to down-type and up-type quarks, respectively. However, those are not the physical field $H$ and $H'$ we can observe. They are related by a rotation:
$$\begin{pmatrix}H\\H'\end{pmatrix}=\begin{pmatrix}\cos\varphi&\sin\varphi\\ -\sin\varphi&\cos\varphi\end{pmatrix}\begin{pmatrix}H_1^0\\H_2^0\end{pmatrix}$$
As a result, the both of the neutral Higgs can couple to $q\bar{q}$ for any type of quark. So can the pseudo-scalar Higgs. And of course, the two charged Higgs couple to $u\bar{d}$, $s\bar{c}$, or $b\bar{t}$ and the charge conjugates of those for the other Higgs charge.
I did learn most of what I have just explained in [1], which I remember finding rather didactic.
[1] Abdelhak Djouadi, The Anatomy of Electro-Weak Symmetry Breaking. II: The Higgs bosons in the Minimal Supersymmetric Model. https://arxiv.org/abs/hep-ph/0503173
