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A partial answer: "I do not see a coupling between the MSSM fields and the messenger fields" There are gauge interactions between observable and messenger fields. Let us discuss with fig $(1)$ page $11$ of this reference. You have not direct interactions between observable sector gauginos ($\lambda$) and s-fermions ($\tilde f$), and the superfield ...

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If you have two terms then you would have two vertices which contribute to a certain graph. For your first term, as far as I can tell, you would have a vertex for $\phi_i+\chi_j\to\phi_k+\chi_l$ given by $\propto g_3^2(\lambda^a)_{ik}(\lambda^a)_{jl}$. The general recipe to derive the Feynman rules is to feed your Lagrangian into the path integral and just ...

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This answer is mostly rephrasing Trimok's correct answer in other words. The super-Poincare group is supposed to be an extension of the Poincare group, which contains the Lorentz group and translations. We will complexify the Lorentz group. The Lie group $G:=SL(2,\mathbb{C})\times SL(2,\mathbb{C})$ is (isomorhic to the double cover of) the complexified ...

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It is maybe simpler to consider all the generators as representations of $SL(2,C)$, so, using spinor indices, you will have : $M^{\alpha \dot \alpha \beta \dot \beta}, P^{\beta \dot \beta}, Q_\alpha, \bar Q^\dot\beta$ Indices are raised and lowered with the Levi-Civita symbols \$\epsilon_{\alpha \beta}, \epsilon^{\alpha \beta},\epsilon_{\dot \alpha \dot ...

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Yes, physics has learned things on both concepts, but only gradually. The value of the mass 125 GeV is in the sub-130-GeV region that favors supersymmetry, or makes it necessary according to some, because the pure Standard Model predicts a catastrophically unstable vacuum for such low Higgs masses. It is also below 135 GeV which is where it should be ...

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Let me first refer you to three references pedagogically treating Instantons in quantum mechanics: 1)Riccardo Rattazzi's lecture notes treating instantons in nonsupersymmetric quantum mechanics. In these notes the anharmonic oscillator model is elaborated with great detail 2) Philip Argyres lecture notes treating instantons in supersymmetric quantum ...

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