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This might be an incredibly naive question, but I'm wondering if there are a set of rules for "translating" between Standard Model and SUSY. For instance, if I want want to go from a Standard Model feynman diagram to a SUSY diagram, can one write down a set of rule including things like:

"replace quarks with the corresponding squark"

with the caveat of course that R-parity is conserved (so two SUSY particles at each vertex). Given the underlying symmetry between SM particles and their superpartners, it seems like there should be some type of correspondence between SM feynman rules and the SUSY feynman rules. It seems like it would be incredibly difficult to go through and learn a completely new set of interactions and rules for SUSY. Are there things that carry over from SM Feynman rules that can be used as rules of thumb for figuring out what are the allowed SUSY diagrams for a particular process?

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Are you looking for a 'heuristic' way of extracting the Feynman rules and/or vertices in the analogous SUSY theory? I'm sure there is: I remember my PhD advisor, under his breath, reciting some of these mnemonic trying to gain intuition of what would happen to supersymmetrized version of a model we were discussing. –  QuantumDot Nov 17 '12 at 22:20

2 Answers 2

Supersymmetry being a symmetry just imposes additional restrictions on the "space of viable QFTs", which means that the number of supersymmetric Lagrangians is reduced compared to the number of "conventional" Lagrangians. Supersymmetry should therefore not change the basic (Feynman) rules that give for example a recipe for calculating scattering amplitudes from the terms present in the Lagrangian of the theory. In the same way, R-symmetry disallows certain interaction terms in the Superlagrangian, that would violate lepton and baryon number conservation.

In the MSSM, the number of particles is doupled compared to the content of the SM and it has 5 potentially observable higgs scalars. Since the superpartners differ from the SM particles just by their spin and their mass (but the charge is the same), they interact via the same coupling constants which are present in the SM too. So the basic Feynman rules to calculate things in the MSSM are not changed, but there are additional sparticles to play with. At the level of Feynman diagrams, R-symmetry has the effect that there are no interactions coupling a single superpartner to two SM particles.

However, in the context of the superspace formalism, which is very useful and efficient to derive supersymmetric "ordinary Lagrangians" from Superlagrangians, there exists a generalization of the well known Feynman diagrams called Supergraphs. These are diagrams similar to the Feynman diagrams, wherein the ordinary quantum fields are replaced by superfields (that depend in addition to the conventional spacetime coordinates on Grassmanian coordinates), to calculate things from the allowed interactions between the superfields described in the Superlagrangian.

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This is the half-joke explanation I give to undergrads who work on LHC SUSY searches:

  • Start with SM diagrams
  • Replace quark with corresponding squark
  • Replace $W^\pm$ with $\tilde{\chi}^\pm$
  • Impose the conservation of twiddles (R-parity)
  • The neutrilino ($\tilde{\chi}^0$) caries one unit twiddle and couples to anything a $W$, $Z$, or $H$ would couple to.

Bingo, you have SUSY Feynman diagrams. As I said, this is only partly serious, but it usually holds up pretty well.

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