This is a difficult question to phrase succinctly, so I hope the title makes sen

Question

This is a difficult question to phrase succinctly, so I hope the title makes sense. What I want to understand is what seems like a lack of symmetry (besides SUSY-breaking) between the SM sector and their superparters.

In SUSY we add a second higgs doublet, so we end up with 8 degrees of freedom. Three are eaten by the SM gauge bosons, leaving 5 higgs bosons. My questions is: why are the 3 degrees of freedom eaten only by SM particles rather than 3 SM and 3 SUSY particles: why the asymmetry? Would the situation be different without SUSY-breaking?

If it helps to visualize the problem, the asymmetry is most striking if you imagine that we lived in a world where the mass scales where reversed: the SM is off at some high SUSY-breaking scale, and our world consists of superparters. Would we not have gauge theory and electroweak symmetry breaking, or would the gaugino sector require electroweak symmetry breaking?

Explanation / Answer

Gauginos are spin-1/2 fermions, and they don't carry forces like the W and Z bosons do. They aren't connection coefficients, they don't superpose to macroscopic fields.

There is never a complete symmetry between bosons and fermions, even in a supersymmetric theory. The fermions are fermions and the bosons are bosons, they have completely different physical properties. The supersymmetry transformation is not like a spatial rotation--- it isn't as physical. If you rotate a sock, all the particles in the sock rotate. If you super-rotate a sock, it becomes a superposition of rotating one-particle at a time of the sock. Most of the sock stays the same, but one constituent is turned to its superpartner, and there is a quantum superposition over which constituents are flipped. The result is still mostly the original sock.

This is analogous to the notion of an infinitesimal generator, since an infinitesimal transformation acts on products one factor at a time. The SUSY transformations can be thought of as permanently infinitesimal, because their parameter squares to zero.

Supersymmetry tells you for each particle that the scattering amplitude of a boson is simply related to the scattering amplitude of the fermion. This relation is particle by particle. So supersymmetry just isn't a symmetry of objects, at least not in a useful classical sense. So in your example of the reversed heirarchy, the Higgs mechanism would still give W's and Z's a mass.

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