In general, much of the stuff that one has learned through years of sweating on books slowly degrades and becomes "fuzzy". That fuzzy stuff still give you a warm feeling that you have grasped the important concepts and that you have acquired the necessary culture. But much better than the ignorance of culture is the precise knowledge that a continuous study provides. So when one is forced to re-study what one has forgotten, because of the need to teach a course, the result is pleasing.
I was reading today an essay by Stephen Martin (hep-ph/9709356), "A Supersymmetry Primer", before I lecture on the topic to my students later this afternoon. Supersymmetry is not in the program of my course, but it is a nice "addendum" which I provide in a final lesson. My approach is quite experimentally-driven, so I only care to provide the basic ideas of the theory, and then move to discuss the possible signatures at colliders and the status of present searches (whew, by writing the above I realize this is a lot of stuff for a single lesson -I will have to be synthetic).
Anyway, I found an argument about why SUSY has never cared to show up at the many rendez-vous we have set up with her in the last thirty-something years. As you may know, the failure of super-symmetric particles to be discovered in collider experiments, and the higher and higher lower limits set on their masses, is one of the forces driving many simple-minded beings like myself to be dissatisfied with that particular model of new physics. Martin has a simple argument to address that issue. On page 11 we read:
"One might also wonder whether there is any good reason why all of the superpartners of the Standard Model particles should be heavy enough to have avoided discovery so far. There is. All of the particles in the MSSM that have been found so far [TD's note: he is referring to the known SM particles here!] have something in common; they would necessarily be massless in the absence of electroweak symmetry breaking. In particular, the masses of the W±,Z0 bosons and all quarks and leptons are equal to dimensionless coupling constants times the Higgs VEV ∼ 174 GeV, while the photon and gluon are required to be massless by electromagnetic and QCD gauge invariance. Conversely, all of the undiscovered particles in the MSSM have exactly the opposite property; each of them can have a Lagrangian mass term in the absence of electroweak symmetry breaking. For the squarks, sleptons, and Higgs scalars this follows from a general property of complex scalar fields that a mass term m2|φ|2 is always allowed by all gauge symmetries. For the higgsinos and gauginos, it follows from the fact that they are fermions in a real representation of the gauge group. So, from the point of view of the MSSM, the discovery of the top quark in 1995 marked a quite natural milestone; the already-discovered particles are precisely those that had to be light, based on the principle of electroweak gauge symmetry. There is a single exception: one neutral Higgs scalar boson should be lighter than about 135 GeV if the minimal version of supersymmetry is correct, for reasons to be discussed in section 7.1. In non-minimal models that do not have extreme fine tuning of parameters, and that remain perturbative up to the scale of apparent gauge coupling unification, the lightest Higgs scalar boson can have a mass up to about 150 GeV."... and unluckily for us, a 135 GeV Higgs boson is not the easiest thing to stumble on.
So, okay. I am willing to give SUSY another chance to meet. SUSY, if you are there, take note: the LHC, some time in 2011, about 100 meters underground. A coloured dress will make it easier to spot you.
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