### Sidebar

causes:propaganda:susy

# Supersymmetry

Supersymmetry (SUSY) is a perfect example for how propaganda in physics works. There are four main motivations for SUSY that are repeated over and over in talks, textbooks and papers. However, if you ask students or even senior SUSY researchers questions about these arguments for SUSY, it almost always quickly turns out that they never really spent time thinking about them. The arguments for SUSY that are quoted over and over again are certainly not as strong as they are made to be. However, the real problem is that too many people don't know about “the other side”. Instead of an open and honest discussion the standard story is repeated over and over again, until everyone believes it.

So here are the four standard arguments and possible ways to see things differently:

1. SUSY helps to avoid the fine-tuning problem that arises when one considers loop corrections to the Higgs mass. Because of this motivation everyone was certain that SUSY shows up at the LHC, just as everyone was certain that SUSY shows up at LEP or the Tevatron. (And sure, the 100 TeV collider certainly will find SUSY.) However, there is no experimental evidence for anything beyond the standard model and certainly no signal that hints towards SUSY particles. The fact that the LHC did not find any SUSY particles is a big problem for SUSY fans, because now one main motivation is no longer valid (SUSY as a solution of the naturalness problem). However, in addition:
• These naturalness arguments hat the cosmological constant sitting at the top of them as a crushing weight. Because exactly the same arguments […] that lead you to make a prediction for new physics at weak scale, the hierarchy problem lead you to predict new physics at the $10^{-3}$ ev scale for the cosmological constant. The cosmological constant is around $(10^-3 ev)^4$. …. Length scale associated is a millimeter and we can all do the experiment in real time [looks at his hand]: no there is no new physics at a millimeter. Okay? So that's wrong. The basic philosophy is wrong. …. Everyone knew it. This is the even bigger elephant in the room.” N. Arkani-Hamed in his talk “Where in the World are SUSY and WIMPS?”
• It has been shown that a different renormalization scheme (BPHZ) needs no fine tuning of the bare parameters. […] Before summarizing our conclusions let us add two comments on issues which have been widely discussed and sometimes obscured the real content of the gauge hierarchy problem: the problem of quadratic divergences and the use of supersymmetry to “improve” the gauge hierarchy problem. The quadratic divergences only affect the formal relation between physical parameters and bare couplings. (we recall that this relation depends on the renormalization scheme.) They do not contribute at all to the RGE. They play no rule in the relations between physical parameters at short and long distances or between different sets of short-distance parameters. In brief, the quadratic divergences are completely irrelevant for the naturalness and fine-tuning problems involving the physical parameters.” from “Fine-tuning problem and the renormalization group” by C. Wetterich
2. SUSY makes the unification of the three standard model forces possible. However this argument is rather weak, because any BSM theory with as many free parameters as SUSY can be easily fitted such that the couplings unify. In addition, there is no need that a big unified symmetry (SO(10), E6) breaks directly to SU(3)xSU(2)xU(1). Instead an intermediate symmetry group between the unification and the standard model group, like the Pati-Salam group can exist. If this is the case the couplings ALWAYS unify with SUSY or without. Moreover, you can get unification of the gauge couplings much cheaper. To quote Ernest Ma in “Efficacious Additions to the Standard Model”: “If split supersymmetry can be advocated as a means to have gauge-coupling unification as well as dark matter, another plausible scenario is to enlarge judiciously the particle content of the Standard Model to achieve the same goals without supersymmetry.”
3. SUSY solves the Dark Matter problem. This argument is rather weak, too. Any expansion of the standard model with additional particles contains a dark matter candidate if we impose an additional discrete symmetry to guarantee its stability, which is what SUSY does (R-parity).
4. The Coleman-Mandula-Theorem and the argument that SUSY is the only possibility to “unify” the internal and spacetime symmetries. This motivation is also flawed and one can say many words on this topic, but in short:
• SUSY doesn't help to understand why fermions and bosons behave so differently (which is one of the biggest mysteries in modern physics), because this difference is simply the assumption at the start of SUSY.
• SUSY doesn't unify spacetime and internal symmetries. SUSY is an extension of the Poincare algebra and hence a spacetime symmetry.
• SUSY does not unify fermions with bosons. It only unifies some fermions with some bosons. A real unification would mean that we write all fermions and all bosons into one big object and then have operators that mix all of them. In SUSY, for example, there are no operators that connect standard model fermions. Instead standard model particles are only related to other, so far unobserved particles. There is no relation among observed particles. Such relations would be really really cool and this was what people hoped for in the early days of SUSY. However, this doesn't work because SUSY generators do not carry internal quantum numbers and therefore can only connect particle with identical quantum numbers. There are no candidates that could be connected like this among the standard model particles (maybe except for the Higgs and neutrinos).
• And finally, there are many other loopholes in the famous Coleman-Mandula and the Haag–Łopuszański–Sohnius theorem. These are usually not discussed, because stating these would significantly weaken the case pro SUSY.

Now the first one is no longer valid and maybe never a good idea in the first place. The second, third and fourth are weak arguments anyway. Thus it is not surprising that many SUSY researches are stopping to work on SUSY topics now. However there is a group of researches that can not stop and thus needs to find new motivation for SUSY: string theorists. SUSY must be correct, because otherwise string theory is in deep trouble. Therefore lots of smart people start thinking spent lots of time to find some good sounding reasons why SUSY is inevitable. This is how we end with an article like this. Lots of highbrow mathematics and complicated wording, which impresses students and laymans and leaves the impression that SUSY is inevitable.

One last thing. Everything here could be completely wrong. However, the thing we want to point out is that there is no open discussion of these issues. The textbooks and papers all repeat the standard lore without any critical and balanced discussion of alternative points of views. This illustrates how propaganda works in physics. Some arguments that sound reasonable at a first glance a repeated over and over again until almost everyone believes them. Then every discussion about possible flaws in these arguments are immediately killed by citing authorities and calling everyone with different views a crackpot.

• Supersymmetry and the Crisis in Physics by Joseph Lykken and Maria Spiropulu