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I have been reading up on supersymmetry and how it was developed to fill the supposed gaps presented left by the Standard Model of Particle Physics. What is one main example of this gap?

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  • $\begingroup$ One use is for removing the infinities that renormalisation removes in QFT; string theory makes it look more natural. $\endgroup$ – Mozibur Ullah Dec 5 '17 at 19:55
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    $\begingroup$ Supersymmetry as a solution of hierarchy problem $\endgroup$ – Andrei Geanta Dec 5 '17 at 20:21
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    $\begingroup$ I would say the hierarchy problem is NOT a main reason to consider it, so it's not really a duplicate of that question $\endgroup$ – OON Dec 5 '17 at 21:05
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  • The so-caled hierarchy problem, connected to the naturalness and fine-tuning. The Higgs boson is light even though being a scalar its mass should be a sum of large contributions coming from all physics at very high energies. So one may expect that some mechanism exists that would explain this peculiar value. If SUSY existed at energies $\sim$ 1 TeV that would explain this cancellation beautifully. However results from LHC pose quite a problem for this scenario. SUSY also doesn't provide a mechanism to get rid of another fine-tuning of the cosmological constant. From the very beginning, long before LHC started to work, people recognized all sorts of phenomenological issues (unobserved flavour violating neutral currents and extra CP violation) connected with this scenario and studied models with SUSY broken at higher energies. Frankly for me that's not its main attractiveness.
  • Another thing about the Higgs mass is that it's suspiciously close to the stability bound. I.e. if it were a bit lighter the Standard model would be unstable due to the quantum effects on the potential. In contrast low energy SUSY models could explain even lighter Higgs mass without any stability problems.
  • The electroweak and strong sectors in the Standard model are practically disconnected from each other. If you look at the evolution of the gauge couplings at higher energies straight to $10^{16}$ GeV you may see that they come closely. That suggests that at much higher energies $10^{16}$ GeV all three interaction are unified in a single interaction with simple gauge group - the Grand Unified theory. Some of this unified theories also help to explain the huge differences in masses and mixing angles in the fermionic sector. However without SUSY those gauge couplings don't meet exactly at one point, they form a triangle that's rather large actually. Because of that non-SUSY GUT scenarios are usually plagued by fast proton decay and many of them are already closed without any collider experiments at such high energies! In contrast if superpartners have sufficiently low masses this triangle becomes much smaller and supersymmetric GUT scenarios are much more viable. For me personally this is the main attractiveness of the low-energy SUSY.
  • The low energy SUSY provides us with natural candidates for the dark matter particles that are completely absent from the Standard Model, telling us how they should interact and how we can find them.
  • And of course there's the most fundamental motivation in the form of string theory (the best... oh, come on! the only working quantum gravity theory we know now) that requires SUSY at Planck energies. Of course in strings SUSY doesn't have to survive to the low energies. But if it does the string theory may quickly become much more relevant to the particle physics.
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    $\begingroup$ I agree with everything you say here (and, let me add, I always found the fact that $m_h$ is almost identical to the stability bound as perplexing as it gets. What on earth does that mean? Surely it must mean something!). I would add that according to Haag-Łopuszański-Sohnius, SUSY is the only possible modification of the SM that does not consist of simply throwing new fields into the mix at random. It is therefore a very natural scenario to study. $\endgroup$ – AccidentalFourierTransform Dec 5 '17 at 21:51
  • $\begingroup$ why are you not discussing the anomaly cancelation ? If I remember correctly that was the main reason supersymmetry was first discussed as a probable extension of the standard model? $\endgroup$ – anna v Dec 6 '17 at 7:08
  • $\begingroup$ @annav Was it? I looked some early papers on supersymmetric Standard Model extensions and their motivation is mostly "more restricted theory - less parameters" (yeah, they didn't yet realized the need of $\mathcal{L}_{soft}$ with hundred of parameters...) As for anomalies Fayet in 1976 cites Bouchiat, Iliopoulos and Meyer paper on anomaly cancellation in SM. And that paper is why I'm not discussing anomaly cancellation - is there any issue? SM is perfectly good in that respect and I don't see really how SUSY would help make it even better. $\endgroup$ – OON Dec 6 '17 at 13:57
  • $\begingroup$ Thanks , I am probably mixing it it up with superstring arguments but the question is about the standard model. $\endgroup$ – anna v Dec 6 '17 at 14:13

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