Have we ruled out the Minimal Supersymmetric Standard Model (MSSM)?

Question

This question is inspired by a Physics Stackexchange question posted 8 years ago (The future of supersymmetry). The question that I have is very similar to the question in the above link, except that the above question has been posted and asks about the status of supersymmetry 8 years ago, whereas I would like to know the status right now. Therefore, I am opening this new question.

As of now, there is generally a lack of any experimental evidence from the LHC and other smaller experiments for supporting the idea of supersymmetry. There are only 2 experimental anomalies: one from the $g-2$ experiment and another from the LHCb experiment. Taking into account of these:

• Is it true that we have ruled out the Minimal Supersymmetric Standard Model (MSSM)? and, perhaps, many of the other most popular supersymmetric models?
• What implications do these have, regarding supersymmetry?

Answer 1

A very good source to consult on this matter is the PDG reviews, specifically the 2019 reviews$^{1,2}$. The implications of collider results are vast, and not easy to collect in a single answer.

The most general, unconstrained avatar of the MSSM has 105 free parameters, which is intractable from a phenomenological standpoint. One needs to reduce the parameter space to make more easily falsifiable models, which experimental evidence may then be pick off one at a time. Consequently, ATLAS, CMS and friends have directed their efforts towards disproving, or finding evidence for, these simpler models - particularly the phenomenological MSSM (pMSSM), which reduces the number of parameters down to just 19, under 3 reasonable assumptions, and mSUGRA/CMSSM, which is even more tightly constrained.

With regards to possible supersymmetric loop contributions to the anomalous magnetic moment of the muon, the well-known $3\sigma$ variation is consistent with some regions of the pMSSM parameter space, although it is difficult to reconcile with CMSSM (the latter is also under severe pressure from the various LHC measurements of e.g. light squark and gluino masses, Higgs mass, SUSY breaking mechanisms, etc.). Nevertheless, the BMW lattice calculations may be correct anyway and consistent with the SM itself.

However, the MSSM is not even remotely ruled out, let alone supersymmetry as a whole. Although there is no direct evidence for weak-scale supersymmetry yet, MSSM models with e.g. >2 TeV gluino and squark masses, and even a large space of pMSSM models with these masses below 1 TeV, are completely consistent with all experiments thus far, though not immediately falsifiable.

The absence of new weak-scale SUSY processes may seem contradictory to one of the main purposes of SUSY - to solve the hierarchy problem without introducing new fine-tuning. There are multiple consistent resolutions to this - extending the MSSM further by adding a Higgs singlet superfield, bounding sparticle masses, accepting the new "little hierarchy problem", etc. which are once again all consistent with experiment too.

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$^1$Supersymmetry, Part I (Theory), Section 110.7. https://pdg.lbl.gov/2019/reviews/rpp2018-rev-susy-1-theory.pdf

$^2$Supersymmetry, Part II (Experiment). https://pdg.lbl.gov/2019/reviews/rpp2018-rev-susy-2-experiment.pdf

$^3$https://arxiv.org/abs/2104.07597