This is a republication of a post at the Physics Forums with some minor edits.
Is supersymmetry still possible or has it been proven wrong?
Short Answer
Supersymmetry is still possible because it has many adjustable features that can be tweaked to remove it from the exclusion ranges of existing parameter space (keep in mind that SUSY is a class of theories and not just a single theory). But, the kinds of SUSY theories that are still possible are increasingly unlike the ones that theorists had hoped for when they came up with SUSY and the versions that remain possible do increasingly little to solve the unsolved problems in physics that it was invented to solve.
So, confidence that SUSY is an accurate description of the universe and the popularity of SUSY related research is declining, although this decline is lagging behind the experimental and theoretical disappointments that have emerged because so many individual physicists and so many major physics experiments have invested so much in exploring this possibility.
Long Answer
There is no positive observational evidence for supersymmetry. And, because many supersymmetry theorists had expected to see signs of it at the Large Hadron Collider, or in other kinds of observations, this has considerably dampened enthusiasm for this class of theories, although it remains an area of vigorous and high volume investigation.
A substantial share of the papers published by the collaborations at the Large Hadron Collider consider how the data collected (which is basically always consistent with the Standard Model in areas pertinent to supersymmetry theories) limit the parameter space of various varieties of simplified or generic supersymmetry theories. For the most part, various supersymmetric particles (sparticles) are excluded in mass ranges up to several hundred GeV to 1 TeV.
There are also indirect probes of higher masses such as the potential muon g-2 discrepancy, the beta function of Standard Model constants, the mass of the Higgs boson, and the similarity of the observed Higgs boson to the predicted properties of a Standard Model Higgs boson of that mass. Those indirect measurements disfavor SUSY, although not definitively, up to about 10 TeV mass scales for the lightest supersymmetric particles.
The mass of the Higgs boson is particularly important because at the observed mass, the Standard Model equations do not pathologically break down and produce non-physical results (like probabilities that do not add up to 100%) at any energy scale up to the GUT scale (the hypothetical scale at which gauge unification can take place in SUSY theories). At many other possible Higgs boson masses, the Standard Model equations would have broken down, making some sort of beyond the Standard Model physics necessary to explain reality at high energies.
The Higgs boson mass also implies that the universe is at least "meta-stable" (i.e. stable on time lengths comparable to the age of the universe), while many other possible Higgs boson masses would have been unstable, which would mean that the universe shouldn't exist, which would imply the need for beyond the Standard Model physics such as SUSY to prevent this from happening. So, again, the Higgs boson mass actually observed makes this kind of new physics unnecessary.
None of these kinds of observational evidence can completely rule out supersymmetry, because at a sufficiently high energy scale, supersymmetric phenomena "decouple" from low energy phenomena and do not have effects on low energy phenomena that are large enough to discern. But, if SUSY phenomena can only be discerned at such high energy scales then it probably can't be seen not just at the LHC, but also at the next generation collider, which is not something that generates great research enthusiasm for a theory. If SUSY doesn't give rise to any phenomena different from the Standard Model at energy scales below 10,000 TeV, for example, it is much less salient to the nature of the universe and to physicists who have no way to study those energy scales in the foreseeable future. A scenario in which there are new beyond the Standard Model physics at extremely high energies, but there is nothing new between what we have already observed and those extremely high energies, is called a new physics "desert", or the "nightmare scenario" for today's high energy physicists.
Another difficulty is that as the parameter space of possible SUSY theories is constrained by experiment after experiment, the kinds of SUSY theories that can be consistent with the data grow more and more baroque and hence more disfavored by Occam's Razor. The most minimal realization of SUSY, the MSSM, for example, is either ruled out or very nearly ruled out, by existing evidence, although less minimal realizations of SUSY are still possible.
More generally, there are basically no anomalous results in high energy physics relative to Standard Model expectations that are explained well by SUSY. If there was really such a dramatic departure from the Standard Model with so many new particles and interactions lurking just around the corner in terms of energy scale, you would expect to see, at a minimum, lots of anomalies over a wide range of experiments that were individually subtle but collectively all seemed to point in the same direction. But, we aren't seeing that.
Certainly, there are unsolved questions and anomalies in high energy physics. For example, we still have no meaningful ability to predict in advance the spectrum of scalar and axial vector mesons that are observed at colliders. But, most of these unsolved questions and anomalies involve situation in quantum chromodynamics where measurement imprecision and calculations that are very hard to do precisely because the math is very difficult are present but SUSY and the Standard Model would make essentially the same predictions, or in some other area (like the "strong CP problem") where SUSY does not provide a ready, long anticipated explanation.
SUSY was originally formulated to make phenomena at the "electroweak scale" of low hundreds of GeVs to be more "natural" in a technical sense. Even if SUSY was discovered at 10 TeV it would not serve the purposes for which it was originally devised very well.
Another motivation to formulate SUSY was that it provided candidate particles beyond the Standard Model for dark matter, called SUSY WIMPs, with an expected range of masses and some fairly well defined properties. But, while dark matter particles are not ruled out experimentally (and indeed are supported by lots of evidence and lots of researchers), the particular varieties of WIMPs that would be expected to be dark matter candidates in SUSY theories (whose interactions with other particles and properties except mass are largely predicted by the theory), are almost completely ruled out by LHC experiments, direct dark matter detection experiments, and the dynamics of dark matter that can be inferred from astronomy observations. The "hot" candidates for dark matter like sterile neutrinos, axion-like dark matter, "warm dark matter", self-interacting dark matter, and primordial black holes, are all inconsistent with the SUSY WIMP dark matter candidates that had seemed so appealing before evidence was collected.
SUSY was also popular because it was seen as the primary or exclusive low energy realization of string theory, at a time when there was a widely shared naive hope that a single possible string theory variant would uniquely define the reality that we observe if we just developed the theory a little further. But, as the problem of connecting high level abstractions in string theory to low energy phenomenology proved much more murky than anticipated, and in the last year or two, it became apparently that most or all realizations of string theory have properties that are inconsistent with the observed universe in a categorical and generic way, yet another motivation for SUSY has been undermined, although not entirely eliminated.
Even one of the great "beautiful" features of SUSY (gauge unification at the GUT scale) in the minimal supersymmetric model (MSSM) that seemed to hold true at the time it was originally formulated, is no longer consistent with existing more precise measurements of physical constants and the beta functions of SUSY constants predicted in the MSSM.
SUSY is more mathematically tractable than the Standard Model in many respects and as a result, its predictions about systems that are difficult to analyze analytically or numerically can help give us useful intuition about high energy physics systems, because SUSY and the Standard Model are necessarily very similar to each other at low to intermediate energy scales. But, enthusiasm for SUSY and its low energy theory of everything counterpart, SUGRA (supergravity), has waned considerably because of these recent developments.
However, SUSY is still an attractive target because it is a coherent alternative to the Standard Model that makes predictions that can be calculated for any given set of parameters, and has lots of moving parts that prevent it from being ruled out definitively. Many of the alternative beyond the Standard Model theories in particle physics such as "Technicolor" (a composite Higgs boson theory) and composite Standard Model fermion theories, are in an even greater shambles in the wake of the discovery of the Higgs boson and nothing else at the Large Hadron Collider. And, less objectively, lots of theorists and phenomenologists also have a lot of sunk investment in supersymmetric theories which they have devoted many years and sometimes whole careers to master and develop and can't easily develop some new research agenda at this stage of their career.
Post Script
As my explanation above suggests, I am not among those who think that supersymmetry is an accurate description of reality.
