Current LHC SUSY Exclusions

Supersymmetry, and its further elaboration, string theory, have turned out to be the biggest wrong turns in the history of high energy physics. They produced a few mathematical insights and better understandings of some deeper points about the Standard Model of Particle Physics along the half century journey, but ultimately these theories and these lines of inquiry were dead ends.  These theories continue to receive academic and experimental attention now, mostly because so many tenured physicists built their careers on these theories before their flaws became apparent.

(In due time, I expect that concepts like dark matter, dark energy, and cosmological inflation in astrophysics will similarly be found to have been plausible, but ultimately mistaken wrong turns, as well. Indeed, supersymmetry was originally one of several important reasons that dark matter particles received wider popularity as an explanation of dark matter phenomena and that the LambdaCDM model of cosmology gained wide initial acceptance, because it provided dark matter particle candidates that were well-motivated at the time, in roughly the right quantities in a thermal freeze out scenario in what was called the "WIMP miracle" until observational and experimental evidence ruled it out.)   

Supersymmetry is a theoretical framework in physics that suggests the existence of a symmetry between particles with integer spin (bosons) and particles with half-integer spin (fermions). It proposes that for every known particle, there exists a partner particle with different spin properties. There have been multiple experiments on supersymmetry that have failed to provide evidence that it exists in nature. If evidence is found, supersymmetry could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics. . . . 

There is no experimental evidence that either supersymmetry or misaligned supersymmetry holds in our universe, and many physicists have moved on from supersymmetry and string theory entirely due to the non-detection of supersymmetry at the LHC.

From Wikipedia (the emphasis in bold is mine). The chart below related to the theory sets forth the components of supersymmetry in one of its simpler forms (placing some of the terms used in the material quoted below in a clearer context):

A preprint of a commissioned review article for the Encyclopedia for Particle Physics, submitted on May 3, 2025 by Hyun Min Lee, entitled "Supersymmetry and LHC era" updates the experimental bounds on supersymmetry (SUSY) theories based upon the Large Hadron Collider (LHC) data. 

The author tries to paint this limitations in a positive light for supersymmetry, but the hard basic facts are that supersymmetry is now all but dead as a viable explanation of the real world, and that supersymmetric particles (a.k.a. "sparticles") don't exist.

Some of articles' more specific conclusions are as follows:

[T]he gluino masses up to about 2.4 TeV and the squark masses up to about 1.8 TeV have been ruled out by ATLAS. Similar limits from CMS can be also found. . . . stop masses up to about 1250 GeV have been ruled out from ATLAS data and there are similar bounds on the stop mass from CMS. . . . the mass ranges up to about 700 GeV for sleptons and about 1200 GeV for chargino or heavier neutralino have been excluded.

Some supersymmetric models are inconsistent with the current W boson mass (apart from the anomalous and deeply flawed CDFII measurement that is 7 sigma from the global average measurement of more recent and more precise experiments and from the other experiment at Tevatron). For example, this constrains the slepton mass.

More supersymmetric models are inconsistent with the agreement between the experimental value of muon g-2 and the Lattice QCD prediction for its value (rather than the flawed "white paper" value which is 5.2 sigma from the experimental value). The white paper estimate of the muon g-2 deviation from the Standard Model expectation is about 2.5 ± 0.5 * 10^-9, while the Lattice QCD prediction which is confirmed by more recent experimental date is closer to 0.5 * 10^ -9. The paper examine several supersymmetric particle parameter models at values from 1.56 to 2.24 * 10^-9 noting that:

In the left of Fig.3, we present three benchmark models which are consistent with the muon g−2 anomaly within1σ (Model II and III) or 2σ (Mode I) in general gauge mediation.We listed the masses for electroweak superpartners in general gauge mediation and the predictions for ∆aµ and ∆MW. In particular, ModelIII is also consistent with the W boson mass measured by CDFII within1σ. 

In the right plot of Fig.3, we also show the general independent mass parameters for superpartners, namely, m˜ qL ≃m˜ uR ≃m˜ dR, M1, M2, M3, m˜ lL and m˜ eR. 

The paper doesn't even try to devise a set of parameters of supersymmetry with the much smaller muon g-2 anomaly that the overwhelming evidence suggests is actually the case when the Standard Model expectation is calculated correctly. It does note, however that:

There are two typos [sic] of supersymmetric interactions relevant for the muon g−2. One Yukawa type interaction of the muon is to a neutral scalar ϕ with mass mϕ and a charged fermion F with charge −1 and mass mF . . . . Another Yukawa type interaction of the muon is to a charged scalar χ with charge −1 and mass mχ and a neutral fermion λ with mass mλ[.]

So, given the actual muon g-2 consistency between experiment and the predicted Standard Model value, the mass of the superpartners on the order of 400 GeV in the Model I scenario would have to be much higher. It would probably have to be at least in the 800s GeV, if not more, as estimated by me using linear interpolation from the other models in what is actually a non-linear relationship that probably sets the lower bounds even higher.

We comment on the dark matter candidates and collider signatures with electroweak superpartners in the benchmark models. 

In Model I, the neutralino is the LSP, so it can be a dark matter candidate. In this case, due to small splitting between the slepton masses and the neutralino mass, the decay products of the sleptons may be composed of soft jets or leptons (See the left plot in Fig. 4). If the gravitino is lighter than the neutralino, then it can be a dark matter candidate, but displaced decays of the neutralino can lead to distinct signatures at the LHC (See the right plot in Fig. 4 for the results from ATLAS). 

On the other hand, in Model II and III, smuon or sneutrino is the LSP, so there is no dark matter candidate within the MSSM. However, if the gravitino is lighter than the sleptons, the MSSM LSP is long-lived, decaying into a pair of the gravitino and charged leptons(neutrinos) at the displaced vertex from the production point (See the right plot in Fig. 5 for the results from ATLAS). In all the benchmark models, the heavier neutralinos or charginos have been searched for from their prompt decays, as shown in the left plot of Fig. 5.

The paper doesn't connect the dots, but because we know from direct dark matter detection experiments that there is no supersymmetric particle consistent with being a dark matter particle in anything approximating these mass ranges, that the paper's Model I's lightest supersymmetric particle (LSP) cannot be a dark matter candidate.

Proton decay also rules out much more of the SUSY parameter space if one doesn't resort to Baroque convolutions in the theory to suppress it:

In the minimal SU(5) unification with TeV-scale masses for superpartners, the dimension-5 operators generated at the mass scale of the colored Higgisnos are problematic for the proton lifetime. Even in the scenarios with split masses between colored and non-colored superpartners in general gauge mediation, the problem remains because of a large decay rate of the proton coming from the stop, the light stau and the Higgsinos in loops. However, the problem of the proton lifetime can be solved when the model is embedded in the orbifold GUTs where the Higgsino wavefunctions get suppressed at the orbifold fixed point, so do the dimension-5 operators for the proton decays.

Finally, not to put too fine a point on it, but there is absolute zero positive experimental evidence for supersymmetry or superpartners, despite the fact that looking for them was what the LHC was optimized to do. The exclusions are only as low as they are due to the constraints of the instrumentation to explore higher energies.

The bottom line is that supersymmetry is absent up to the TeV level, and the non-detection of proton decay, the lack of a muon g-2 anomaly, and the W boson mass all disfavor it at masses for superpartners at least up to the 10s of TeVs level.

Supersymmetry doesn't address the hierarchy problem is was devised to address, doesn't provide a dark matter candidate, doesn't explain any well established anomalies in the observational or experimental data. In general, supersymmetry no longer well-motivated as a beyond the Standard Model theory.

Moreover, because supersymmetry is a low energy approximation of the lion's share of string theories given serious examination by theoretical physicists, these experimental bounds also strongly disfavor string theory.

Of course, supersymmetry advocates and string theory advocates can try, as they have many times  over the last fifty years or so since it was proposed in the late 1960s and early 1970s, to move the goalposts of their predictions for its parameters "just around the corner" from the experimental limits that rule out or strongly disfavor it to values that can't yet be ruled out, even though these parameter values would no longer address anything that motivated this theoretical approach in the first place. 

But, increasingly, "just around the corner" means energy scales that cannot be reached even at the next generation of particle collider, but which might be reached at the next generation particle collider after that one, maybe several decades in the future.

Footnote

Another preprint today looks at dark matter particle candidates whose properties are strongly fixed by existing measurements in an SU(6) Grand Unified Theory (GUT) model. 

The allowed parameters for these dark matter candidates, however, are ruled out by astrophysics observations (the single digit plus TeV mass candidates are too massive to be directly ruled out by direct dark matter experiments).

Finally, yet another preprint today also considers a two component dark matter particle model suggested by a different GUT, which is ruled out by direct dark matter detection experiments, unless the GUT is twisted in a manner specifically designed to overcome this problem that otherwise has no observational or theoretical motivation. This elaborated version of the GUT does create a theoretical basis for neutrino mass, but also establishes a dark matter candidate that is ruled out by astronomy evidence, even though it isn't ruled out by direct dark matter detection experiments or high energy physics experiments.