Sorry if this is a loose question, or if it is worth to be asked.
What is the current status for "the principle of supersymmetry"?
Was it observed in any experiment?
Do we still believe it could exist?
Is it confirmed to exist?
Are experiments beginning to discard supersymmetry because it was not observed where it should have been?
I am a physics student, not an expert in standard model nor supersymmetry.
From a standard physics perspective the experimental situation with supersymmetry is terrible. We might as well be honest about it, and I say this as somebody who finds considerable beauty in supersymmetry and supergravity. The supersymmetric pair of the top quark, the Stop squark, was thought to have a mass around (within a few 100 GeV) that of the Higgs particle, but so far there is no sign of it. There are no signs of supersymmetric forms of the Higgs field or particles either. The supersymmetric version of the the standard model, sometimes called the minimal supersymmetric standard model (MSSM), is on the verge of being falsified.
Supersymmetry is a framework almost more than a theory. It is just a way of relating spacetime symmetry or the Poincare group with the quantum states of fermions and bosons. By itself it says nothing other than if you have a boson or fermion of a certain mass there is then a corresponding fermion or boson with the same mass, and where these two fit in a pair within a superfield defined with generators that have bracket structures that give a Poincare transformation. It really does not tell us anything about these masses or the particles in the theory. These are inserted by the analyst, and of course the obvious choice has been the standard model.
What one does to model physics we know with supersymmetry is to break supersymmetry. We obviously do not have bosons with the mass of an electron and charge running around. The same for the rest of particles. So the idea is to think of supersymmetry as some sort of global symmetry that from a local, local meaning not just space but momentum and energy as well, perspective has some breaking. The analogue is with magnetization where the atoms in a material are all oriented in a certain direction locally. We may be able to set up a lattice vibration that communicates this elsewhere, and this is a sort of Goldstone boson. If the breaking is “mild” it is similar to the splitting of atomic level by a magnetic field in Zeeman splitting. By the same thinking the mass difference for particles and their supersymmetric partners, in particular the more massive particles, is not that large. By not that large it is compared to Planck scale physics. With the Higgs particle it has a funny regularization because of the quartic nature of the potential, and so it turns out the super-partner of the Higgs can't be “that huge.” We would not expect it to be over a TeV in mass or so. The same holds for the Stop squark. If it is more massive then that quartic potential would tend to induce a huge renormalized mass comparable to the Planck scale. This would mean the symmetry breaking of particles in the standard model is not a small perturbation, but instead huge.
A problem that never seems to be mentioned is that unbroken supersymmetry is physics with zero vacuum energy. Inflationary cosmology is a situation where the false energy induced cosmological constant is close to the Planck energy, which means we would expect supersymmetry to be wildly broken. Supersymmetry may not be that consistent with inflationary cosmology on a de Sitter vacuum. Curiously it has consistency within string theory in anti-de Sitter spacetime which has a negative vacuum energy. The relationship between anti-de Sitter spacetime and de Sitter spacetime that is similar to the observable spacetime of the cosmology we observe is an interesting subject. Vafa thinks this may involve something called swampland.
The MSSM appears to be false and as of now it appears beyond rescue. Thousands of theorists built careers, think of Gordon Kane, on this and it all appears this is not how nature works. Does this mean we must abandon supersymmetry? Not necessarily, but it does mean we have to rethink its application. An example of this is supersymmetric stochastic dynamics. It is also appearing in solid state physics work. So not all is lost by any means, and I also think supersymmetry will appear in the deepest level of physics, but just not in the way originally thought.
What is the current status for "the principle of supersymmetry"?
Was it observed in any experiment?
Do we still believe it could exist?
The experimental community studying the data at LHC still searches for supersymmetry in the existing data and certainly in the future planned experiments. The search has not been successful up to now, but think: for how many years experiments have been searching for the Higgs?
Are experiments beginning to discard supersymmetry because it was not observed where it should have been?
No, experiments give limits that are not at this time able to falsify the possible existence of supersymmetry in the data. They can just give limits.. The interest is still very strong.
What you do not discuss but is an important factor in persisting for supesymmetric searches is that supesymmetry is a component in string theories, and a large part of the theoretical community proposes string theories for a Theory Of Everything. If supersymmetry is found, it is a strong validations for a string TOE model.
The importance of string theories comes because they are the only current proposed models which can include quantization of gravity and the current standard model of particle physics.
Thus the stakes are high, and the search for sypesymmetric particles will continue.
