With the aid of current LHC + (all the known HEP experiments)+ (astrophysical and additional laboratory measurements)...
Is SUSY natural? Is it simple? More specifically, what reasons people had (or have) in order to argue the "naturalness" of SUSY? Why (despite the fact it doubles the particle spectrum!) some people says that SUSY is "simple" or a simple solution to the "most" important theoretical issues in physics?
Bonus question: can a non minimal supersymmetric model be both "natural and simple", according to these definitions? I define naturalness in the sense of 't Hooft: a QFT is natural when its coupling constant is of order one (with respect to, e.g., the electroweak -EW- scale).
A theory is "simple" when it reduces the number of degrees of freedom of previous "effective" theories.
In my (completely subjective) opinion, current data strongly suggest that:
i) SUSY is not natural. There is a relatively "large" gap between the electroweak scale and the SUSY breaking scale, if it (SUSY) exists...Then, the coupling constant of SUSY is not of order "one" with respect to the EW scale. The size of the SUSY breaking scale makes it to suppress the production of SUSY particles.
ii) SUSY is not simple. People use to argue...And I agree with it...that SUSY provides a natural lightest supersymmetric particle (LSP), and thus there is a natural Dark Matter candidate. It also "unifies" forces in such a way the 3 SM forces and their coupling constants unify at certain large energy. The unification of coupling is "simple" and usually it is given as a "proof" that SUSY is OK. Maybe it is true. However, gravity is not included in that calculation. I mean, I have not seen a calculation of the running of G in the framework of SUSY. Moreover, despite its goodness providing a natural particle/field for the dark matter, SUSY enlarges the number of particles (and the degrees of freedom) without (yet, please, I don't give up the idea of SUSY myself, I am trying to offer a cold criticism of its problems) experimental evidence beyond that dark matter we do not know what it is made of... SUSY is NOT simple because, from the purely mathematical viewpoint, it enlarges the number of free parameters and particles with respect to the SM.