Which low energy SUSY models are compatible with LHC and tevatron data so far?

Question

The LHC data has eliminated huge swaths of permissible low energy SUSY breaking models. But not all. Which regions of parameter space are still open?

Answer 1

There are many SUSY models. First, we may divide them according to the field content. The simplest SUSY model is the MSSM, the minimal supersymmetric standard model, which has about 105 new parameters. Many corners of this 105-dimensional space remain viable. It's a hard question to map (and there may be still lots of other, non-minimal low-energy SUSY models which are not MSSM, including "alternative" minimal ones with the Higgs sector represented by new generations of fermions and sfermions).

However, one may study natural subspaces of this 105-dimensional space. The most constrained such a subspace, mSUGRA with just a few (say three) parameters inspired by the grand unification, has been largely excluded by the LHC. (The LHC data have already rendered all Tevatron results on SUSY obsolete and irrelevant; the Tevatron couldn't compare with the LHC in finding new physics since the Spring 2011 or so which means that all of its data may be ignored without a loss of information.)

Somewhat larger theories, with more parameters, such as CMSSM (constrained MSSM) and NUHM1 etc. are also constrained but still contain viable regions of their parameter space.

If SUSY is the right explanation of the lightness of Higgs and if the R-parity is exact (if the superpartners may only be created or annihilated in pairs), we should have seen many missing energy events. But we haven't. The most rough conclusion is that they don't exist: the neutralino-like dark matter particle isn't stable (of course, this conclusion isn't quite "proven" by the data yet, but you may make a bet that this could be the outcome). Quite generally, the LHC data have disfavored models with exactly conserved R-parity. The R-parity-violating models seem to be quite alive, may be very natural, and may be even getting some mild positive experimental support, some hints of (multilepton etc.) signals from the CMS.

It seems clear to me that much of the SUSY phenomenological activity will go to (previously rather unpopular) R-parity-violating models in following months. One could argue that they have been irrationally understudied in the past. The R-parity-conserving models haven't been quite excluded but many of their classes have to be made contrived in order to agree with the LHC data.

In the R-parity-symmetric world, it's clear that the activity will be redirected towards models with hierarchies between the superpartner masses – some superpartners are much heavier than others. Many models of this kind remain compatible with the observations, too – even those that do predict many new particles below 1 TeV.