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The G2-MSSM is supposed to be the low-energy theory of a hypothetical class of M-theory compactifications studied by some phenomenologists. It is just the MSSM, but in a particular region of parameter space. The high-energy theory is M-theory compactified on a manifold with G2 holonomy. The MSSM fields come from a specific part of that manifold, while fields in other parts break supersymmetry and stabilize the extra dimensions. The "G2 region" of MSSM parameter space is singled out by a mixture of bottom-up arguments (phenomenological necessities) and top-down arguments (nature of the high-energy theory).

Late in 2011, Kane, Kumar, Lu and Zheng came out with a claim that the G2-MSSM implies a Higgs boson mass in the range 105-129 GeV. A year later, this had become the claim that "the Higgs mass was predicted to be 126 +/- 2 GeV before the measurement". That looks more like a retrodiction to me.

Also, the abstract to the second paper states "The derivation has some assumptions not related to the Higgs mass, but involves no free parameters", which means there are no quantitative fudge factors; but perhaps those "assumptions" are acting as qualitative fudge factors. The argument is far from transparent, and one has to wonder whether these authors are retrospectively discovering the refinement of their qualitative assumptions that is needed to single out the desired mass.

But it's true that there were supersymmetric arguments for a Higgs mass in the mid-120s or less than 130, years before this. So let us at least suppose that Kane et al have produced a valid example of such an argument, made in an M-theory context.

However, unlike Higgs mass predictions based e.g. on metastability or near-criticality of the SM vacuum, this one comes packaged with supersymmetry. For example, we are told to expect particular signatures of gluino pair production at the LHC. And this brings me to my real question:

How is the G2-MSSM doing, as one supersymmetric model among many, amid the ongoing falsification of "pre-LHC expectations" regarding supersymmetry?

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It's a scenario that has heavy scalars and relatively light gauginos, so it's one example of a class of "split SUSY" or "mini-split SUSY" scenarios that have survived most of the constraints. In this kind of scenario, collider bounds put the lightest superpartners, namely the winos, above about 270 GeV. Gluinos are constrained to be somewhere north of a TeV, depending on the exact details of the spectrum.

The biggest problem with this scenario is that it predicts a large amount of light wino dark matter from moduli decays, which is ruled out by gamma ray data. The constraints push the moduli heavier than desired, and also would tend to push them to a region where the "moduli-induced gravitino problem" becomes another worry. (Full disclosure: that link is a self-citation.) That constraint can be avoided if there's a significant amount of $R$-parity violation, or perhaps some other modifications to the model.

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Just to add to the previous answer, the G2-MSSM, in addition to heavy scalars also has heavy trilinear couplings A~1.5xM_{3/2}, which is important for alleviating the little hierarchy problem. Note that in the 'usual' split-SUSY scenario, both gauginos and trilinears are assumed light due to an R symmetry. Also, the Wino LSP story has been a bit oversold in the G2-MSSM scenario. While Wino LSP is possible, Bino LSP is much more typical when one examines the G2-MSSM parameter space using the GUT-scale boundary conditions. Kane et al always excluded the Bino LSP case, assuming R-parity conservation. However, R-parity conservation is an-hoc assumption in this model, not a prediction. On the other hand, ultra-light axions are definitely a robust prediction of the model and constitute an excellent dark matter candidate. The Higgs mass value being of order 125-127 GeV is not at all surprising in this model, given the mini-split spectrum with scalars O(10-100) TeV. However, in my opinion, the more interesting predictions are contained in the coefficients relating the scalar masses, trilinear couplings and gaugino masses.

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