Kane, Lu and Zheng have a paper today summarizing how they obtain a Higgs of about 125 GeV within the G2-MSSM (M-theory compactified on a "G2 manifold" so as to give the supersymmetric standard model). I'm not a big fan of this prediction, the machinery behind it is very complicated and I would prefer something like Shaposhnikov-Wetterich; but I do still want to see how it works. The final stages of the calculation can be seen symbolically in the figure on page 6 and the mass matrix at the bottom of page 7. The need for a working cosmology is used to obtain a value of about 50 TeV for the masses of MSSM up and down Higgses, stop squark, etc, at the GUT scale (see the right of the figure); then renormalization group equations are used to run these masses down to low energies. These quantities enter into the mass matrix on page 7, at low energies the smaller eigenvalue of this matrix is about 125 GeV, and this object will behave like a SM Higgs. That's about as much as I understand so far. The paper lists the starting assumptions on page 4, but the text only describes the argument informally. I would like to get the argument into deductive form, with links to papers containing the detailed calculations, so that a total novice could follow the logic of it. But that might take a while.