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How Kane et al get the Higgs mass 
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#1
Nov1212, 05:12 AM

P: 751

Kane, Lu and Zheng have a paper today summarizing how they obtain a Higgs of about 125 GeV within the G2MSSM (Mtheory 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 ShaposhnikovWetterich; 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. 


#2
Nov1212, 08:25 AM

P: 751

Some general remarks on the framework employed by Kane et al:
They work in M theory. So there are ten dimensions of space and one dimension of time, with a metric field, a fermionic field called the gravitino, and an electromagnetismlike "threeform" field called the Cfield. There may also be "twobranes" and "fivebranes" flying around, as sources of the Cfield. They work in M theory compactified on a sevendimensional space called a singular G2 manifold. So at each apparent point in our three macroscopic dimensions of space, there is in fact a planckscale sevendimensional space. As well as being a sort of complicated hyperdonut with about 100 size and shape parameters, this 7manifold contains "singular 3surfaces" which might be conceptualized as "creases" or "ridges" in the 7manifold where the metric becomes a little singular. There will also be points on these 3surfaces, conical singularities, where the metric becomes even more singular. There are nonabelian gauge superfields on the 3surfaces, and chiral superfields (in representations of the gauge group) at the conical singularities. So for each singular 3surface in the 7manifold, there is a supersymmetric GUT. The superGUTs on different 3surfaces also interact gravitationally through the bulk of the 7manifold. These 3surfaces are really the Mtheoretic counterpart of a "braneworld". So returning to the macroscopic perspective, if you were to zoom in on a point in space, you wouldn't just discover a 7manifold, you'd find a 7manifold with a number of 3surfaces embedded in it. Since the same 3surfaces are found at every "macroscopic point", they each really define a volume of six space dimensions, three large, three small; like a 6+1dimensional KaluzaKlein world embedded in the larger 10+1dimensional KaluzaKlein world of Mtheory. In the G2MSSM scenario, there are always at least three of these "Mtheory braneworlds" coexisting in the larger space of "macroscopic Minkowski space times 7manifold". Each of them contains a separate superGUT. The visible world is contained in just one of them. For example, there might be SO(10) gauge superfields, three conical singularities each of which contains a SM generation (a 16dimensional representation), and a fourth point which contains a Higgs superfield. All those fields would be contained in just one of the 3surfaces, and then this SO(10) GUT would be broken to the MSSM by a Wilson line of flux within the 3surface. The other 3surfaces contain "hidden sectors". One of them will be a strongly interacting superGUT which dynamically breaks supersymmetry; susybreaking is then transmitted by gravity to the other 3surfaces, which is how susy gets broken in the visiblesector MSSM. The reason one wants at least two hidden sectors is to stabilize the shape and size of the 7manifold, in a way that makes it rigid at energies below 50 TeV or so (two hidden sectors are required for algebraic reasons I haven't tried to understand). This rigidity means that you won't get physical effects resulting from tremors in the shape of the 7manifold, at energies that we can measure. 


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