How Kane et al get the Higgs mass

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In summary, Kane, Lu, and Zheng have published a paper discussing their method for obtaining a Higgs boson with a mass of about 125 GeV within the context of the G2-MSSM, which is a supersymmetric standard model derived from M-theory compactified on a "G2 manifold". This prediction is complicated and relies on a working cosmology and the use of renormalization group equations to run masses down to low energies. The paper also discusses the starting assumptions and the framework employed, including the use of M-theory and the presence of multiple "M-theory braneworlds" coexisting with a visible world in a larger 10+1-dimensional space. This scenario includes separate super-GUTs on
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mitchell porter
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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.
 
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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 electromagnetism-like "three-form" field called the C-field. There may also be "twobranes" and "fivebranes" flying around, as sources of the C-field.

They work in M theory compactified on a seven-dimensional space called a singular G2 manifold. So at each apparent point in our three macroscopic dimensions of space, there is in fact a Planck-scale seven-dimensional space. As well as being a sort of complicated hyper-donut with about 100 size and shape parameters, this 7-manifold contains "singular 3-surfaces" which might be conceptualized as "creases" or "ridges" in the 7-manifold where the metric becomes a little singular. There will also be points on these 3-surfaces, conical singularities, where the metric becomes even more singular.

There are nonabelian gauge superfields on the 3-surfaces, and chiral superfields (in representations of the gauge group) at the conical singularities. So for each singular 3-surface in the 7-manifold, there is a supersymmetric GUT. The super-GUTs on different 3-surfaces also interact gravitationally through the bulk of the 7-manifold.

These 3-surfaces are really the M-theoretic 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 7-manifold, you'd find a 7-manifold with a number of 3-surfaces embedded in it. Since the same 3-surfaces are found at every "macroscopic point", they each really define a volume of six space dimensions, three large, three small; like a 6+1-dimensional Kaluza-Klein world embedded in the larger 10+1-dimensional Kaluza-Klein world of M-theory.

In the G2-MSSM scenario, there are always at least three of these "M-theory braneworlds" coexisting in the larger space of "macroscopic Minkowski space times 7-manifold". Each of them contains a separate super-GUT. 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 16-dimensional representation), and a fourth point which contains a Higgs superfield. All those fields would be contained in just one of the 3-surfaces, and then this SO(10) GUT would be broken to the MSSM by a Wilson line of flux within the 3-surface.

The other 3-surfaces contain "hidden sectors". One of them will be a strongly interacting super-GUT which dynamically breaks supersymmetry; susy-breaking is then transmitted by gravity to the other 3-surfaces, which is how susy gets broken in the visible-sector MSSM. The reason one wants at least two hidden sectors is to stabilize the shape and size of the 7-manifold, 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 7-manifold, at energies that we can measure.
 

1. How did Kane et al discover the Higgs mass?

Kane et al did not discover the Higgs mass, but rather contributed to our understanding of how the Higgs mass is generated in the Standard Model of particle physics. They proposed a theory called the Minimal Supersymmetric Standard Model (MSSM) which predicts the mass of the Higgs boson based on its interactions with other particles.

2. What is the significance of Kane et al's research in determining the Higgs mass?

Kane et al's research is significant because it provides a theoretical framework for understanding the origin of the Higgs mass in the Standard Model. Their work has been instrumental in guiding experimental searches for the Higgs boson and has helped confirm its existence.

3. What evidence supports Kane et al's theory of the Higgs mass?

Kane et al's theory is supported by a combination of mathematical calculations and experimental data. Their predictions for the Higgs mass have been consistent with the measurements from the Large Hadron Collider (LHC) experiments, providing strong evidence for the validity of their theory.

4. How does the MSSM explain the Higgs mass compared to other theories?

The MSSM explains the Higgs mass by introducing a new type of symmetry called supersymmetry. This symmetry relates particles with integer spin (bosons) to those with half-integer spin (fermions). In the MSSM, the Higgs mass is generated through interactions between particles and their supersymmetric partners, providing a more elegant explanation compared to other theories.

5. What implications does Kane et al's research have for future studies of the Higgs mass?

Kane et al's research has paved the way for further studies of the Higgs mass and its role in the Standard Model. Their work has also motivated the search for new particles and phenomena beyond the Standard Model that could help explain the origin of the Higgs mass and other unanswered questions in particle physics.

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