Ali H. Chamseddine, Alain Connes, and Matilde Marcolli argue in their paper

The new paper again shares the gauge coupling unification with GUT theories - which I think is still put in - but it also argues that they can relate the top quark mass to the W mass. More precisely, they argue on page 4 that at the unification scale,

- sum (3 generations) m_e^2 + m_nu^2 + 3 m_d^2 + 3 m_u^2 = 8 M_W^2.

Expert readers should try to decode the mathematically rich formalism and understand where their relation comes from.

The left-hand side is originally constructed from the squares of the Yukawa couplings. To have an idea what it means, realize that the left-hand side is dominated by 3 m_{top}^2, so you roughly get

- m_{top} = sqrt(8/3) M_W

**Update:**In 2008, Alain Connes became the most hapless scientist who ever tried to predict the Higgs mass. The CDF and D0 combined data at the Tevatron were able to falsify one particular possible value of the Higgs mass and it happened to be 170 GeV. See the article about this ironic story involving Connes. ;-)

If you're interested in skeptical results of a Harvard discussion:

- It is not so difficult to predict reasonable values of the Higgs boson: All models that are well-defined at high energies inevitably lead to a Higgs mass in a reasonable window 115-170 GeV. If the mass were below 115 GeV (the same as the observational lower bound), the quartic coupling would run negative at some scale between a TeV and the GUT scale and destabilize the vacuum. On the other hand, if the mass were above 170 GeV, we would encounter a Landau pole below the GUT scale. The Connes et al. value is close to developing the Landau pole at high energies.

- The relations between the masses of the fermions and W bosons can't hold generally at low energies because the equation is not invariant under the RG flow. If they mean something, they describe physics at high energies. But at high energies, one could probably construct many models that would lead to very different predictions - e.g. GUT with all the extra gauge bosons. With this viewpoint in mind, the prediction can't be viewed as a natural consequence of the simple low-energy limit but rather a randomly chosen extrapolation of it to high energies.
- I was trying to conjecture that the relations of these kinds could hold at the string scale for masses in a broad class of models extracted from quantum gravity. This conjecture can be quickly falsified. In braneworlds and probably even in heterotic strings, one can obtain exponentially small Yukawa couplings as long as the Weyl fermions are localized at distinct brane intersections and/or different orbifold singularities so that the couplings are dominated by worldsheet instantons. On the other hand, the W boson masses are unsuppressed because they live in the "bulk" as opposed to intersections or singularities.
- A general relation between the squares of the Yukawa couplings and the gauge couplings is not an unexpected feature because the models based on deconstruction typically generate the Yukawa couplings from the same parameters as the gauge couplings - from some higher-dimensional gauge couplings. But the spectrum of possibilities how to do that is probably large and Connes et al. just proposed one possibility from a large landscape of possibilities.

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