### Midsummer Fairies

At the Summertown laundromat this morning we ran into a newcomer in town, namely the friendly string phenomenologist Stuart Raby, recognisable from a recent conference T-shirt. After sorting out, with some difficulty, which coins one should use in which washing machines, Raby expressed suitable horror at the idea that the Higgs might not exist. Anyway, after some discussion about the recovery of a weakly constrained MSSM from a heterotic string compactification, he admitted to having also considered mass matrices and mixing data using more interesting GUT models, in particular in this paper from 2005.

In contrast with Connes' failed prediction of the Higgs mass, this paper still meets experimental constraints, with a prediction of around 120 GeV. The parameters and best fit fermion masses are given on page 12, and neutrino masses on page 13. The neutrino mass sum is much less than 1 eV, in agreement with Carl Brannen's estimate, but the neutrino mixing deviates from tribimaximal.

In contrast with Connes' failed prediction of the Higgs mass, this paper still meets experimental constraints, with a prediction of around 120 GeV. The parameters and best fit fermion masses are given on page 12, and neutrino masses on page 13. The neutrino mass sum is much less than 1 eV, in agreement with Carl Brannen's estimate, but the neutrino mixing deviates from tribimaximal.

## 4 Comments:

Interesting predictions. There is some field that gives mass to particles in the gauge symmetries such as those of the SM, and since mass/energy is the charge of quantum gravity.

In general relativity a gravitationa field has energy and is therefore a source of gravitation itself.

This causes quantum gravity to be looked at like as some kind of Yang-Mills field where the field quanta must carry charge itself, i.e. the mainstream sees general relativity as evidence that quantum gravity is non-Abelian.

You would however expect from the fact that quantum gravity appears to involve only

onesign of charge (mass-energy always falls downward in a gravity field) together with apparently justonetype of field quanta, that quantum gravity is a simple Abelian U(1) gauge theory.U(1) x SU(2) x SU(3) has to be supplemented with a Higgs field to break the U(1) x SU(2) symmetry thus separating the electromagnetic and weak forces by giving the weak forces mass.

Woit has made the point in his early blog post "The Holy Grail of Physics" that this electroweak symmetry breaking seems to go hand-in-hand with the way that the SU(2) field quanta which gain mass at low energy (limiting the range of the weak force to very small distances) also have the property of only partaking in left-handed interactions.

The left-handedness of the weak force seems due to an intrinsic property of the weak field gauge bosons. The simplest way to put quantum gravity and mass into the Standard Model is to leave the short range nuclear force SU(2) x SU(3) symmetry alone, but to change electromagnetism from U(1) to SU(2) with massless weak gauge bosons. I.e., half the weak gauge bosons gain mass to give the left-handed weak force; the remainder mediate electromagnetism. So you have negatively charged radiation mediating negative electric fields around electrons, instead of a neutral photon with 4 polarizations. The equilibrium of radiation exchange means that (1) magnetic curls cancel preventing the usual problem of infinite self-inductance for the propagation of charged massless radiation, and (2) this necessary perfect equilibrium of exchange physically prevents the charged field from affecting electric charges, so that the Yang-Mills equation for SU(2) electromagnetism automatically collapses effectively to Maxwell's equations, since the Yang-Mills term for the charged field to modify fermion charges will be zero, and the equation is otherwise identical to Maxwell's.

Hence, in SU(2) x SU(3) you then have electromagnetism, weak force and strong force. Because there is only need for one sign of gravitational charge (mass/energy) and one graviton, a U(1) theory can be added for quantum gravity and mass, with the U(1) field boson mixing with the neutral SU(2) field boson in the SM way to produce both a graviton and massive weak Z_0. I'd expect the massive U(1) gravitational charge to be identical to that of the Z_0, 91 GeV (already observed in 1983 at CERN).

Completely out of topic! I found a generalization of twistor concept to 8-D context using number theoretic ideas. This notion allows to get rid of the condition that particles are massless since massive particle in M^4 can be regarded as massless particle in M^8.

The resulting octo-twistor space is 3*8=24-D (triality of three 8-D representations of SO(7,1) allows to fuse them to twistor like entity just as the duality of spinor and its conjugate in case of ordinary twistors). If one allows the overall phase for real spinor and conjugate one obtains 26-D situation.

Reality of 8-spinors (apart from overall phase) would be analogous to Majorana condition and would make sense at partonic 2-surfaces (analogs of closed strings) as boundary conditions but not everywhere. One can also consider the analog of Majorana property for the induced gamma matrices or modified gamma matrices appearing in modified Dirac equation.

It's a pretty generic propertry of SUSY models which employ radiative electroweak symmetry breaking (REWSB) to have a Higgs mass in the range 114-120 GeV.

Nige, I think you must be thinking of models with Left-Right symmetry based on the gauge group SU(3)x SU(2)_L x SU(2)_R.

Yes, the Higgs prediction is rather generic, but I don't think AF has mentioned it before, because fairy fields are less interesting than real observables.

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