Sunday, 12 June 2011

Symmetry Breaking, Groups E8 and E6

Reviewing articles at ArVix its come to my attention, that most popular super-symmetry and String phenomenologist aren't choosing the right models of symmetry breaking, ignoring classic papers, and proofs, just so they can use too easy but wrong models to fit Higgs bosons into a grand unified theory of the universe. In particle physics a phenomenologist is a physicist that tries to make the bridge between mathematical elegant models produced by theorists, and the experimental results. Because theories like super-symmetry and super-gravity are so remote from practical energy scales and can produce so many different result depend upon how our universe has broken these symmetries, phenomenology is very difficult subject, but it is perhaps the most important, it is where theory lives or dies depending on weather it describe a universe looking like our universe.

The most popular models start with string theory or supergravity which only allows certain mathematical groups to produce self consistent theories. In particular group E8 * E8, is often the starting point. This leads to two copies of matter in the universe so presumably mirror matter should be a favourite model of the missing matter in the universe. In fact mirror matter is only relatively vary investigated though it still looks very consistent with the DAMA and Cogent observations. E8 is particularly nice because choosing it automatically gives the three generations of quarks and leptons share the same forces, as observed, and describe by the standard model. E8 also is the biggest finite lie alegebra (248 roots), and self adjoint, meaning it contains both the groups needed to represent particles and forces in the same represention. That makes is automatically super-symmetric, you get 248 spin-1 force carriers and 248 spin-1/2 particles, see Steven L. Adlers classic paper: . What you don't get is any scalar bosons, so your Higgs particles have to be composites condensing out of the particles that are attracted to themselves with such strength that the lowest energy state of the vacuum contains a sea of these particles. Breaking E8 to three generations of a smaller group E6.

Now E6 has 27 particles its fundamental representation, and when you ask how it breaks symmetry by vacuum condensing, the computation been done and its either $E6 -> F4 * U(1) $ but with every force carrier picking up a mass (clearly not our universe), or $E6 -> SU(2) * SU(6), 27 -> 15 + 12$. The vacuum condensation is complicated enough that it was to be done in simulation by a computer, but the result stands. And do phenomenologists use it? no they don't, again and again they break E6, to SO(10)*U(1), and them have Higgs bosons, (doublets) in the group. Somehow they of they own choice have added scalar multiplets to the models that isn't suppose to have scalars in it, and further, have choosen SO(10) just because its a favourite GUT model, (not one that works, as it predicts faster proton decay than could be real without it have been measured by now. In fact SO(10) is a left-right symmetry theory, while E8 is left-right symmetric and E6 is chiral (chooses a particular direction), so when phenomenologists use E6->SO(10), have broken parity, unbroken it, and rebroken it at second time along there trail. This seem to happen because they of course start with a popular model and see what happens down the trail to low-energy, forgetting what made the popular model, popular in the first place.

To my mind, and using a axial-force, E8, contains U(2) left , U(2) right which will eventually break to U(1)_em, U(1)_axial, SU(2)_left weak force, SU(2)_right, breaking at the same time as 3 seperate generations of particles has formed., then E6 has SU(3) color, U(1)_axial, U(1)_em and SU(2)_left weak force in its SU(6), leaving a SU(2) grouping splitting E6 into the 15 known particles of the standard model grouped into left handed and right handed E6 multiples, and 12 extra quarks grouped into particle and anti-particles multiplets. All the anomalies of U(1)_em and U(1)_axial cancel in this representation, which I wouldn't have found, if I wasn't so keen on having a U(1) axial force. The extra vector-like quarks (i've called terra quarks, borrowing the name from different model by Gamor), then need to gain extra mass, and may form a left-right symmetry breaking condensate reacting with the generation permuting right handed neutrinos that appear when breaking E8 to E6. We have a rather complex vacuum condensate, which will need computational analysis, instead of a standard model Higgs, so phenomological prediction won't be easy from this model, but it does follow the spirit of E8 down to low energy, and doesn't introduce ad hoc scalars, but compute scalar condensates them from first principles. I'm blogging to try and promote this model to someone with the time to compute it.

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