Carl's Upcoming Talk at Hawaii Conference

[Kea]

A Model of Elementary Domain appearing in the deepest space of the Standard Model
All spatial points are arranged on triangular lattices, and they can also be on square lattice points.

Yes, sounds interesting. You know, truncations of cubes by hyperplanes is what operad polytopes are all about...It would be good if you could get a reference for this.

That is not because I have been convinced that the fashionable belief is the truth, but because I have observed that the unfashionable beliefs are ignored and so cannot be tested for truth.

Unfortunately, in times such as these one must be prepared to yell out sacrilege at the top of one's lungs and hope at least one person (in a position to do something about it) is listening.

 

[CarlB]

The conference is over. I'm about to check out of the hotel and take a cab over to the airport.

I made a tactical error Thursday and again Friday (yesterday). I forgot to apply the baby powder. The result was that when I walked out to have an inexpensive lunch on Friday (expensive ones being available in the hotel), I was in such pain that I decided to leave off the last afternoon of the conference and so I continued walking back to the hotel.

When I got back, I took a shower, and being extremely hungry, I powdered myself, went downstairs, and walked to the McDonalds. Since I still wasn't figuring on seeing the tail end plenary lectures, I didn't bring my computer or backpack. The result of being freshly fed, bathed and powdered, and not carrying my heavy accouterments, was that I had a new burst of energy and walked on to the Waikiki Sheraton to attend the last afternoon lectures.

All the lectures were good, but the final lecture of the day stood out as an example of the art:
http://www.phys.hawaii.edu/indico/contributionDisplay.py?contribId=760&sessionId=23&confId=3

It was by Francis Halzen, whose lucky students learn at the University of Wisconsin:
http://icecube.wisc.edu/~halzen/webpages/aboutme.htm

He began with Fermi's paper of 1934 on the weak interactions that presaged the mass of the W. From there he went to discussing the Higgs, which he called, with reason, "the ugly particle", and discussed various ways its mass might be calculated. But he made it clear that it required a certain amount of fine tuning.

The other fine tuning problems he discussed were baryogenesis, the cosmic coincidence (inflation), and the cancellation of all but 1/10^10 of matter against antimatter.

He discussed several subjects close to my heart. He talked about heavenly accelerators that may solve earthly problems, the "cosmic haze". Eventually I realized that it was the cosmic rays that were being discussed, but I better like the poetry of the words I heard.

He said that Lorentz invariance will likely be violated at very high speeds, and those very high speeds are likely to be detectable by neutrinos. Since I don't believe in Lorentz invariance as a fundamental principle of physics (rather than an approximation that can be derived from the geometry), this was very heartening.

So he talked about a lot of neutrino detectors, particularly Antares. The pilot project for Antares was DUMAND, and it turns out that yours truly designed the ECL gate array that measured the PMT outputs from that experiment. To hear the name again after so many years was nice.

I have notes from the other talks and various things, but I'm exhausted and even if I were not, I could still use the excuse that I need to get ready to go. I understand that the first snow of the season shut the pass east of Seattle this week. That important freeway goes on through the corn and barley growing regions of central Washington (where Liquafaction's ethanol plant is located), through the volcanic badlands of eastern Washington, then the mountains of Idaho, Montana, and eventually on to Chicago and points east.

Carl

 

[Kea]

CarlB

Thanks a lot for the blogging effort ... I almost feel like I was there!

 

[CarlB]

After I blogged that last comment, I went downstairs, checked out of the inexpensive ($50 per night) and colorful hotel (which has permanent residents who get their mail downstairs, along with the sort of things that would lead me to suspect that this would be a reasonable place to look for illegal drugs to purchase if that were desired), I mentioned to the clerk that I had run out of cash and would be paying for my ride back to the airport by credit card. He responded that taxicabs in Honolulu do not accept credit cards!

I asked him where there was a nearby bank that was open on a Saturday, and he pointed me towards a nearby bank that turned out to be closed. From around here I got very useful direction to how to walk out of Waikiki to the residential district near Diamond Head where there was a Bank of Hawaii that was open on Saturday.

By the time I got to the Bank of Hawaii and back, I was drenched in sweat. And Honolulu airport requires its passengers to walk remarkably long distances for such a small island. But I made it back to Seattle which is cold, raining and very comfortable to me.

My buddy's plan on selling our ethanol factory appears to be falling apart due to the purchasing company having made a financial mistake so severe that it will likely destroy them. I hate to admit it, but I think this is good news because I thought that the purchasing company was so incompetent as to be dangerous to sell to. So I need to spend some time helping look for a buyer for a plant that makes about 48 million liters of 100% pure ethanol per year. Just think of the party you can have with just one week of production, about a million liters.

Meanwhile, I thought of a way of translating my density operator formalism result for the leptons into a guess on the symmetry of the mass terms in the usual field theory and will write this up when I can find the time. Basically, one guesses that instead of having Dirac mass terms like $$m\bar{\nu}_L\nu_R+m\bar{\nu}_R\nu_L$$, one guesses that there is a sterile neutrino inserted in the sequence, and one gets instead something like:

$$m\bar{\nu}_L\nu_R + m\bar{s}_L\nu_L + m\bar{s}_Ls_R + m\bar{\nu}_Rs_L$$

where "s" is a sterile neutrino.

Assuming I didn't reverse L and R, the above is experimentally indistinguishable from the usual Dirac mass because experiments always produce neutrinos with 99.9999% of their energy in kinetic form rather than mass form. So if you lose a few neutrinos to sterility by the above process, you will never see it experimentally.

Then one asks, what is the effective mass of the above neutrino? Feynman has a calculation which gives mass to a massless propagator (1/p) by assuming that a massive propagator is made from any number of massless propagators that interact with amplitudes m. This set of trivial Feynman diagrams can be easily summed:

$$\begin{array}{l} 1/p + (1/p)m(1/p) + (1/p)m(1/p)m(1/p) + ...\\ =(1/p)(1 + m/p + (m/p)^2 + ...)\\ = (1/p)(1-m/p)^{-1}\\ =p/(p-m)\end{array}$$

When you apply the same sort of resumming to the modified neutrino mass, my intuition says that you're going to pull a factor of m^2 out instead of m. But to get this to work, you have to assume to assume that you are operating in a sufficiently complicated algebra that you don't have the intermediate terms (i.e. the sterile neutrinos) interfere with the usual ones.

If you are a little more careful in your Feynman diagrams, you will distinguish between left and right propagators, and in doing the above resummation you will derive the massive Dirac propagator from the massless ones. That is, instead of doing one summation, you will have four to make, that is, the initial state either L or R, and the final state either L or R. These four summations you can then glue back together to obtain the massive Dirac propagator derived from the massless one. I highly recommend this as an exercise.

This means that you have to be a little careful in your summing the terms. You can't add apples to oranges and expect them to add, but you must instead keep separate totals for the apples and oranges. When you do this with the sterile neutrinos included you will end up with m^4 in the denominators instead of m^2. Now think of 11 sterile neutrinos instead of just 1. You end up with m^{24} in your denominator instead of m^2. This is exactly the sort of thing you need to get a 3^{24} difference in magnitude between the neutrino and charged lepton masses.

So you can postulate a mass interaction which is the same for charged and neutral leptons despite their very large disparity in mass. And of course, when you include the Koide formula for inter generational mass differences, you can also expect that there will be that factor of pi/12 that pops out.

Making this sort of change will increase the number of neutrinos by a factor of 12. Since the heaviest neutrino is around 0.05 eV (assuming normal hierarchy and all that), this means that the total of the neutrino masses is not around 0.05 eV, but is about 12 times that. The interesting thing about this, is that it brings the total mass of neutrinos very close to the limit (i.e. 0.7eV) that the cosmologists have placed on them.

Carl

 

[CarlB]

An update on my talk in Hawaii last October. The formula for the neutrino masses (which was first discussed here on Physics Forums) now has 4 journal citations:

Neutrino Mass and New Physics;
R. N. Mohapatra, A. Y. Smirnov; Department of Physics, University of Maryland, Abdus Salam International Center for Theoretical Physics, Institute for Nuclear Research RAS;
Annual Reviews of Nuclear and Particle Science, 56 (2006) 569-628
http://arxiv.org/abs/hep-ph/0603118v2

Heuristic Development of a Dirac-Goldhaber Model for Lepton and Quark Structure;
Gerald Rosen, Drexel University;
Modern Physics Letters A, Vol. 22, No. 4 (2007) 283-288
http://www.worldscinet.com/mpla/22/2204/S0217732307022621.html

Tribimaximal Neutrino Mixing and a Relation Between Neutrino and Charged Lepton-Mass Spectra;
Yoshio Koide, University of Shizuoka;
to be published in J. Phys. G (2007).
http://www.arxiv.org/abs/hep-ph/0605074

S_3 Symmetry and Neutrino Masses and Mixings;
Yoshio Koide, University of Shizuoka;
to be published in Euro. Phys. J C (2007).
http://www.arxiv.org/abs/hep-ph/0612058

I declared a blog party and discussed the citations here:
http://carlbrannen.wordpress.com/2007/06/29/to-help-miss-cite-reb-eretics-simple-hot/

In retrospect, I think the reason this got notice was because it put Koide's formula into eigenvector / eigenvalue form. Maybe this makes it easier to fit into other ideas, or maybe it just makes it more attractive.

The problem for the standard model is that masses are supposed to arise from renormalization group effects and these aren't very compatible with Koide's formula, in the usual form or the eigenvalue form. Rewriting his formula in eigenvalue form suggests that the usual methods of quantum mechanics should also work for the pole masses. I think that a natural leap of logic is to suppose that there should be a way of writing quantum mechanics as a perturbation series around bound states instead of a perturbation series around free states. Then eigenvalue problems naturally arise.

Carl

 

[arivero]

Heuristic Development of a Dirac-Goldhaber Model for Lepton and Quark Structure;
Gerald Rosen, Drexel University;
Modern Physics Letters A, Vol. 22, No. 4 (2007) 283-288
http://www.worldscinet.com/mpla/22/2204/S0217732307022621.html

Interesting guy, I failed to notice his work when compiling the "long thread".

The problem for the standard model is that masses are supposed to arise from renormalization group effects and these aren't very compatible with Koide's formula, in the usual form or the eigenvalue form.

Indeed the problem is that if the masses are going to meet in a single multiplet in the GUT scale, it must be possible to predict them from its equality in such multiplet. The jargon says that any low energy formula must be "protected by a symmetry".

Of course this is not true if the masses at GUT are zero (or infinite).