Koide Mass Formula for Neutrinos

[arivero]

I can't figure out that notation, maybe it's my browser (Fireforx).

Meanwhile, in my quest to get into grad school, I just got back my results for the physics GRE test; I maxed it out, 990 out of 990. If nothing else, it means that my applications will be carefully read.

Hmm do you need the GRE for graduate too? I thought it was for undergraduate? While it is important in any case, it is not the same to be in the 1% top sample of all the physics undergrads that the 1% of all the physics grads. Absolute congratulations, of course.

The notation is:

square root of a n-tuple (term by term)
average of the tuple (thus a single term)
square of it

equal to

one half of
average of the same n-tuple.

If instead of one-half, we put unity, then the only solution is the degenerated one. The -arguable- advantage of the notation is that it hiddens the number of generations.

 

[CarlB]

Okay I got it. Actually I end up using a simplified notation like this when I do computations that involve of lot of these.

The GRE is required for students wishing to enter physics graduate school in most schools in the US. Students typically take it while a senior. It's supposed to cover only undergraduate work. A 990 is around the 95% percentile this year, according to the voice I heard over the phone but I understand that that sometimes changes. To get a good score mostly means that you know a wide variety of basic physics and don't make a lot of mistakes in a timed test. In any case, I maxed it out so at least it means that they can't reject me from graduate school because of a low GRE.

 

[arivero]

A 990 is around the 95% percentile this year, according to the voice I heard over the phone but I understand that that sometimes changes.

Funny, I had expected them to calibrate each year, to set 500=50%, 990=99%. Ok, of course, not gaussian shape.

 

[CarlB]

They recalibrate the tests so as to maintain an approximately equivalent scores but they are scaled linearly. They give the percentages separately.

The high scores are dominated by international students as the best of the international students outnumber the best of the US students. But for money reasons, US schools give preference to US students. A plot of "highest ranked" institution making an offer of admission versus Physics GRE score is given here:
http://www.physicsgre.com/viewtopic.php?f=1&t=3474#p29723

It's not necessary to get a 990 to get into the top schools but it helps.

 

[arivero]

Koide [Y. Koide, Lett. Nuov. Cim., 34 (1982), 201]:
$$tan \theta_c = \left(\frac{\sqrt{m_\mu}-\sqrt{m_e}}{2\sqrt{m_\tau}}-\sqrt{m_\mu}-\sqrt{m_e}}\right)^{1/3}$$

Hmm there are some typos in the LaTeX source. From Phys. Rev. Lett. 47, 1241–1243 (1981), it is

$$tan \theta_c = \frac{\sqrt 3 (\sqrt{m_\mu}-\sqrt{m_e})}{2\sqrt{m_\tau}-\sqrt{m_\mu}-\sqrt{m_e}}$$

I guess that this is a manip of the same formula used for the phase delta_1 here, isn't it? Actually I think it is more elegant to see it as a phase that as Cabibbo angle, but it could be interesting to review the argument of Koide to tell that it is the Cabibbo angle

Also, I found that Koide and Oneda did some use of the same kind of formulae for mesons here
http://ptp.ipap.jp/link?PTP/81/199/
http://prd.aps.org/abstract/PRD/v36/i3/p815_1