Tuesday, June 22, 2010

MINOS Neutrinos II

Expanding on my last comment, recall that Carl Brannen's phase for the neutrino Koide mass matrix is

$\delta = \frac{2}{9} + \frac{\pi}{12}$

which results in the eigenvalue set

$\sqrt{m_{i}} = \mu (1 + \sqrt{2} \textrm{cos} (\delta + \omega_i))$

for $i = 1,2,3$ and $\omega_i$ the three cubed roots of unity. The value $2/9$ and the factor $\sqrt{2}$ are shared by both neutrinos and charged leptons. This $\delta$ gives three neutrino masses and a $\Delta m^2$ in agreement with known measurements. If, on the other hand, we took a phase

$\delta = \frac{2}{9} - \frac{\pi}{12}$

for the same scale $\mu$ and same eigenvalue equation, we obtain three masses with a $\Delta m^2$ in perfect agreement with the new MINOS results. Note that the $\overline{m}_{2}$ mass dominates the $\Delta$, so it does not much matter if we are considering $\overline{m}_{1}$ or $\overline{m}_{3}$.

It is not yet clear why conjugation on the $\pi /12$ should correspond to antineutrinos, but recall that conjugation is a standard feature of phases for antiparticles in the braid spectrum. The $2/9$ component appears to be shared by all particles, irrespective of their quantum numbers.


  1. We have been talking about that damned $2/9$ for years now ... but this may be the first real world clue as to how it differs from the other phase components, which tend to be rational multiples of $\pi$.

  2. Now I hear rumours that the MiniBooNE experiment has also found evidence of oscillation differences for neutrinos and antineutrinos. Gee, how I wish I was in Athens this month!

  3. ... OK, so here are the MiniBooNE slides.

  4. ... and in the Fermilab news this week.

  5. I read: MiniBooNE collaborators announced that they had obtained a result consistent with the findings from LSND. In fact, analyzing the data in the context of a standard two neutrino mixing model favors an LSND-like signal at a 99.4 percent confidence level. However, model-independent tests show there is still a three percent chance that background fluctutations could mimic the data.

    If there are three varieties, maybe also four...
    Three superpositions? The trinity?

  6. Ok. You are the expert.
    I just meant to remind you of what is basic. It is not matter. If you look in the mirror and smile, and the mirror looks back and cry, where is the failure? What has happened? Broken symmetry? And you looks from the wrong side? A hierarchy with broken symmetry? Remember the possible fourth gen too?

    Otherwise cool.

  7. Lol, Mitchell, but I suspect that many young graduate students are studying these things nowadays. His blog is nice, but I don't like the name: The Superconformist.

  8. Ulla, the new papers are not even available to read yet. There is much to consider.

  9. Well done for dealing with real problems in this post, neutrino masses.

    I don't like the fact that you write in this post about your model being "in perfect agreement with the new MINOS results".

    I'd prefer you to be quantitative about the amount of agreement (how many significant figures, how accurate is the MINOS result, etc.) because writing about "perfect agreement" rings alarm bells.

    Also, you should try to repeat and simplify the basic matrix in any new post you write, so people don't have to keep referring back to previous posts. You should keep each post self-contained as far as possible, with the key information there in the post. People should only need to click on links for further information and historical developments, not to get the basic information they need. Otherwise, trying to understand any post you write turns into a parlor game where you have to keep jumping about.

    But, hey, as you keep reminding critical commenters, it's your blog and you can write whatever you like, and delete/vilify a comments you disagree with. Some of us have to be anonymous to be rigorously objective here, or you get attacked in a personal way by the confident-to-the-point-of-rude blog owner; I predict now you will respond with the following angry response (copy and paste the following to save time!):

    "Thanks anonymous for giving me permission to delete comments from my own blog (now I have to point out to you that sarcasm is intended, because you are so stupid you will otherwise take that as a genuine thank you). Blah blah ... [paranoid attack on general stupidity and evil of certain people] ... It's so cool that I'm now so clever I'm attracting mad comments from internet surfers."


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