Neutrinos Again
A paper by Altarelli and Feruglio on tribimaximal mixing was mentioned in talks at Neutrino 08, so I thought I should take a look at it. They begin by describing the 3 dimensional representation of $A_{4}$ which has generators $S$ and $T$ satisfying $(ST)^{3} = S^{2} = 1$, just like the modular group, and also the relation $T^{3} = 1$. Then, letting $\omega$ be the cubed root of unity, one has for $T$ the matrix
1 0 0
0 $\omega^{2}$ 0
0 0 $\omega$
and for $3 S$ the circulant matrix
-1 2 2
2 -1 2
2 2 -1
The 12 elements of $A_{4}$ are given by all possible combinations of these generators. Gee, it already sounds a bit like M Theory. I can't imagine what they want with all the fairy fields and SUSY's mumbo jumbo, although in short shrift the tribimaximal mixing matrix appears.
1 0 0
0 $\omega^{2}$ 0
0 0 $\omega$
and for $3 S$ the circulant matrix
-1 2 2
2 -1 2
2 2 -1
The 12 elements of $A_{4}$ are given by all possible combinations of these generators. Gee, it already sounds a bit like M Theory. I can't imagine what they want with all the fairy fields and SUSY's mumbo jumbo, although in short shrift the tribimaximal mixing matrix appears.
posted by Kea | 5:40 PM
5 Comments:
Hi Kea,
Feruglio is a colleague in Padova... I'll give a look at the paper!
Funny how one is blissfully oblivious at times of what colleagues working in the adjoining office do.
Cheers,
T.
... and thanks for the link ;')
Cheers,
T.
Cool, Tommaso! Check out his nice slides.
This reminds me of qutrit MUBs, i.e. see matrix M.
And your S, is closely related to 1+J+J^2.
Why yes, Carl, indeed. I'm wondering why I can't find any papers that explain this connection .... dammit, does that mean I have to write another paper?
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