With improved evidence for a non zero $\theta_{13}$ (assuming for now that neutrinos and antineutrinos share the same mixing parameters) we must ask once again: why, oh why, does the tribimaximal matrix fit so nicely with the charged lepton triplet? Perhaps quark lepton complementarity provides a clue.
Observe that with mirror neutrinos, quark color reflects the three lepton sectors: $e^{\pm}$, $\nu$ and $\nu^{m}$. And in perturbative gravity at least, color and generation are closely associated. Each $R_2$ factor in a mixing matrix is thus associated to either generation or color. So the zero parameter in the tribimaximal matrix could be associated to the lack of mixing for charged leptons, forming one third of the color spectrum. Similiarly, the closeness to the identity of the CKM quark mixing matrix reflects the appearance of all three colors in the quark set. Moreover, a (down) quark braid is somehow a mixture of $(e^{\pm}, \nu, \nu^{m})$ strands, meaning that there exist mirror quarks formed through a mirroring of neutrino components. Recall that the CKM matrix is similar to a reordering of a three parameter neutrino matrix.
What would that mean for neutrino and mirror neutrino mixing? We can create a neutrino braid with, for instance, one strand from each of a $(u,d,d)$ triplet, by cancelling the charges. Thus conversely, the neutrino matrices come from the quark ones.
14 years ago
Kea, two things I found that may be of interest. Note his use of the term Triality.
ReplyDeletehttp://uduality.blogspot.com/2011/11/m-theory-111111.html
Also on national public radio Science Friday an interview with three ladies in three cities. I send the one in Oakland, CA as she included under representation of women as well as minorities. The USA is 27th in science and engineering and only 40% graduate in 5 yrs. 9% of the minorities.
But of course you should be in research.
ThePeSla
Yes, ThePeSla, plenty of women graduate with PhDs in the physical sciences these days. That is one reason why it is so shocking that very few of them get jobs. People say, don't worry, the younger generation will move up and get real jobs one day. But I was a successful young scientist myself once, so I am not so easily fooled.
ReplyDeleteI'm not keeping up, but since you mention neutrino and mirror neutrino mixing... From the "N=8 Gell-Mann perspective", the mirror neutrinos are the goldstinos which give the SU(3)-triplet gravitinos their mass. Presumably these goldstinos are tachyons in the same sense as the "unbroken Higgs" is a tachyon in the standard model - having imaginary mass. So if the OPERA result holds up, one might seek to explain it through mixing between the known neutrinos and superluminal mirror neutrinos.
ReplyDeleteThat's right, Mitchell, the big question is, how do the two neutrino sets combine. We already have a Koide phase pair $2/9 \pm \pi /12$, where the minus phase gives the CMB temperature. And even the latest MINOS antineutrino results indicate a difference between what one usually calls 'neutrinos' and 'antineutrinos'.
ReplyDeleteIt's interesting that the neutrino lines cross the charged lepton lines at the unit circle (innermost, dotted), forming a pi/2 angle between them, as shown on the java applet.
ReplyDeleteDave, that is just basic trigonometry. Take $5 \pi/12$ from $\pi /6$ at half a corner of a $\nu$ triangle, leaving the required $\pi /4$.
ReplyDeleteBut yes, it is interesting that the $r = 1$ point only occurs for the lepton $\sqrt{2}$ radius and the phase $\pi /12$.
ReplyDeleteI just had a funny thought about "neutrino gravity". According to the KLT relations, graviton amplitudes are gauge-boson amplitudes squared. I wonder if this can be justified in terms of virtual fermion loops, that "bind" the gauge-boson propagators together?
ReplyDeleteWhat I'm thinking is that this is how a mirror neutrino condensate can be responsible for gravity. It seems to imply that the graviton is a bound state of weak force bosons.
That is vaguely the idea, Mitchell, but I just don't think in terms of these standard ideas, because they are the wrong way of looking at it. All gauge symmetry is emergent, of course. But yes, we can put the braid pieces together to get effective 'gravitons'.
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