As everyone has no doubt heard by now, the T2K experiment has released a new paper indicating a non zero value for $\theta_{13}$ in the neutrino mixing matrix. That is, the six observed electron neutrino events, that pass all cuts, indicate a positive value greater than $\sin^{2} 2 \theta_{13} = 0.03$. This indicates that we may have to add a third $R_2$ factor to the tribimaximal mixing matrix, as is done for the quarks. The T2K paper fixes $\theta_{23}$ at $\pi/2$, which means we can keep the original parameter $1$.

Recall that the two parameter form for the tribimaximal matrix, with parameters $(1,\sqrt{2})$, was invariant under permutation of the factors, whereas this is not true for a three factor matrix. The choice $(\sqrt{2},1,x)$, for a small parameter $x$, fixes the constant row of the tribimaximal matrix to give a mixing matrix of the form where $\epsilon$ replaces the original zero. One may instead fix the central column and apply the $\delta (x)$ and $\epsilon (x)$ offsets to the other columns. It would be nice to keep the exact value for $\theta_{23}$, since it relates neatly to the Koide mass triplets. But triality allows a general mixture of offsets. Now on reordering the $R_2$ factors to $(\sqrt{2},x,1)$, we obtain a completely different mixing matrix. This one roughly resembles the CKM matrix, which also has one small parameter. The neutrinos are looking more like the quarks every day!

7 years ago

The most interesting possible criticism that I have yet heard, regarding this result, is that all candidate events occured in one region of the Superkamiokande tank. But in the paper they point out that a surface region was used as a cut, and that no events in this region make it unlikely that the event coincidence is due to an upstream neutrino source.

ReplyDeleteI am still in favor of making epsilon=0. T2K observed 6 events, 1.5 are expected background. Given more statistics, I will become a believer. Unfortunately, more statistics will not be available soon because of the damage done in the Tsunami/earthquakes.

ReplyDeleteDaya Bay, when they start taking data, should only require 3-6 months of data taking to confirm sin^2(theta_13)=0.03.

Interesting times!

Thanks, hibida. Yes, $0$ would be much neater. I agree we should just wait for Daya Bay.

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