## Saturday, June 18, 2011

### New Neutrino News

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!

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