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!