$\sin^{2} 2 \theta_{13} = 0.085 \pm 0.029 \pm 0.042$

in agreement with the non zero value from MINOS and T2K! Wow! This appears to strengthen the non zero $\theta_{13}$ hypothesis, bringing the neutrinos in line with the three parameter CKM mixing. Note that the central MINOS value of $0.04$ is well within experimental limits. However, all $\theta_{13}$ measurements are still

*roughly*consistent with zero, and the count of $\overline{\nu}_{e}$ events is open to alternative interpretations.

With a third $R_2$ parameter of $c = -0.15$ from this $\theta_{13}$ result, we obtain a (perturbed tribimaximal) neutrino mixing matrix:

ReplyDelete0.1211, 0.5774, 0.8075

0.7359, 0.5774, 0.3537

0.6662, 0.5774, 0.4721

which maintains the equal $1/3$ column.

Note that $0.472$ squared is close to that damned number, $2/9$. This gives approximate elements of the (squared amplitude) matrix in terms of simple rationals:

ReplyDelete1/72, 1/3, 47/72

13/24, 1/3, 1/8

4/9, 1/3, 2/9

We should continue to ponder the following. Fact 1: the exact tribimaximal matrix at $(1,\sqrt{2})$ is closely associated to the known charged lepton Koide rule. Fact 2: experiments appear to favour a non zero $\theta_{13}$ for neutral lepton mixing. Hypothesis 1: quark lepton complementarity suggests combining the different lepton rules to obtain an operator related to the CKM matrix.

ReplyDeleteFor instance, the central MINOS value of $\sin^2 2 \theta_{13} = 0.036$ (which matches determinants for CKM and neutrino matrices) gives a small $c$ parameter for neutrinos such that $c_{\nu} = 27 c_{q}$, where $c_{q} = 0.0035$. But ...

Fact 3: neutrinos and antineutrinos (as falsely denoted EW states) are not really the same thing! Hypothesis 2: perhaps the neutrino mixing and antineutrino mixing combine to give the CKM, as an 'almost identity'. The identity can be obtained from $M M^{T}$, where $M$ would be like a complex tribimaximal matrix. But how exactly?