**Theta13**

The value of the sine squared of two times Theta13 are as follows (collapsing errors with multiple components by adding in quadrature):

Daya Bay: 0.084 +/- 0.005

Reno: 0.101 +/- 0.0128

Reno (n-H ISD method): 0.095 +/- 0.029

Double Chooz (primary result): 0.09 +/- 0.03

Double Choosz (alternate method): 0.06 +/- 0.04

Combining the results by weighting them relative to the inverse of their margin of error (the technique used by the Particle Data Group to get its world averages), produces a Neutrino 2014 average of 0.0875, which corresponds to Theta13 of 8.6 degrees (0.15 radians). The results are inconsistent with zero at far more than a five sigma discovery threshold and have been for years.

I don't have the precise margin of error but it is probably fairly similar to the Daya Bay margin of error that dominates the average result (with a 54% weight). All of the new results are consistent with the Neutrino 2014 average within two sigma.

This compares to a best estimate of 9.1 +/- 0.6 degrees of April 3, 2013 and of 8.9 degrees in a June 28, 2012 paper (both reported in the PMNS matrix entry at Wikipedia).

Thus, the estimates of this PMNS matrix parameter have stabilized at the low end of the range allowed by recent experimental measurements, and have reached almost 6% precision. This foundation will make it easier to determine the still unknown neutrino property parameters (e.g, the CP violation phase, the question of whether the neutrino mass matrix is normal or inverted).

Tri-bi-maximal neutrino mixing (which assumes that Theta13 is zero), which is theoretically popular, has been empirically falsified.

The difference in mass squared between the second and third mass state in a normal hierarchy is 2.39+0.10/-0.11*10^-3 meV^2 at Daya Bay and 2.37+0.09/-0.09*10^-3 meV^2 at MINOS. In an inverted hierarchy it is -2.49+0.10/-0.11*10^-3 meV^2 at Daya Bay and -2.41+0.11/-0.09*10^-3 meV^2 at MINOS. The two sets of results are consistent with each other at less than a one sigma level.

This translates to about a 48.8 meV mass difference in a normal hierarchy and 49.5 meV in an inverted mass hierarchy.

**Theta12**

A combination of KamLand and solar data presented at the Conference shows sine squared of Theta12 to be 0.308+/-0.013 which corresponds to 33.7 +/- 0.8 degrees (a 2.4% precision).

The delta mass squared difference between states 1 and 2 of (7.5+0.19/-0.17)*10^-5 eV^2 (which implies an absolute value of the mass difference of 8.66+11/-0.10 meV). Thus the mass difference between the first and second states has a +/- 1 standard deviation confidence interval of 8.56-8.77 meV.

Both results are generally consistent with previous estimates.

**Theta23**

**The best fit to Theta23 presented at the Conference shows sine squared of Theta23 equal to 0.55 based upon combined Super-Kamiokande and T2K results. This corresponds to Theta23 of 47.9 degrees. The best fit for SK results alone was 49.0 degrees. The confidence intervals aren't clearly stated in as many words.**

IceCube reports a best fit of sine squared Theta23 equal to 0.512 (68% CI of 0.422-0.600) in a Normal Hierarchy and 0.509 (68% CI of 0.417-0.594) in an Inverted Hierarchy. These are closer to the 45 degree value that it takes at 0.500.

The best fit results do not differ in normal hierarchy and inverted hierarchy scenarios and there is not statistically significant data to support one of those scenarios over the other from the Super-Kamiokande experiment.

Note that the sum of the three theta mixing angles in the PMNS matrix are equal to approximately 90 degrees (alternately, the sum of the sine squared of each the mixing angles is very nearly 1.00).

**Other Parameters**

**The absolute value of the neutrino masses, the question of whether the neutrinos have a "normal", "inverted" or nearly "degenerate" hierarchy of masses, the CP violating phase or phases of the PMNS matrix, and the quadrant of theta23 remain unsolved problems in neutrino physics.**

One experiment that a few years ago had best fits weakly favoring an inverted neutrino hierarchy, now weakly favors a normal neutrino hierarchy. Bounds on the maximum neutrino masses from various kinds of experiments are reported throughout the Neutrino 2014 posts at this blog and aren't terribly strict at this point, with the lowest bounds and the highest ones differing by almost an order of magnitude.

More progress has been made in determining the CP violating phase of the PMNS matrix. A value of + pi/2 (i.e. + 90 degrees) is quite strongly disfavored by some experiments. A value of - pi/2 (i.e. - 90 degrees or equivalently, + 270 degrees) is quite close to a best fit value and is consistent with a number of experiments. A value of zero CP violation is not ruled out, but is increasingly disfavored relative to a value with some CP violation in neutrino oscillations. Improved precision in the measurement of Theta13 has been particularly important in closing in on the CP violating phase value, but an experimental determination of the precise value of the CP violating phase of the PMNS matrix isn't imminent either.

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