Experiments Constrain Theta 13

Neutrinos oscillate from one flavor (e.g. electron neutrino, muon neutrino, tau neutrino) via the weak force in consistent probabilities that are expressed in the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix, which can be expressed through a number of parameters, of which is Theta 13, an angle that influences among other things, the probability that a muon neutrino will turn into an electron neutrino, is among the least well established experimentally. (The equivalent matrix for quarks is called the CKM matrix).

According to Wikipedia, previous studies have suggested that the full range of constants involved if there are three flavors of neutrinos (the minimum number as three have been observed) have values as follows:

sin^2 2θ13 = 0.08. (If it turns out to be much smaller or zero, the small wiggles shown here will be much smaller or non-existent, respectively.)
sin^2 2θ23 = 0.95. (It may turn out to be exactly one.)
sin^2 2θ12 = 0.86.
δ = 0. (If it is actually large, these probabilities will be somewhat distorted and different for neutrinos and antineutrinos.)
(Delta mass)^2 12= 8 x 10^-5 eV^2
(Delta mass)^2 23 approximately equal to (Delta mass)^2 13 = 2.4 x 10^-3 eV^2

The mass differences between flavors are self-explanatory. The three thetas govern probabilities of conversion of one flavor to another. The sigma estimate to be zero is a charge-parity violating term (a phenomena not observed so far).

The MINOS experiment at Fermilab, has released new data that is consistent with, but constrains results earlier this year from the Tokai-to-Kamioka (T2K) experiment in Japan. Both experiements are measuring the theta 13 parameter, but the experiments use different methods to do so.

The results are usually expressed not in terms of the value of the variable itself, but in terms of the sine squared of double the theta 13 parameter. The result from MINOS is 0.04 with a range of values from 0 to 0.12 within the margin of error. The result from T2K is 0.11 with a range of values from 0.03 and 0.28 that would be statistically significant. The range of values consistent with both experiments are 0.03 to 0.12, with the average of the two central predictions being 0.075.

Neutrinos are an attractive place to look for new physics. We've recently confirmed contrary to some theoretical expectations and experiments that showed a mass consistent with zero, that neutrinos do have mass and have constrained the amount of difference between the masses of the different flavors, although the absolute mass of any given flavor of neutrino has not been determined.

At least a couple of experiments within the last year have also shown a best fit to a result with more than three flavors of neutrinos, which would imply at least one beyond the standard model particle, and also makes the possiblity that there are more than three generations of quarks and electrons seem more plausible.

Extra flavors of neutrinos could also help explain how neutrinos get their mass (there are competing theories regarding that point right now), and could provide a dark matter particle if they were stable and heavy enough.

Since SUSY, which is a class of grand unified theories (i.e. GUTs) which explain all of the laws of physics except gravity in a single unified theory and is necessarily a part of the theory of everything (i.e. TOE) which explains all of the laws of physics in a unified way called string theory or M theory, this could be huge deal. By some accounts, four generations of massive spin-1/2 particles are inconsistent with string theory and SUSY.

The comparable constants in the CKM matrix for quarks are known which much more precision than those for leptons and are as follows: θ12 = 13.04±0.05°, θ13 = 0.201±0.011°, θ23 = 2.38±0.06°, and δ13 = 1.20±0.08.

Footnote from the Economist:

Maybe nature is up to more than its usual tricks.

In light of the latest result, it remains unclear whether either the American or the Japanese experiment is precise enough to measure delta. In 2013, however, MINOS will be supplanted by NOvA, a fancier device located in another Minnesota mine 810km from Fermilab's muon-neutrino cannon. That ought to do the trick. Then again, nature has the habit of springing surprises.

And in more ways than one. Days after T2K's run was cut short by the earthquake that shook Japan in March, devastating the muon-neutrino source at J-PARC, the country's main particle-accelerator complex, MINOS had its own share of woe when the Soudan mine sustained significant flooding. Fortunately, the experiment itself escaped relatively unscathed. But the eerie coincidence spurred some boffins, not a particularly superstitious bunch, to speak of a neutrino curse. Fingers crossed that isn't the case.