## Thursday, June 16, 2011 ... /////

### T2K: hint of neutrino oscillations driven by theta13

There are three light weakly interacting neutrino flavors. In fact, this figure has been measured by experiments that investigated the decay width of the Z-boson. This width is proportional to the number of the relevant neutrino species and allows you to say that there are roughly 3.01 plus minus 0.02 of them - or something like that. ;-)

Neutrinos were first claimed to exist by Wolfgang Pauli who used energy conservation. But they were given their name by someone who has found many things about them and the processes in which they participate, Enrico Fermi (picture above). He chose the funny little Italian suffix -ino not only to distinguish them from neutrons but also to place a piece of Italian terminology into physics for the future times when his nation may possibly become an ethnic group of savages who will deny that the nuclei store lots of cheap energy.

The Standard Model assumes that only left-handed neutrinos (and right-handed antineutrinos) are light enough; their right-handed neutrino (and left-handed antineutrino) partners are probably very heavy - near the GUT scale. Those heavy partner masses are Majorana masses. Then there are electroweak-scale Dirac masses mixing the light and heavy components.

When the heavy partners are integrated out, we obtain just the light species with new Majorana masses that are very light. They're lighter than the Dirac masses by the same factor as the Dirac masses are lighter than the heavy Majorana masses (so the Dirac masses are near the geometric average of the tiny and huge Majorana masses we have mentioned). That's why the mechanism leading to this relationship is known as the seesaw mechanism.

In experiments, neutrinos are usually produced with a well-defined handedness so there's really no detectable mixing between neutrinos and antineutrinos in the experiments we can perform. Even though the masses are Majorana masses, the two sectors - neutrinos and antineutrinos - are separated pretty much by the angular momentum conservation law.

See my report on Neutrino oscillations and Majorana/Dirac neutrinos from the last century for a more technical presentation of spinors, oscillations, and experiments testing various aspects of this science. Some things have changed but most of them have not.

However, there is a mixing between the 3 generations. The SU(2) partners of the electron/muon/tau charged lepton mass eigenstates are not necessarily mass eigenstates themselves. In an analogy with the CKM matrix for the quarks, the mixing of the neutrinos is described by a unitary PMNS matrix. Just like its CKM cousin, the PMNS matrix depends on 3 real angles and 1 additional CP-violating phase. The latter can't really be measured and it's assumed to be zero.

Several kinds of neutrino oscillations have been observed. The oscillations depend on the differences of m², the eigenvalues of the squared mass, and the mixing angles θ_12, θ_23, θ_13. The solar neutrino oscillations (causing a smaller inflow of neutrinos from the Sun relatively to the solar models) are caused by Δ(m²)_12, the difference between the two smallest m² eigenvalues in the matrix. That's not hard to understand: the Sun-Earth distance is long so the lowest-frequency processes are the most important ones.

The atmospheric neutrino oscillations are caused by the remaining Δ(m²)_13 and Δ(m²)_23 - the higher frequencies - and moreover, it empirically seems to be the case that these two quantities are nearly equal: |Δ(m²)_13| = |Δ(m²)_23|.

However, it's actually not known whether Δ(m²)_23 is positive or negative. These two "qualitatively separated options" consistent with the data are known as the normal and inverted hierarchy, respectively. The absolute value of Δ(m²)_{23} is 0.0024 eV² or so. One more mass difference may be measured but the absolute additive shift of all mass² parameters is hard to measure and remains unknown because the oscillations are only affected by the differences. The known parameters are:

• sin² (2θ_13) = 0 or 0.08 or so
• sin² (2θ_23) = 1 or 0.95 or so
• sin² (2θ_12) = 0.86 or so
• Δ(CP) = 0; if it is large, one may get differences for neutrinos vs. antineutrinos (there is a normal CP-violating phase to deal with before you scream that you violate CPT!)
• Δ(m²)_12 = 0.00008 eV²
• Δ(m²)_23 = Δ(m²)_13 = 0.0024 eV²; the sign is unknown (hierarchy)
All the known oscillations measured so far depend on θ_{12} and θ_{23}. Moreover, it seems that θ_{23} is almost exactly 45 degrees - so its squared sine is nearly equal to one. This is the "maximum mixing" because a mixing by 90 degrees would already be nothing else than the exchange of the eigenvalues. The angle θ_{12} is also high so it doesn't make much sense to approximate the neutrino mass eigenstates by the flavor eigenstates - they're very different things.

Now, this 2010 preprint explains the T2K experiment, a long-baseline neutrino oscillation experiment in Japan using Super-Kamiokande. Today, the collaboration has released its results:
Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
In the T2K device, they detected 6 electron neutrinos created out of muon neutrinos. When they compared it with the lower predictions, they claim that this is a 2.5-sigma evidence that θ_{13} responsible for this enhancement is nonzero. Their preferred sin²(2.θ_{13}) is about 0.15 plus minus 0.1 or so.

It's not a terribly accurate or safe measurement so far but it may get better in the future. The today's paper may be viewed as the first reasonably robust experimental evidence with many authors - listed on the first 5 pages - that the angle is nonzero. Let me mention that their result - that sin²(2.θ_{13}) is higher than 0.03 at a high confidence level - directly contradicts PDG 2005 where exactly the opposite condition is stated above (13.30). So it's surely not a solid result yet.