Theta-one-three

I have been feeling dizzy all this week and I blame it on the neutrino flux. It happens to be more intense than ever - within 7 days there were 4 neutrino seminars here at CERN. I could not help but learn something about the quest for $\theta_{13}$ from the Thursday seminar by Silvia Pascoli.

Neutrino physics is the only branch of particle physics that can boast of a discovery in the last twenty years (the top quark, some may say, but that was as unexpected as election results in the former Soviet Union). The experimental progress in the last decade has been really impressive. Since the 1998 discovery of neutrino oscillations we have acquired a great deal of data concerning the neutrino masses and mixings. Yet from a theorist's perspective neutrinos are boring. It all amounts to a 3-by-3 unitary matrix that relates flavour eigenstates to mass eigenstates. The matrix is called the MNS matrix and looks like this

As usual, a 3-by-3 unitary matrix has three angles and three phases. Two of these angles were pinpointed by numerous observations of solar and atmospheric neutrino oscillations, as well as by reactor and accelerator experiments. The last angle, the notorious $\theta_{13}$, remains elusive and we only know the upper bound of 12 degrees. The other two angles are much larger than that, which gives hope to the experimenters that the last one is just behind the corner. So, while cosmologists are studying such sexy matters like dark matter or dark energy, the neutrino community is struggling to measure an angle.

One way to measure $\theta_{13}$ is by observing oscillations of muon neutrinos into electron neutrinos. The probability of this process is sensitive $ \sin^2 (2 \theta_{13})$,
$P(\nu_\mu -> \nu_e) = \sin^2 \theta_{23} \sin^2 (2 \theta_{13}) \sin^2 (\Delta m_{13}^2 L/2 E)$.
At the moment, there is an ongoing search for electron neutrino appearance by the Minos experiment that shoots the beam of muon neutrinos from Fermilab to a detector in Soudan mines in Minnesota. This one is however not designed specifically for that search and no great improvement in sensitivity should be expected. In near future (2009-ish) starts another accelerator experiment called T2K (Tokai to Kamioka in Japan, where else) whose sensitivity to $\sin^2 (2 \theta_{13})$ will reach 0.01, (or 3 degrees after some complicated trigonometry). In parallel, there are reactor experiments in preparation, who will play with anti-neutrinos that escape from nuclear reactors and pollute the air. The strategy is to put two detectors close to a reactor and look for disappearance of electron anti-neutrinos on the way between the two. The next reactor experiment to start is Double Chooz, the continuation of the Chooz experiment who already put a bound on $\theta_{13}$ in the past. The Chinese also enter the race with their Daya Bay experiment. These two reactor experiments will have a similar sensitivity to $\theta_{13}$ as T2K.

The measurement of the angle $\theta_{13}$ is very important because it will open the way to measure another angle. More precisely, the CP violating phase $\delta$ in the MNS matrix. The point is that CP violating effects, that is differences in oscillation patterns between neutrinos and antineutrinos, are proportional to $\sin \delta$ but also to $\sin \theta_{13}$. If the latter is large enough, the future superbeams, beta-beams or neutrino factories may discover CP violation in the leptonic sector.

In summary, the future looks bright and gay for neutrinos, as on the picture below


No slides available.