Daya Bay experiment just announced the measurement of one of the last unknown fundamental parameters in the Standard Model (understood as the old Standard Model extended by the neutrino mass operators). The parameter is called the theta13 mixing angle and, roughly speaking, controls the oscillation probability of electron neutrinos. One way it could manifest itself is via appearance of electron neutrinos in a beam of muon neutrinos sent over several hundred kilometers. Another possible manifestation is via oscillation of electron neutrinos into the other flavors over a distance of a few hundred meters. More precisely, the survival probability of an electron neutrino with the energy E at the distance L from the source is given by
where Δm31 is approximately equal to the "atmospheric mass difference" known to be of order 0.05 eV.There is no theoretical reason for theta13 to be zero, however it is known to be a bit smaller than the other two neutrino mixing angles (who are known quite precisely). Several experiments have been racing to measure it: T2K in Japan, Minos in the US, Double Chooz in France, RENO in South Korea, and Daya Bay in China. Recently, there has been a few experimental hints that the value is about 10 degrees, although none of the experiments could by itself present a 3 sigma evidence.
Now it seems the first prize has been snatched by the Chinese. Daya Bay looks for disappearance of electron antineutrinos produced in nuclear reactors (if an electron neutrino transforms into other flavors it cannot be detected by this experiment, so effectively it "disappears"). Comparing the observed flux in near (~500 m) detectors and a far (~1500m) detector they conclude that about 6% of the electron neutrinos disappear in between. Based on that they quote the value of the mixing angle
or theta13 ≈ 9 degrees in more familiar units. This result suggests that neutrinos are anarchists. Unlike the quark mixing angles that display a highly hierarchical structure, the neutrino mixing angles are of similar magnitude and apparently random. The deeper reason for either of these 2 facts is currently a mystery...So the last thing we don't know about the Standard Model is the absolute scale of the neutrino masses, and the CP violating phase in the neutrino mixing matrix. We'll probably learn those too before the end of the century.
16 comments:
... the neutrino mixing angles appear to be random with no clear structures.
Hmm. I see theta12 + theta13 = theta23 if I squint hard enough. Or is this just numerology?
" ... by the end of the century".
I hope you're not unduely pessimistic. I can't wait that long.
It is numerology, I doubt you can find a model predicting that. Although I don't doubt that, once theta13 has been measured, there will be 100 papers claiming that the value is exactly what author's favorite model predicts.
Martin, don't worry, immortality is almost at hand.
Smirnov (and no doubt others) pointed out some years ago that the following roughly holds:
theta12 + CKM12 = pi/4
theta23 + CKM23 = pi/4
leaving theta13 as a match to the small CKM angle, which of course is non zero. Congratulations to Daya Bay for bringing neutrino mixing into the modern era!
Jester,
If standard model neutrinos get their masses through some sort of seesaw mechanism with a sterile neutrino at ~ GUT scale, would you expect the mixing angles to be similar?
I think both logical possibilities -- hierarchical or structureless mixing angles -- are perfectly consistent with the see-saw mechanism. Depends e.g. whether or not the Yukawa couplings of the neutrinos obey some additional symmetries.
My favorite prediction for large neutrino angles: “Neutrino mass anarchy” L.J. Hall, H. Murayama, and N. Weiner, Phys. ReV. Lett. 84, 2572 (2000)
http://arxiv.org/abs/hep-ph/9911341
Would Opera have found this if they hadn't been distracted?
No, OPERA was looking for nu_mu to nu_tau transitions which are practically independent of the theta13 angle.
Is there a short way to describe what theta13 "means"? I gather it's not directly related to the probability of electron neutrino to tau neutrino oscillation, or is it? The way it's presented suggests sin^2(2 theta13) is the probability of electron neutrino oscillation to either of the other flavors. Also, how can delta (CP violating phase) be described?
At the phenomenological level, theta13 > 0 make possible short-baseline (~1km) oscillations of the electron neutrino into others, and long baseline (~100km) oscillation of the muon neutrino into the electron one. At a more rigorous level it's a tad more complicated, maybe I'll try to write an explanatory post one day. Delta > 0 would mean CP violation, for example the probability of the electron *neutrino* turning into the muon neutrino could be slightly different than that of the electron *antineutrino* turning into the muon antineutrino.
The sensitivity obtained looks like it is about a year behind the scheduled performance of the experiment as of 2007 (see page 20).
@Daney Basically, sine squared two theta13 and the CP violating phase of the PMNS matrix show up in the same term of the PMNS matrix used to figure out how many missing neutrinos to expect. Since theta13 also shows up in a separate cosine theta13 term without a CP violating phase in it that contributes to interactions, if you can pin down everything else in the equation with sufficient precision (which should definitely be possible sometime before 1% precision for theta13 is reached for values of theata13 more than two degrees), in is possible to infer the CP violating phase as well. In generally, the larger the value of theta13, the less precision you need to get a meaningful experimental measurement of the CP violating phase. Since theta13 is looking like it is about 9 degrees, it should be possible to get an experimental value of the CP violating phase with quite a bit less precision than 1%, although the lack of a pressure release claiming CP violation is detected suggests that the current 20% precision is not sufficient.
Given the projected curve of experiment duration to precision and how far along the reported results are now, I'd expect to see a measurement of the CP violating phase from Daya Bay sometime between late 2012 and late 2014, barring the kind of experimental mishap that neutrino experiments seem to have such a fine knack for producing.
"So the last thing we don't know about the Standard Model is the absolute scale of the neutrino masses, and the CP violating phase in the neutrino mixing matrix...."
Hi Jester,
I think you missed out the strong CP phase that can be measured by neutron electric dipole moment experiments. Predictions for it and also on relation between
strong and weak CP phases: http://xxx.lanl.gov/pdf/1203.2772v1.pdf
Ravi
@Andrew Oh-Willeke
In disappearance experiments (Daya Bay, RENO, Double Chooz) you are not sensitive to the CP violating phase.
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