DOE’s Fermilab has switched on its newly upgraded neutrino beam. This is in preparation for the NOvA experiment, which will study neutrinos using a 200-ton particle detector at Fermilab and a 14,000-ton detector in northern Minnesota. Story here.
This experiment is to test "flavor changes" in neutrinos. What does current theory predict in terms of flavor changes? Ie. does a electron neutrino change to a muon neutrino every so many milliseconds?
You may check the Wikipedia page for neutrino oscillations
where you may also find the derivation of the formula for the neutrino oscillations in the case of two flavors (in which case the oscillations are harmonic and simple)
$$ P_{\alpha\rightarrow\beta, \alpha\neq\beta} = \sin^{2}(2\theta)\, \sin^{2} \left(\frac{\Delta m^2 L}{4E}\right)\quad \mathrm{(natural\,units)} $$
Numerically, in SI units, that is
$$ P_{\alpha\rightarrow\beta, \alpha\neq\beta} = \sin^{2}(2\theta) \, \sin^{2}\left( 1.267 \frac{\Delta m^2 L}{E} \frac{\rm GeV}{\rm eV^{2}\,\rm km}\right). $$
You may see that the probability depends on the length $L$ in kilometers – you may write $L=ct$ using the time $t$ as well, if you wish, $c$ is the speed of light (their speed is undetectably different from $c$). However, the frequency also depends on the neutrino energy $E$ expressed in ${\rm GeV}$ above.
The factor $\Delta m^2$ is the difference between the eigenvalues of $m^2$. For the three species, these are $$\Delta m_{12}^2 = 7.59\times 10^{-5} {\rm eV}^2$$ $$\Delta m_{32}^2 \approx \Delta m_{13}^2 = 2.32 \times 10^{-3}{\rm eV}^2$$ Two of the neutrino mass eigenvalues are very close to each other. This results in very slow oscillations (solar oscillations, $12$). The remaining third eigenvalue is further from them and it results in faster oscillations (seen in atmospheric oscillations, $23$).
At any rate, the units in the formula above are designed so that $E$ is of order one (i.e. GeV). Because $\Delta m^2$ is 3-5 orders of magnitudes smaller than 1, $L$ of the wavelength is of order between thousands and millions of kilometers which translates roughly to something between milliseconds and seconds. You may calculate the precise frequency for yourself – the periodicity is proportional to the neutrino energy.
Most of these things have been known for a few decades. What was observed in the last year was a matrix element that allows the $13$ transmutation "directly". The previous solar and atmospheric oscillations de facto measured the angles and mass differences $12$ and $23$ only. The accuracy of all the parameters is rather close to one percent these days.
