# Neutrinos at the OPERA experiment

The probability that a neutrino oscillates from a species $a$ to a species $b$ is given by

$$P(a \to b) = \sin^2 (2 \theta_{ab}) \sin^2 \left( 1.27 \frac{\Delta m^2 L}{E_\nu} \right)$$

Which means that the minimum distance $L$ that maximizes neutrino oscillation is

$$L = \frac{E_\nu}{1.27 \Delta m^2 (\pi/2)}$$

For a neutrino beam with energy $E_\nu$, the distance at which the detector should be placed is $L$, where the probability that the neutrino changed flavour is maximum.

Here's what I don't understand - the experiment OPERA, which operated under $E_\nu = 17 \, GeV$, has $L \approx 8500$ km, considering oscillations $\nu_\mu \to \nu_\tau$. But, of course, the detector was at a much smaller distance to the beam than this, at 730 km. Why this distance with this beam energy, then? The T2K experiment, for instance, has $L \approx 300$ km, and the distance between the beam and the detector was 295 km. These distances are close to each other, but that doesn't happen for the OPERA experiment.

• It was probably a compromise so as not to have to build a neutrino detector further away than the radius of the Earth. – probably_someone Jan 17 '18 at 18:17
• Why not lower the energy, then? 17 GeV is quite above tau production, which has a mass around 1.8 GeV. For a lower energy, the distance for which the probability is maximum would also be lower. I don't see the reason for working with 17 GeV... – Sth99 Jan 17 '18 at 18:23
• The experiment's sensitivity to anomalous CP violation is a function of neutrino energy, so it might be because of that. – probably_someone Jan 17 '18 at 18:26
• "17 GeV is quite above tau production" That would be true in center of momentum kinematics, but this is fixed target kinematics. Many people are surprised by how much higher (than the mass of the desired product) the threshold energy for fixed target kinematics can be. (This is the fundamental 'Why?" of bothering with expensive and difficult colliders in the first place.) – dmckee Jan 17 '18 at 20:21