# Role of the ratio L/E in neutrino experiments

Why is it that the neutrino experiments are designed by keeping constraints on the energy E of the neutrinos and the length L which they travel from the source to the detector. What decides actually the ratio $L/E$ for a neutrino experiment? To be more specific, for example, why is it that NO$\nu$A experiment operates with $E \approx 2$ GeV (corresponding to the maximum neutrino flux and length $L=810$ Km. The T2K experiment uses $E\approx1$ GeV and $L\approx2$ Km.

Are these experiments designed with some specific aims? If so, how is this ration ($L/E$) going to be so important a factor?

• Well, the energy of the source and the distance from source to detector are what decides $L/E$, obviously, but I suspect that isn't what you are actually asking. Is this perhaps a question on the design of experiments? But that is complicated by the question of what sources are available, what detectors (or detector sites) are available, what is already know at the time of the design and as always by money, money, money. Perhaps you could be more specific. – dmckee Oct 5 '17 at 18:39

The phase of the oscillation is proportional to $\Delta m^2\frac{L}{E}$. For the two experiments you quote, neutrinos are produced by dumping a proton beam into a target to produce pions/kaons and use their decay to produce neutrinos. Thus, experimentalists can play with that setup to vary $E$ and independently choose $L$ before hand, so that they can target the range of $\Delta m^2$ of interest.