# In neutrino oscillation experiment, what are the Feynman diagrams involved for the *detection of the neutrino* in the detector?

In neutrino oscillation experiment, for example NOvA [but it could be other if you prefer], what are the diagrams involved for the detection of the neutrino in the detector ?

I have explored inside many PhD theses to understand a bit, but none are very clear, and the authors seem not really to master the physics of the interaction at the detector (they seem to just copy/paste the explanation on the previous theses, etc.), and none are exhaustive for the involved interactions.

Here are the diagrams that I have created with jaxodraw and that is a synthesis of those diagrams that I found from various documents.

My question is : for detecting the resulting oscillated neutrino at the far distance detector :

-which of these diagrams (maybe there are additive ones ?) correspond to the signal ?

-which correspond to the background ?

In particular, do elastic scattering contribute to the signal ? (authors of PhD theses most often skip the purely elastic diagrams, for unknown reason)

Do neutral current contribute to the signal (for example elastic netural current)

By the way : QE=quasi elastic, RES=resonant production of pions, DIS=deep inelastic scattering, COH=coherent production of pions.

To start with, one has to keep in mind that detectors detect, by recording interactions in a medium. As neutrinos leave no track in the detectors, the final state neutrinos are useless for detecting. In principle, if the neutrino beam were mono-energetic, using conservation of energy and momentum one could fit for a missing neutrino, by just detecting the lower vertex outputs, $$Δ^{++}$$ or whatever it is, but neutrino masses are very small (only limits are known), so the energy balance even if possible would not give accurate enough four vectors to differentiate the masses

So what are the experiments for oscillations looking for:

They know the percentages of neutrino flavors in the beam, by construction of the beam

They go many kilometers away and measure the percentages of neutrino flavors, using detectors which are sensitive to electromagnetic scattering of the products of the neutrino interaction with the nuclei of the detector. The detector can record the momenta or energies of charged tracks, and thus identify an electron,a muon or a tau and from the numbers know the percentages of flavors that hit the detector. The difference between input and output flavor percentages show the oscillation.

-which of these diagrams (maybe there are additive ones ?) correspond to the signal ?

The signal is to see a lepton and determine its lepton number. This will identify that the incoming neutrino has a specific flavor, which is the objective of the experiment

which correspond to the background ?

the background will be the experimental misidentifications, no need for diagrams. One is not measureing a crossection.

In particular, do elastic scattering contribute to the signal ? (authors of PhD theses most often skip the purely elastic diagrams, for unknown reason)

As mentioned above neutrinos leave no track in detectors.

Do neutral current contribute to the signal (for example elastic netural current)

If the outgoing is a neutrino/antineutrino it cannot be seen in the detector.

• Thank you @anna v. I do understand that neutrino are not seen in detector and that we see only the leptons. So do I understand that all Feynman diagrams with a lepton in the final state are part of the signal ? Dec 24 '19 at 15:53
• For background, you deal with so-called reducible background, with a fake lepton. Are there irreducible background among those diagrams above ? (irreducible meaning with same final state as the signal). Also, in the elastic neutral current, there is indeed the neutrino, but there is also the electron, so somehow, I would think that since the electron would gain energy, this diagram would belong to the list of Feynman diagrams that allow identifying that a neutrino has interacted. Would you agree ? Dec 24 '19 at 15:53
• I have tried to explain that the experiment is not about the crossection (i.e. interactions as shown in your series of feynman diagrams) but that of identification of the flavor, i.e. if the interaction was of an electroon neutrino, muon neutrino ,or tau neutrino. This is uniquely identified by "seeing an electron, a muon, or a tau in the interactions in the detector. It is the relative numbers of the types that is measured, the percentage of each type to be contrasted with the input percentages, that is what oscillation means, a difference input versus output percentages. Dec 24 '19 at 17:58
• If you are asking about the lower diagram on the right, the answer is no, 1) it is a very improbable reaction , a neutrino to interact with an electron, the flavor of the neutrino cannot be known because it cannolbe detected, just an electron in the reaction gives no information about flavor of the incoming Dec 24 '19 at 20:04
• It is not enough to know a neutrino must have interacted. One needs to have a determination of the flavor of the outgoing, and since the outgoing does not interact one cannot learn the flavor Dec 24 '19 at 20:06