# Can neutrinos be produced/detected incoherently?

In the wave-packet approach, different neutrino mass eigenstates have different mass and thus
propagate with different speeds. This will eventually lead to wave-packet separation and decoherence. My question is, can neutrinos be produced/detected incoherently? (In other words,
can different neutrino mass eigenstates be produced/detected incoherently?) If they cannot, it should in principle be possible to have wave-packets sufficiently separated so that neutrinos become undetectable during the interaction time interval available in a detector.

## Answers and Replies

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Orodruin
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My question is, can neutrinos be produced/detected incoherently?
What do you mean by incoherently here? Assuming you just mean "can the separated wave packets be detected?", then yes, they can. They will interact with their corresponding probabilities of being in a particular flavor state. The corresponding thing in the quark sector happens all the time in charged current weak interactions.

What do you mean by incoherently here?
Produced/detected incoherently: produced/detected as separate mass eigenstates with no interference from different mass eigenstates. (See arXiv:0905.1903)
Assuming you just mean "can the separated wave packets be detected?", then yes, they can. They will interact with their corresponding probabilities of being in a particular flavor state.
Thank you. Do you have a reference to experiments where neutrinos are produced/detected incoherently?

Orodruin
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Do you have a reference to experiments where neutrinos are produced/detected incoherently?
You cannot tell this on an event basis. You need to do statistics and see how the transition probability behaves. For solar neutrinos, the mass eigenstates generally decohere before reaching the Earth.

mfb
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While we get separate mass eigenstates, we cannot measure mass eigenstates - we have to observe neutrinos via their weak interaction, so we always see weak eigenstates.

ChrisVer
You cannot tell this on an event basis. You need to do statistics and see how the transition probability behaves.
Sure, statistical evidence for incoherent neutrino detection would be fine. Does this exist?
For solar neutrinos, the mass eigenstates generally decohere before reaching the Earth.
But for solar neutrinos, the wave-packet separation is so small that coherence is restored in the detector during the detection process. Thus the detection of solar neutrinos is in itself not evidence for incoherent neutrino detection.

A simple estimate shows this: the speed difference between two mass eigenstates is, for ultrarelativistic neutrinos, Δvij=c/(2E)Δmij2c4. With Δm322=2.4×10-3 eV2, this yields Δv32≈10-6 - 10-5 m/s for neutrinos in the interval 150 keV to 500 keV. For solar neutrinos, this corresponds to a time lag of Δt32≈10-12 - 10-11 seconds for the most massive neutrino eigenstate compared to lightest one. Furthermore, a neutrino mass of about 0.05 eV corresponds to a gamma factor in the interval 106 - 107 for neutrinos in said energy interval. Therefore, solar neutrino detection is evidence for incoherent neutrino detection only if the interaction time in the detector is Δτweak≈10-19 seconds or less, which is unrealistic.

While we get separate mass eigenstates, we cannot measure mass eigenstates - we have to observe neutrinos via their weak interaction, so we always see weak eigenstates.
Yes, but the question was if these weak eigenstates can be produced incoherently, i.e., from e.g. only one mass eigenstate without interference from other mass eigenstates. As Orodruin said in #2, this is certainly possible in theory, but does it have experimental support?

Orodruin
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But for solar neutrinos, the wave-packet separation is so small that coherence is restored in the detector during the detection process.
No, this is incorrect.
See http://dx.doi.org/10.1088/1126-6708/1999/08/018
The wave packet size computation is based on both creation and detection processes.

That being said, the incoherent state is indistinguishable from the effects of observing neutrinos at different energies and at different path lengths.

vanhees71 and mfb