How can we experimentally tell that neutrinos are EM neutral?

Question

Neutrinos are elementary particles, to our current knowledge they do have rest mass, but they are the lightest particles (with rest mass).

What we observe in neutrino experiments?

I do understand that they are EM neutral theoretically, but experimentally it is not obvious.

Neutrinos interact with oridnary matter weakly, so just detecting them is hard.

The mass of the neutrino is much smaller than that of the other known elementary particles.[1] The weak force has a very short range, the gravitational interaction is extremely weak, and neutrinos, as leptons, do not participate in the strong interaction. Thus, neutrinos typically pass through normal matter unimpeded and undetected.[2][3]

https://en.wikipedia.org/wiki/Neutrino

Now since they interact with ordinary matter weakly, and they travel as close as you can get to lightspeed, the only way to tell if they are EM neutral is if we tried to deflect them in a EM field, and they flew straight. But since even detecting them is hard, how can we tell whether they interact with an EM field, and get deflected or not?

Neutrinos can interact via the neutral current (involving the exchange of a Z boson) or charged current (involving the exchange of a W boson) weak interactions.

https://icecube.wisc.edu/outreach/neutrinos

The reason I am asking is because if the neutrino has very little rest mass, and flies near light speed, and only has a fraction of the elementary charge (like 10^-10e), that it weakly interacts with the EM field too, it could be hard to detect its charge (EM interaction) at all.

Question:

1. How can we experimentally tell whether the neutrino is EM neutral?

Answer 1

If neutrinos were charged, you could stop them with a thin sheet of aluminium or a few metres of air, like beta electrons with similar energies.

Answer 2

If neutrinos were charged, then beta decays (the problem whose solution required the proposal of the neutrino) wouldn't conserve electric charge.

If neutrinos were charged, they would emit Cherenkov radiation in matter. They don't. (But particles which are scattered by neutrinos do. The IceCube detector in Antarctica detects neutrinos by looking at Cherenkov radiation from their charged scattering products.)

Charged neutrinos would create a trail of electron-ion pairs in matter, by interacting with the strong electric fields inside of atoms. But they don't. A useful search term is "minimum-ionizing particle."

For most neutral particles, the Particle Data Group summary includes an upper limit on the magnitude of the charge, and an annotated bibliography for that limit. You should read the one for neutrinos.

Answer 3

[...] the only way to tell if they are EM neutral is if we tried to deflect them in a EM field, and they flew straight. But since even detecting them is hard, how can we tell whether they interact with an EM field, and get deflected or not?

Our detectors detect electromagnetic interactions directly. You wouldn’t try to detect the neutrino twice; you’d just detect the actual interaction. Reducing the charge doesn't affect the nature of these interactions, just the rate, so they continue to show up in standard detectors.

And there is, of course, a limit on the exclusion provided by null experimental measures. That fact is—in and of itself—vastly uninteresting. It only becomes interesting if you have a reason to wonder about the inaccessible range. Random spitballing doesn't generally count as "a reason".¹

Now, I have no idea what the currently available lower limits are, but the first scheme that comes to my mind for setting one is examining the up-down asymmetry of elastic-scattering rates in a large, low-background, imaging detector such as Super-K. In that measurement you are simply using the body of the Earth as an absorber and looking for rate reductions.² By setting a sufficient energy threshold for the measurement you can remove flavor considerations and thereby reduce your dependence on calculation of the matter effect. You do, however, have to disentangle the effects of weak interactions other than forward scattering and the theoretical uncertainty on that background probably sets the limits for the measurement.

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¹ By which I mean you won't get funding on that basis.

² In an earlier post I made an estimate of how much absorbtion to expect from Venus.