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on page 13 I read that "the present plan is to provide nu_mu neutrinos with an energy between 5 and 30 GeV."

Wikipedia neutrino article says that neutrinos are electrically neutral.

What is the justification of giving a non-electrical particle the units of electricity?

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An electronvolt is a non-SI unit of energy, about $1.602 \times 10^{−19}$ joules, so a gigaelectronvolt is about $1.602 \times 10^{−10}$ J, and $5$ to $30$ GeV is a range of about $0.8$ to $4.8$ nanojoules (nJ).

Electrical charge does not come into this.

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One minor point that I don't think either Henry or Luboš Motl have made (though it's mentioned in the link Henry gave) - one electron volt is the energy gained by an electron as it moves through a potential difference of one volt. So it was originally defined in the context of electricity. However as both Henry and Luboš have said, it is just a unit of energy. You could just as well define it as the work done in applying a force of 1 Newton for 1.602 × 10$^{−19}$ metres, though I'm sure you'll agree this isn't as easy to remember!

The unit was first used by experimenters accelerating charged particles using an electrical potential, so it was a natural choice. As to why it's still used, well it turns out to be quite convenient. For example the electron mass is about half a MeV, the proton mass is about a GeV and we expect exciting new physics at about a TeV.

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The sentence about Wikipedia suggests that by "electricity", you mean the electrical charge.

However, GeV isn't a unit of the electric charge. It's a unit of energy; the usual macroscopic unit of the same quantity – energy – is 1 joule. It is something completely different than the electrical charge whose unit is 1 coulomb.

The neutrinos have charge $Q=0$ but energy $E\sim O(10)~$GeV. The rest mass is, by the way, also nonzero but much smaller than the equivalent of the energy, about $m_0\sim O(1)~$meV/$c^2$.

By the way, from the terminological viewpoint, the original title of this question "units of neutrino" is nonsensical. There may be units of physical quantities by neutrinos are not physical quantities.

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