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Source

KATRIN weighs neutrinos produced by the nuclear decay of tritium, a radioactive isotope of hydrogen. When a tritium nucleus transmutes into a helium one, it ejects an electron and a neutrino (or, more accurately, a particle with an equal mass called an antineutrino). The neutrino is lost, but the electron is channelled into a 23-metre-long, steel vacuum chamber shaped like a Zeppelin airship, where its energy is measured precisely.

The electron carries almost all of the energy released during the tritium’s decay, but some is lost with the neutrino. The value of this shortfall can be used to calculate the particle’s mass.

This sounds like a straightforward particle physics homework problem. However, I don't see how to calculate the mass of the neutrino. If we know the energy of the tritium nucleus, the helium nucleus, and the electron, then conservation of energy gives a number for the energy of the neutrino. But then:

$E_{neutrino} = \gamma m c^2$

which still leaves two unknowns with only one equation - $v$ (contained in the Lorentz factor $\gamma$) and $m$. Neither can we approximate the neutrinos as moving at light speed - that would lead to an infinite Lorentz factor.

How does KATRIN measure the neutrino mass? If it is via the above analysis, what other equation does KATRIN use to solve for the two unknowns?

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It is an ingenious way of measuring the average momentum of electrons from the collective beta decays:

Therefore the spectrometer acts as an integrating high-energy pass filter.

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Varying the electrostatic retarding potential allows to measure the beta spectrum in an integrating mode.

So it is not just a simple formula.

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  • $\begingroup$ I looked at the link but it seems only to be measuring the energy of the electrons? How do you get from the energy of the electrons to the mass of the neutrino? $\endgroup$
    – Allure
    Feb 23, 2022 at 9:26
  • $\begingroup$ in general in particle physics experiments one uses all possible conservation laws, energy, momentum, angular momentum plus quantum number conservation according to the interactions, lepton number, baryon number ..to get a complete mathematically measurement for an interaction. they just use the average value as if it were one event, balancing momentum and energy. the first paragraph of the link describes this. $\endgroup$
    – anna v
    Feb 23, 2022 at 11:05

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