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Exactly what paper by W. Pauli introduced the idea for the existence of a neutrino and how was its existence confirmed experimentally (who did that and in what paper)?

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Pauli didn't publish the idea--- it seems to be in a private correspondence with Meitner, according to Wikipedia. Enrico Fermi named the particle and published the four-fermion interaction theory of beta decay in 1934, in this article:

E. Fermi "Versuch einer theorie der $\beta$-strahlen" I.Z. Physik 88,161 (1934)

I found a quick review of the history here:http://cdsweb.cern.ch/record/779702/files/CERN-ARCH-PBC-328-5.pdf (there are some confusing editing bloopers in the layout).

The detection of the neutrino is well documented on Wikipedia, because it won the detecting team the 1995 Nobel, and I don't have anything to add to that. The documentation on the earlier history is more scant.

The prehistory of this affair is Bohr's reluctance to accept energy conservation as fundamental. He thought of energy conservation as a thermodynamic statistical law in the 1920s, and was willing to throw it away in order to get quantum theory to make sense. One of the paradoxes of early quantum theory is that you can have a spread out quantum of light, which passes over many atoms. Then the photon must be absorbed by one and only one atom, by conservation of energy. But locality seems to imply that if an atom over here can absorb the photon, and an atom over there can absorb the photon, then if they cannot signal, they can both absorb the same photon. I am not sure that Bohr would have said it this way in 1924, I don't think he believed in photons yet. He would have talked about a classical electromagnetic field washing over many atoms, and the response going at the speed of light, but the absorption being quantum, so the energy cannot be conserved.

In modern quantum mechanics, this is not true, because you have a global wavefunction which means that the different atoms absorb the photon in different Everett branches, or, if you prefer, the absorption of the photon collapses the wavefunction nonlocally to prevent the absorption somewhere else. But in 1924, all this was two years in the future, and Kramers Bohr and Slater proposed that energy is just not conserved, and that atomic transitions are governed by something similar to a semiclassical electromagnetic field interacting with a quantum atom. This description only gives energy conservation on average, because the same electromagnetic field can dump energy into far away atoms at once, and in the semi-classical electromagnetic field approximation, you ignore the quantum structure of the field, so if the field represents a single photon, that single photon can be absorbed by different atoms. This is now interpreted as saying that single photons are not well described by a semiclassical field, but that wasn't BKS's interpretation.

Heisenberg's 1925 quantum theory put an end to BKS, and restored energy conservation. This was a major motivation for Heisenberg--- he knew he was on the right track when he realized that the interpreting energy as the Hamiltonian matrix makes energy conserved. Bohr was very unhappy with the fate of his theory, which really was the first coherent attempt at a description of photons and atoms, and deserved more recognition. It was attacked by Einstein, and it died even before Matrix mechanics. In Feynman's 1950's book on quantum electrodynamics, he shows how far you can take the semi-classical field idea, that you can reproduce all of quantum electrodynamics just from semi-classical fields interacting with particles, so long as at the end you understand that the semiclassical calculations are only guidelines for getting the proper Feynman rules for single photons. I think this type of presentation is descended from BKS (although it is quantum mechanically correct of course, and it is ab-initio, as was Feynman's way).

The detection and confirmation that the electrons in nuclear beta decay can come out with any energy less than the maximum possible, by Meitner and collborators, led Bohr to revive the earlier discredited statistical conservation of energy. This idea was now much less motivated than before, and Pauli decided that there is just something carrying away the extra energy.

Pauli had a publication aversion, for some reason, and tended to write things in letters. This is a great pity, because his published papers are so good. I couldn't find the neutrino letter online, and I don't read German anyway. The Fermi paper is probably the best source for the early ideas, but this theory is replaced by the V-A theory in the 1950s.

The paper I linked to suggests that Pauli didn't want to publish a four-Fermi theory because he knew that this theory would have terrible perturbation theory infinities. He does write that Fermi's theory leads to terrible infinities at higher order of perturbations, but this is a property shared by all quantum field theories in a non-covariant formalism.

Now we know that Fermi type theories are nonrenormalizable in 4d, but if you attribute this view to the 1930's Pauli, I think it is an anachronism. Even quantum electrodynamics is infinite at one loop, after all, and the order of the divergence was only established to be logarithmic by Weisskopf in the 1940s. In the 1930s, people weren't sure exactly how it blew up, but probably they expected a power law, like the self-energy in classical electrodynamics. The divergence in quantum electrodynamics is only softened to a log because of the contributions of positrons, and it is important to have a relativistically invariant formulation to know the exact divergence order, because you don't get the right answer if you separate positron and electron contributions.

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According to the German Wikipedia, the neutrino was first suggested by Pauli in a private letter on December 4th 1930. The Letter is available in the CERN archives, although, unfortunately, it is in German. A link to the PDF is here.

The first paragraph basically mentions that in order to explain the continuous spectrum of beta decay, Pauli suggests the existence of a neutral spin 1/2 particle obeying the exclusion principle inside the nucleus. He calls the particle "neutron" and according to him, it should roughly have the same mass as the electron, but certainly not higher than 1% of the proton mass. Later he mentions that this may seem like a cheap trick to explain the spectrum, but in such desperate times one should examine all possible solutions to a problem. Wikipedia does not give any source as to wether this really is the first suggestion of the existence of the neutrino.

Again, according to Wikipedia, in 1956 Cowan and Reines confirmed the existence of a particle with the right properties. They published their result in 'Science' and the paper is available for free here.

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