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I guess I am somewhat confused about all the neutrino press as of late that I'm afraid there are conflicting articles and although there are many related questions similar to mine my wording may be more to the point.

  1. Does the neutrino have a mass?

  2. and has it been measured experimentally? (At the LHC perhaps?)

  3. And related to this one must ask "Does the Standard Model of Particle physics require the neutrino to have no mass or is the neutrino mass one of those add hoc parameters added to the model in order to make it consistent with experimentation?

  4. And of course last but not least if it does have mass is the Higgs the mechanism by which this happens?

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    $\begingroup$ Effectively a duplicate of Speed of neutrinos, though since that question there has been a proposal to make a improved measurement of the beta-decay electron end-point energy (which is a very direct handle on the (mean) mass of the electron neutrino) or Why do neutrino oscillations imply nonzero neutrino masses? if you only want to know about the fact of neutrino mass rather than the value. And most of your secondary queries have also already been answered on the site. $\endgroup$ – dmckee Aug 12 '16 at 19:15
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Does the neutrino have a mass and has it been measured experimentally?

Neutrino oscillations have been observed, and this means that at least two of the flavors have a mass, if not all three, so in this sense the effect of the mass has been seen experimentally but only limits exist from measurements.

"Does the Standard Model of Particle physics require the neutrino to have no mass or is the neutrino mass one of those add hoc parameters added to the model in order to make it consistent with experimentation.?

The original standard model had zero mass neutrinos. The accepted one has modifications to allow for the observed neutrino oscillations, with very small masses for the neutrinos. In this sense the masses are ad hoc, since the original theory has to be modified.

And of course last but not least if it does have mass is the Higgs the mechanism by which this happens?

The Higgs field plays the usual role in inducing masses in the modified SM. Here is a review.

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Neutrino oscillations occur because the mass matrix, or PMNS or CKM matrix, is not diagonalizable with the Hamiltonian of the standard model. This results in the oscillations similar to the kaon oscillations Feynman discusses in the third volume of the Lectures on Physics.

The measurements are not made with the LHC but with the Kamiokande detector. Also the Tevatron has been configured to produce neutrino beams that reach detectors, called if I remember MiniBoon. This is where the neutrino oscillations have been detected. What this measures is the mass differences between the types of neutrinos. The actual masses of neutrinos is not well established.

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  • $\begingroup$ "The measurements are not made with the LHC but with the Kamiokande detector." And SNO and Homestake and KamLAND and OPERA and Daya Bay and ICE CUBE and Minos and... Super-K gets first billing because they had the first definitive evidence. SNO should get second billing for polishing off the question of solar neutrino mixing, but the story is long and involves a lot of evidence $\endgroup$ – dmckee Aug 13 '16 at 4:05

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