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Yes, parity is really violated, even if neutrinos are massive. You seem to be confusing the relationship between parity, helicity, and chirality in the modern standard model with the physical symmetry operation of spatial inversion. Wu's experiment did not measure neutrino helicity. Wu and collaborators prepared a thin layer of a beta-emitting nucleus ...

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Okay, I think I have an answer but I would interested to hear some feedback on this. I initially thought that by writing the left and right handed fields in 2 component notation ($q_L$ and $q_R^c$), they were 'equivalent' objects and can freely rotated between one another. However, I realized now this is not the case. The left and right handed fields are ...

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