Wikipedia only tells neutrino spin 1/2, but no tell parity sign: positive or negative?
What do you mean by "parity sign"?
Because I know protons, neutron, electron all 1/2+ spin with positive sign of parity, but only know neutrino 1/2 spin.
Again, what do you mean by "positive sign of parity"? Please give a reference.
Jπ always comes together, if Jπ = 1/2+, it means spin = 1/2, parity = +1.
I need know neutrino's Jπ, 1/2+ or 1/2- ? At least J = 1/2 is sure, but π = +1 or -1?
Ok, then the answer is that neutrinos do not have a definite parity, since neutrinos only interact via weak interactions and weak interactions do not conserve parity.
Also, in addition to what Peter said, what do you imagine that the parity transformation of a left-handed neutrino is?
I imagine it as left hand ruled direction of angular momentum vector. right or wrong?
Anyway momentum conserves.
No, I asked you what you thought the parity transformation of the left-handed neutrino is. Not what the left-handed neutrino is.
Sorry, no idea, please teach me.
For the neutron decay: n -> p + e + anti-neutrino
If parity of anti-neutrino = +1, then left = +1 = right = (+1)*(+1)*(+1) = +1.
But parity not conserved in beta decay weak interaction, then it seems the parity of anti-neutrino = -1, then left not equal right. Just confused.
Thanks for your answer.
Last little confused:
"do not have a definite parity" means parity of neutrino could be +1 or -1 both possible?
It means that it does not make sense to talk about the parity of a neutrino in the way you are imagining. Weak charged current interactions only couple to left-handed particles, which break parity maximally. There are no right-handed neutrinos in the standard model.
I like to think symbolically and mathematically, and let equation itself tell whether parity conserve. Therefore if there is a value for neutrino parity, then beta decay equation can mathematically show non-conservation of parity, not by fuzzy words.
There is nothing about fuzzy words in the standard model. It is a well defined theory. That you do not understand that some concepts that you have learned previously are not applicable to weak decays does not mean that weak decays are non-mathematical.
The equations governing the weak interactions of neutrinos are easily found in textbooks or online.
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