# Is neutrino spin-parity 1/2+ or 1/2-?

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cairoliu
Wikipedia only tells neutrino spin 1/2, but no tell parity sign: positive or negative?

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Mentor
What do you mean by "parity sign"?

cairoliu
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.

Mentor
Because I know protons, neutron, electron all 1/2+ spin with positive sign of parity

Again, what do you mean by "positive sign of parity"? Please give a reference.

cairoliu
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?

cairoliu
Mentor
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.

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Also, in addition to what Peter said, what do you imagine that the parity transformation of a left-handed neutrino is?

cairoliu
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.

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No, I asked you what you thought the parity transformation of the left-handed neutrino is. Not what the left-handed neutrino is.

cairoliu
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.

cairoliu
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.
Last little confused:
"do not have a definite parity" means parity of neutrino could be +1 or -1 both possible?

Staff Emeritus
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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.

cairoliu
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.

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