Do All Fermions Have Negative Parity?

[benbenny]

Im trying to understand parity in the Standard Model.
Ive read that quarks have positive parity. However I thought that the reason electrons have negative parity is because of the a symmetry of their wave functions, and this is what defines them as fermions. Quarks are fermions as well as I understand - hence my confusion. Shouldn't all fermion have negative parity?

Thanks,

B

 

[diazona]

You're mixing up two different kinds of antisymmetry. Basically, fermions are - by definition - antisymmetric under wavefunction exchange, which means that if you have two fermions, represented by states ψ(x) and φ(y), then ψ(x)φ(y) = -φ(y)ψ(x). But odd parity is something different. It applies to a single particle and says that if you reverse all the space coordinates, the wavefunction switches sign. So ψ(x) = -ψ(-x).

 

[benbenny]

You're mixing up two different kinds of antisymmetry. Basically, fermions are - by definition - antisymmetric under wavefunction exchange, which means that if you have two fermions, represented by states ψ(x) and φ(y), then ψ(x)φ(y) = -φ(y)ψ(x). But odd parity is something different. It applies to a single particle and says that if you reverse all the space coordinates, the wavefunction switches sign. So ψ(x) = -ψ(-x).

And this is basically determined by experiment for different particles?

Thanks.

 

[diazona]

Yeah, pretty much, although certain aspects of it are chosen by convention (when the experiments can't determine something). Wikipedia's article on parity might be an interesting read.

 

[benbenny]

thanks

 

[turin]

The intrinsic parity of a single particle is a convention. However, when treating more than one particle, the relative intrinsic parities can be determined experimentally. In particular, an electron must have an odd intrinsic parity relative to a positron, but the phase factor of the parity transformation of the electron field (which includes a positron part) is arbitrary (to an extent). Also, because the electron-positron pair has an odd intrinsic parity, the photon must have itself an odd intrinsic parity.

 

[benbenny]

hmmmm

I read about the Wu experiment with the cobalt 60 carbon molecule decaying and emitting an electrons in the opposite direction of its spin. I don't understand why this is evidence for parity violations. It seems that if you mirror this experiment you will get the same image in the mirror with both the direction of spin and the direction of emitted electrons reversed.

 

[diazona]

Think about literally reflecting the experiment in a mirror. That's a parity transformation. If the spin axis is parallel to the mirror, the particle and its mirror image will be spinning in opposite directions, but the direction of emission of the electron will not be changed. Now, if you rotate that situation by 180° around an axis parallel to the mirror, you wind up with a mirror particle with the same spin as the original one, but the electron getting emitted in the opposite direction.

If beta decay were parity-invariant, you should get the original situation and the mirror-image situation happening with equal frequency. And it's well known that physics is rotationally invariant, so parity invariance would mean that you'd get the original situation and the reflected, rotated situation happening with equal frequency. But in the Wu experiment, they didn't happen with equal frequency; in fact, almost all the decays observed had the electron coming out in one particular direction with respect to the spin. So that means that the process can't be parity-invariant.