What is the charge for the weak interaction?

[Superfluid universe]

We have the electric charge for the electromagnetic force, the color charge for the strong force. What is the charge for the weak force?

Thank you. :)

 

[Orodruin]

The SU(2)xU(1) of the electroweak interactions are spontaneously broken. The remaining symmetry is the U(1) of electromagnetic interactions coupling to a particular combination of the third component of weak isospin and hypercharge. The component orthogonal to this combination couples to the Z whereas the Ws couple different components of weak isospin.

 

[Superfluid universe]

Hey, Orodruin. Thanks for replying to me. So the charge from what I am getting is Weak isospin, right?

 

[Orodruin]

Hey, Orodruin. Thanks for replying to me. So the charge from what I am getting is Weak isospin, right?

No. Weak isospin is the SU(2) charge. What is typically called "weak interactions", i.e., interactions mediated by Z and Ws, are not the SU(2) gauge bosons (although the Ws are linear combinations of pure SU(2) gauge bosons). The Z is a linear combination of W³ and the hypercharge gauge bosons.

 

[Superfluid universe]

So it's a combination of third component of weak isospin and hypercharge.

 

[Superfluid universe]

Can I ask you, Orodruin, why is Color the charge for the strong force, and not Isospin? I think it's because Isospin is not a gauge symmetry?

 

[Orodruin]

Isospin is a subgroup of the flavour symmetry. This is not a gauge symmetry. Note that isospin is not the same thing as weak isospin.

 

[nikkkom]

We have the electric charge for the electromagnetic force, the color charge for the strong force. What is the charge for the weak force?

Electroweak interaction is actually two interactions, "weak isospin" interaction and "weak hypercharge" interaction, SU(2)*U(1). All "electroweakly interacting" particles have "charges" of one or both of these interactions.

Weak hypercharge interaction is simplest to understand: its structure analogous to electromagnetism. Particles have +/- weak hypercharge (see https://en.wikipedia.org/wiki/Weak_hypercharge for values). The mediating particle is a single, uncharged B boson.

Weak isospin is more complex. Analogously to SU(3) color interaction with three colors as charges, you can consider weak-isospin-interacting fermions as having two "weak colors": "up" and "down". Thus, left-handed neutrinos are "up" particles, and left-handed electron/muon/tau are "down" particles. Exchange of W+/- change their up/down-ness, similarly how exchange of gluons change color of quarks.
Just like color interaction, it is in fact not this simple: force-carrying particles do not carry a simple weak-isospin charge.

Right-handed fermions are not charged under weak isospin.