What is the charge for the weak interaction?

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Discussion Overview

The discussion revolves around the nature of the charge associated with the weak interaction, exploring its theoretical framework and comparison with other fundamental forces. Participants delve into concepts such as weak isospin and weak hypercharge, as well as the distinctions between these charges and those of the electromagnetic and strong forces.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that the charge for the weak interaction can be understood through weak isospin and weak hypercharge, which are part of the electroweak theory.
  • One participant clarifies that weak isospin is the SU(2) charge, while the weak interactions are mediated by the Z boson and W bosons, which are combinations of different gauge bosons.
  • Another participant notes that weak hypercharge is simpler to understand and is analogous to electric charge in electromagnetism, with particles having positive or negative weak hypercharge.
  • There is a discussion about the distinction between isospin and weak isospin, with some participants asserting that isospin is not a gauge symmetry.
  • One participant explains that weak isospin can be thought of in terms of "weak colors," similar to how color charge works in the strong force, but notes that this analogy has limitations.
  • It is mentioned that right-handed fermions do not carry weak isospin charge, which adds complexity to the understanding of weak interactions.

Areas of Agreement / Disagreement

Participants express differing views on the nature of weak charge, with some agreeing on the roles of weak isospin and weak hypercharge, while others highlight the complexities and distinctions between these concepts. The discussion remains unresolved regarding the precise characterization of the weak interaction charge.

Contextual Notes

Limitations include the potential misunderstanding of the relationship between weak isospin and weak hypercharge, as well as the implications of right-handed fermions not participating in weak isospin interactions. The discussion also reflects varying interpretations of the electroweak theory.

Superfluid universe
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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. :)
 
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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.
 
Hey, Orodruin. Thanks for replying to me. So the charge from what I am getting is Weak isospin, right?
 
Superfluid universe said:
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.
 
So it's a combination of third component of weak isospin and hypercharge.
 
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?
 
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.
 
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Superfluid universe said:
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.
 

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