What is symmetry breaking in the Standard Model?

[friend]

I'm trying to figure out where symmetry breaking occurs in Feynman diagrams. I'm just free wheeling here, correct me where needed. But as I understand it, when you have a Feynman diagram where there is an interaction of one particle which decays to others, the incoming particle may obey one symmetry of the SM, but the outgoing particles may have a different symmetry of the SM (I can't think of an example at the moment). But that process of decay is an example of symmetry breaking, is this correct? Thank you.

 

[haushofer]

No. A symmetry means that you perform some action on the whole interaction (e.g., you rotate the physical process in space), without changing its outcome. You shouldn't apply symmetries at "separate parts of the interaction proces", I'm not even sure what that means!

Symmetry breaking appears at different levels in the SM. One example is the notion of "anomalies", in which quantization of the theory breaks symmetries. Sometimes this is bad (if you loose gauge invariance, e.g.), sometimes it's not (e.g., the axial vector current in QED is classically conserved, but not QMically).

Another example is spontaneous symmetry breaking, in which the groundstate of your theory breaks a symmetry of the theory. The Higgsmechanism is usually used for this, to give fermions and bosons their masses.

 

[Physics Monkey]

You won't see symmetry breaking in Feynman diagrams because they represent a perturbative expansion. A symmetry broken system is in a different phase from a symmetry unbroken system, and perturbation theory cannot reach from one phase to the other in flat space.

If you look at Feynman diagrams obtained from a symmetry breaking vacuuum, then you discover new Feynman rules which permit charge to simply disappear into the vacuum. This kind of Feynman diagram is called a tadpole and occurs because the vacuum contains a condensate of the relevant charge.

Hope this helps.

 

[friend]

OK, let's not use Feynman diagrams since they can involve virtual particles. Let's use a real example, say a decay process. Forgive my lack of experience here. You may have to supply a specific example. In the decay process you have a particle that complies with some symmetry group of the standard model, but after decay it breaks into particles that obey a different symmetry group. Would this be a "symmetry breaking" process?

 

[haushofer]

Can YOU give an explicit example? Once again, the notion of symmetry is applied to the theory, not to the "individual particles" which are excitaties of the fields of the theory.

For instance, a photon in QED can go into an elektron and positron. These are different representations of the same group (Lorentz group), and the theory exhibits gauge symmetry. These notions are, as far as I know, not applicable to the individual particles.

 

[friend]

I'm just trying to understand why some particles interact only with some other types of particles. The only thing I can think of is that particles belong to different symmetry groups, and that they decay to different particles that belong to different symmetry groups because there must be something different in the two symmetry groups that allow it. So if particles belonging to a symmetry group are suddenly replaced with particles belonging to a different symmetry, doesn't that sound like the symmetry of the first particle is broken?

For example, quarks can decay to W particles, and W particles can decay to electrons, but quarks do not decay to electrons, why?