I apologize that the posts are too disconnected—the original post has something of a table of contents to help unify everything. Also, if you might want to refer to my lecture notes which I based on these blog posts: http://www.lepp.cornell.edu/~pt267/undergradparticles.html

Otherwise, I’m doing the best that I can to contribute to the blog while doing research full time.

In the illustration for the down quark u_L should be replaced by d_L.
What does the asterisk * mean in the antiquark representation?
Some more detailed description of this subject would be welcome.

I am very impressed with your blog – keep up the good work.

I believe you have a typo (or the equivalent for a figure) – your down quark appears to have a component of a u_L (rather than d_R).

Best wishes,
Harry

Now for the gluons: indeed, 3*3 = 9, so there’s some quark–antiquark pair which does not couple to gluons. It turns out to be the quantum superposition: (red-antired + blue-antiblue + green-antigreen). The reason for this somewhat technical: the matrix of gluon couplings is traceless—this is sort of the “minimal” color structure for a force. In other words, I could have written a theory that has 9 generators, but such a theory is overkill to describe what we know about the strong force.

1. The polarizations refer to spin angular momentum. For a gauge boson (“vector” particle) with quantum spin 1, these spin angular momentum states correspond to the “polarizations” that you’re used to for light—though now I refer to individual quanta rather than a classical wave (e.g. a photon versus a beam of light). You can in principle measure this polarization by measuring the angular momentum of the system, though experimentally this can be tricky. (I think the other bloggers may have a much better answer to this than me!)

2. The portions of the W3 and B in the Z and the photon come in proportions that are dictated by the relative strength of their couplings. Before “electroweak symmetry breaking” (and you don’t need to worry about the details of what that term means), there are two distinct forces: the W force and the B force. After “electroweak symmetry breaking” the W and B forces mix up into the weak force (mediated by the W and Z) and electromagnetism (mediated by the photon).

The W and B forces have different couplings: for example, the W only talks to left-handed matter particles with some coupling strength determined by an overall number and some “group theoretical” factors. The B will talk to both left- and right-handed matter particles but with different coupling strengths. The Higgs talks to both the W and B, and when the Higgs obtains a “vacuum expectation value” (i.e. when “electroweak symmetry breaking” occurs), it mixes up the W and B according to its coupling strength to each.

So yes, there is a nice expression for the portion of W3 and B in the Z boson written in terms of the coupling strengths, and a nice explanation for where this expression comes from. This is another aspect that you would not have seen without writing down the “full” Standard Model instead of the “toy” version at the top of the post.

Great questions!
F

1. Why are the degrees of freedom of the W called polarisations? Can you actually build an experimental stage that acts as a polariser, or is it just an analogy for something else?

2. Do the portions of W3 and B shared in the Z boson and in the photon come in nice portions, like a small reduced fraction? Or is it a constant that should be explained with a deeper theory?