Feynman diagram of how Z is produced at LHC, and info?

[knut-o]

Homework Statement

So, I got this task, which I feel either really dumb, or nobody is able to explain:
I got this question:
Z and W was discovered in 1973 at CERN, how were they produced? Include Feynman diagram and a short description.

Then there is this question: How is the Z and W produced at LHC:
Feynman diagram and short description.

The Attempt at a Solution

So, I have litterly searched for many hours and have only gotten to the point that there is proton-anti proton collision. And that makes the W by up-quark going to down-quark, and other way around.. Or a collision between quark and anti-quark. And some mentioned gluon-gluon making a top, anti-top which emitted W+ and W- going to bottom and anti-bottom.

That is litterly everything I have found related to Z and W and how they are produced. If this is enough information, or not, I have no idea. Doesn't tell me anything, and what about Z? Saying that "it's the result of proton anti-proton collision" isn't really sufficient.

And if it was proton anti-proton in 1973, and it still is, is there any difference? I feel like a retard reading about this.

Edit: It was actually that simple, at least for the W-boson. The Z is still just abstracts to me.

 

[fzero]

The LHC is a proton-proton collider, so quark-antiquark collisions are extremely rare. Most of the collisions are quark-gluon or gluon-gluon. In any case, you should review what types of vertices that the Z is involved with. The Feynman diagrams you want will be formed by sewing that vertex to a collision vertex.

 

[knut-o]

I am familiar with Feynman-diagrams, at least to the degree where it sort of makes somewhat sense.

The problem is that I have large issues understanding the Z-boson, works. I only found a few pictures where it's a Feynman-diagram of two leptons (electrons) that become a Z that after that becomes two leptons again. I have understood that Z is it it's own antiparticle, but really. It doesn't tell me much.
Every site I have looked at, just mentions it's created in proton anti-proton collisions, and that's about it..

And considering some of the questions is based on the history of CERN, I guess it's fair to assume it's been proton anti-proton collisions all along? Just higher energy-levels in LHC (which shows up as the Z' sometimes)?

This is litterly greek to me.edit: Wait a second, hold the phone etc . Does Z suddenly gets emitted from a lepton or quark, and can also randomly be absorbed by a lepton or quark? Or it can decay into a lepton+anti-lepton, quark+anti-quark (jets?) or neutrino+anti-neutrino? But how does proton+anti-proton do this? 1 proton and 1 anti-proton makes 3 Z's?
Can I think of Z as an analogue to the photon in some degree? Other then the fact they are force-carriers in two different "forces".

 

[fzero]

I am familiar with Feynman-diagrams, at least to the degree where it sort of makes somewhat sense.

The problem is that I have large issues understanding the Z-boson, works. I only found a few pictures where it's a Feynman-diagram of two leptons (electrons) that become a Z that after that becomes two leptons again. I have understood that Z is it it's own antiparticle, but really. It doesn't tell me much.
Every site I have looked at, just mentions it's created in proton anti-proton collisions, and that's about it..

The Z particle is a massive version of a photon. Where the photon couples to the electromagnetic current (in diagrams, a particle-antiparticle pair), the Z couples to a linear combination of the electromagnetic coupling and the weak isospin current. The weak isospin current also corresponds to particle-antiparticle pairs, but also involve pairs that are electrically neutral, like neutrinos. So it turns out that for any diagram involving a photon, there is another diagram where the photon is replaced by a Z. To actually compute the amplitude for the diagram, one needs to take the differences into account, like the Z coupling and massive propagator. There will also be similar diagrams coupling neutrino-antineutrinos to the Z, but these can be ignored for your production question.

And considering some of the questions is based on the history of CERN, I guess it's fair to assume it's been proton anti-proton collisions all along? Just higher energy-levels in LHC (which shows up as the Z' sometimes)?

This is litterly greek to me.

There's probably a good reference at the CERN website or wikipedia, but in 1984 when the W and Z were discovered, CERN was operating the Super Proton Synchrotron (SPS) as a $$p\bar{p}$$ collider. Later on, the SPS was used as an injector for the Large Electron-Positron Collider (LEP), which, as is clear from the name, was an $$e^-e^+$$ collider. SPS is now used as an injector for the LHC, which as I said before is configured to collide $$pp$$ rather than $$p\bar{p}$$.

The Z' is still hypothetical. The signal reported last week is not strong enough to claim discovery of a new particle, so it will likely take several months before further analysis can make a confirmation of new physics or just noise.

 

[knut-o]

So, does that mean that the Z, in 1983 was produced with annihilation of the proton and anti-proton? Because that gives two photons, but considering the energies, isn't there possible that some of them (enough to measure) was Z's? And the W⁺'s were then produced when a anti-down "collides" with an up and W^- is when anti-up collides with down?
And with proton-proton, one of the protons can become a neutron by interacting with a gluon and change from up to down and emit a W+, and this neutron can go back to proton and emit a W-?

But the Z is weird. It seems like no pages tries to explain it :p . They can give a long lecture about the W-boson, but the Z is just mentioned as some third wheel.If I am fairly correct, that would be kind of cool.
But sleepytime, my brain hurts from this.

 

[fzero]

So, does that mean that the Z, in 1983 was produced with annihilation of the proton and anti-proton?

Collisions in a $$p\bar{p}$$ collider almost never involve total annihilation of the proton and antiproton. Generally only a single quark or gluon in either initial particle actually collides.

Because that gives two photons, but considering the energies, isn't there possible that some of them (enough to measure) was Z's? And the W⁺'s were then produced when a anti-down "collides" with an up and W^- is when anti-up collides with down?

Yes, you can have the processes $$u + \bar{d} \rightarrow W^+$$ and $$\bar{u} + d \rightarrow W^-$$. We can also have $$u + \bar{u} \rightarrow \gamma$$ or $$u + \bar{u} \rightarrow Z$$, and similarly for $$d+\bar{d}$$.

And with proton-proton, one of the protons can become a neutron by interacting with a gluon and change from up to down and emit a W+, and this neutron can go back to proton and emit a W-?

No, it is impossible for a gluon to change the flavor of a quark. The gluon is associated with a completely separate color quantum number.

What we can actually do to figure this out is note that we can take a reaction like $$u + \bar{d} \rightarrow W^+$$ and note that the same interaction also gives the reaction
$$u \rightarrow d+W^+$$ by replacing the anti-d in the inital state with a d in the final state. The way to interpret this is by noting that the mass of the W is much larger than that of the u, so the u must be in a very energetic state. This state can be created by colliding the u with a gluon, so we can extend the reaction to

$$u +g \rightarrow u^* \rightarrow d+W^+$$

The intermediate state $$u^*$$ denotes the energetic intermediate state. It should be obvious how to write down the corresponding Feynman diagram.

Similarly, since $$u + \bar{u} \rightarrow Z$$ we can also have $$u^* \rightarrow u + Z$$. Namely an energetic $$u$$ sheds some kinetic energy by emitting a Z. It shouldn't be to hard to figure out how to incorporate this into a Feynman diagram.