How do I calculate the cross section for a p p -> Z -> μμ process?

[stefanos.leon]

Hi all.

This is my first time in the Physics Forums.

I would like to ask for guidance in a calculation of a cross section of a process. I know the Feynman graph but I'm completely lost on how to start the calculation..

For example..

p p -> Z -> μμ

Many thanks in advance..

 

[fzero]

Have you studied quantum field theory? Assuming you mean proton-proton in the initial state (and muon-antimuon in the final state), there are no tree-level diagrams for this process. The leading contribution is probably from gluon-gluon fusion and you'd need to know something about hadronic form factors to say anything meaningful with respect to proton-proton collisions.

I'm not trying to be too dismissive, but if you want to learn how to go from a Feynman diagram to an amplitude to a cross section, you should start with a simpler example and a QFT text. The posters here can be helpful at answering specific questions you might have that will come up along the way, but it's not very likely that a discussion forum is going to substitute for starting with the traditional learning sources.

 

[jtbell]

In this case, a process like $e^+ e^- \rightarrow Z^0 \rightarrow \mu^+ \mu^-$ would definitely be easier to calculate. Unfortunately it's been a long time since I did anything like this (grad school 30+ years ago), so I can't help with details. When I retire in a few years it would make a nice project for me to re-learn this stuff.

 

[stefanos.leon]

Thanks for the replies!

Actually I'm an experimentalist and it's not that trivial and easy for me to do these calculations, although I had a QFT course..

I was hoping an analytical description of e.g. the chapter "Production cross-sections for W and Z in pp colliders" of Aitchison.. (22.5)

Many thanks again,
Stefanos

 

[fzero]

Unless there's a new edition of Aitchison and Hey, that section is about $p\bar{p}$ collisions, which are very different from $pp$ collisions. In the former case, you have the tree level $q\bar{q}\rightarrow Z$, which, together with the leptonic decay, forms a Drell-Yan type process.

I'd suggest reviewing $e^+e^- \rightarrow \gamma \rightarrow e^+e^-$, which is covered in just about any QFT text. Next, figure out what changes when you have $\mu^+\mu^-$ in the final state. This is just kinematics, as it doesn't really change the form of the matrix element.

Next, use the electroweak Lagrangian to find the vertices and propagator to replace the photon with a Z, $e^+e^- \rightarrow Z \rightarrow \mu^+\mu^-$. This time the coupling constant at the vertices are different, as is the propagator, so the matrix element is a bit different.

Next, switch the electrons with quarks for $q\bar{q} \rightarrow Z \rightarrow \mu^+\mu^-$. The matrix element is similar, but evaluating the cross section would also involve summing over colors. I think Aitchison has some discussion of how to use form factors to relate this to $p\bar{p}$.

Now, as I said $pp$ collisions are different, since most of the processes that lead to Z production involve at least one gluon and no antiquarks in the initial state. I think Barger and Phillips "Collider Physics" has a few sections on pp, but I'm not sure.

 

[stefanos.leon]

Many many thanks!