# Differential cross-section for partonic collisions

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1. Mar 1, 2015

### WarDieS

I am trying to calculate differential cross-section for partonic collisions (QCD) like
$$q + q \rightarrow q +q$$
$$q + \bar{q}\rightarrow q + q$$
$$g + g \rightarrow g + g$$

I can't find those calculations done anywhere, just the results and maybe some middle tips, thats all. As you may know those processes are hard and I need some help with them. Is there any source where its done in detail?

Thanks

2. Mar 2, 2015

### Orodruin

Staff Emeritus
You would do these as you would any other cross section, but there are some things to take into account. First of all you will never have a clean measurement. Quarks are confined and you cannot do quark-quark collisions without background from other processes. Since they are confined, you do not know the quark momenta, which is usually described as a fraction of the momentum of the containing particles. The probability of having different quarks and gluons with different momenta is usually encoded into parton distribution functions. I suggest you look up deep inelastic scattering and Drell-Yann processes.

Also, your second interaction breaks baryon number and so does not exist in the Standard Model.

3. Mar 2, 2015

### WarDieS

Thanks for your response. I just want to calculate them. The Peskin and Schroeder book proposes problems with the second and third examples I wrote.

I am aware of some of the things you said, but still I want to calculate them, I am asking for a detailed calculation already done or at least a good guide to do so.

4. Mar 2, 2015

5. Mar 2, 2015

### WarDieS

I am sorry there is a typo, the second one is
$$q + \bar{q} \rightarrow g + g$$.

Thanks for the paper, I will look it into detail, Its not what i had in mind but it appears it has some comments about how calculating.

6. Mar 2, 2015

Staff Emeritus
And charge conservation, so does not exist anywhere!

7. Mar 2, 2015

### RGevo

If you send me an email address I can send you notes I had from computing something like,
q qbar -> Q Qbar. This is basically the easiest thing to calculate and would be useful for the other.

The gluon ones need a bit more care because you have to sum over or average (or both) gluon polarisation states. This needs care because you have to limit your self to physical polarisation states, so one should know how to include the ghost term or alter the Feynman rule accordingly (or change gauge).

For these, I'd suggest doing the Compton scattering in chapter 5.5 of peskin then doing the non-abelian case discussed in chapter 16.

8. Mar 2, 2015

### WarDieS

Thanks RGevo, I am aware that I have to take with care the polarization states, ghost term and so on, thats why i am asking for an example, doing this is tricky for me. I will take a look at those chapters you talk about.

Thanks again