Differential cross-section for partonic collisions

In summary: I will use the information you sent me to calculate differential cross-section.In summary, RGevo says that differential cross-section can be calculated by using various methods discussed in other chapters of Peskin and Schroeder's Quarks and Gluons book.
  • #1
WarDieS
23
0
I am trying to calculate differential cross-section for partonic collisions (QCD) like
[tex] q + q \rightarrow q +q[/tex]
[tex] q + \bar{q}\rightarrow q + q [/tex]
[tex] g + g \rightarrow g + g[/tex]

I can't find those calculations done anywhere, just the results and maybe some middle tips, that's 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
 
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  • #2
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
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.
 
  • #5
ChrisVer said:
the second I think should have qqbar on the right side too... that way the baryon number is conserved.
maybe this can be helpful:
http://web.hep.uiuc.edu/atlas/OA_Software/QuarksAndGluonsReviewPaper.pdf
?
I am sorry there is a typo, the second one is
[tex] q + \bar{q} \rightarrow g + g [/tex].

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

And charge conservation, so does not exist anywhere!
 
  • #7
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
Thanks RGevo, I am aware that I have to take with care the polarization states, ghost term and so on, that's 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
 

1. What is the differential cross-section for partonic collisions?

The differential cross-section for partonic collisions is a measure of the likelihood of a specific interaction occurring between two particles, such as protons or quarks. It takes into account the energy and direction of the particles involved in the collision and is an important quantity in particle physics experiments.

2. How is the differential cross-section calculated?

The differential cross-section is calculated using the theoretical framework of quantum field theory and the mathematical technique of perturbation theory. It involves calculating the probability amplitude for the interaction to occur and then integrating over all possible energies and angles of the particles.

3. Why is the differential cross-section important in particle physics?

The differential cross-section provides crucial information about the nature of fundamental particles and their interactions. By studying the differential cross-section at different energies and angles, scientists can test and refine their theories of the strong, weak, and electromagnetic forces that govern the behavior of these particles.

4. How does the differential cross-section change with energy?

The differential cross-section typically increases with energy, as higher energy collisions have a greater chance of producing new particles. However, at very high energies, the cross-section may decrease due to the effects of quantum mechanics, such as particle scattering and production.

5. What is the significance of studying the differential cross-section for partonic collisions?

Studying the differential cross-section allows scientists to probe the fundamental building blocks of the universe and understand the underlying laws that govern their behavior. It also has practical applications, such as in the design and optimization of particle accelerators and detectors for high-energy physics experiments.

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