Cross Section Large Hadron Collider

[genloz]

Homework Statement

b) The Large Hadron Collider (LHC), a 14 TeV proton-proton collider, will produce about a million Z0 per year. Explain why the cross section of such a process can be approximately written as:
$$d\sigma / d\Omega = F_{q/p}(X_{1})F_{q'/p}(X_{2})d\sigma '(qq' \rightarrow Z)/d\Omega$$
where
$$d\sigma '(qq' \rightarrow Z)/d\Omega$$ is the point like cross section.

Homework Equations

None given except as above...

The Attempt at a Solution

I can't really figure this one out at all... any points in the right direction would be greatly appreciated! Thankyou!

 

[Jhero]

Thank you for your question about the cross section of a process in the Large Hadron Collider (LHC). The cross section of a process is a measure of the likelihood of that process occurring. In this case, we are interested in the production of Z0 particles in the LHC.

The cross section for this process can be written as d\sigma / d\Omega, where d\sigma is the differential cross section and d\Omega is the solid angle in which the particles are detected. This quantity can be further decomposed into two parts: the parton distribution functions (F_{q/p}(X_{1}) and F_{q'/p}(X_{2})) and the point-like cross section (d\sigma '(qq' \rightarrow Z)/d\Omega).

The parton distribution functions represent the probability of finding a quark or anti-quark (q and q', respectively) within a proton (p) at a certain momentum fraction (X_{1} and X_{2}, respectively). These functions take into account the fact that protons are composed of quarks and gluons, and that these particles carry a fraction of the proton's momentum.

The point-like cross section represents the probability of a quark and anti-quark interacting to produce a Z0 particle in a point-like manner, meaning that the particles are assumed to be point-like and their interactions are described by the laws of quantum mechanics. This cross section is dependent on the solid angle d\Omega in which the particles are detected.

Therefore, the overall cross section for the production of Z0 particles in the LHC can be approximated by the product of these two factors, as shown in the equation you provided. This approximation is valid when the energies and momenta involved in the process are much larger than the masses of the particles involved, and when the particles are assumed to be point-like.

I hope this explanation helps to clarify the relationship between the overall cross section and the parton distribution functions and point-like cross section. Let me know if you have any further questions.