FIG. 2: (a) Leading order Feynman diagrams. (b) Next to leading order loop diagrams. (c) Next to leading order tree diagrams. At high energies, the strong interactions between two hadrons can be factorized into three components: (a) the probability of finding the partons in the hadrons, (b) the in- teraction between quasi-free partons, and (c) fragmentation and hadronization of the final state partons. The process is schematically shown in Figure 1. The cross section of the hadron-hadron scattering with 4-momenta P$_{1}$ and P$_{2}$ can be written as [13] : The hard interaction between partons i, j is given by ˆ σ$_{ij}$ where p$_{1}$ = x$_{1}$P$_{1}$ and p$_{2}$ = x$_{2}$P$_{2}$ are 4-momenta of the two partons. It is independent of the incoming hadrons’ structure and can be calculated using pQCD. The function f$_{i}$ ( x, µ 2 $_{F}$) is the probability of finding a parton i with momentum fraction x at the scale µ$_{F}$ , and is called the parton distribution function PDF. The sum i, j is over the partons in the two respective hadrons. α$_{s}$ is the strong coupling constant. µ$_{R}$ is the renormalization scale, which is used to remove non-physical σ ( P$_{1}$, P$_{2}$ ) = ∑ i,j ∫ dx$_{1}$ ∫ dx$_{2}$ f$_{i}$ ( x$_{1}$, µ 2 $_{F}$) f$_{j}$ ( x$_{2}$, µ 2 $_{F}$)ˆ σ$_{ij}$ ( p$_{1}$, p$_{2}$, α$_{s}$ ( µ 2 $_{R}$) , Q $^{2}$/µ2 $_{F}$, Q $^{2}$/µ2 $_{R}$) (1) 4