# Parton distribution function and factorization scale

Consider some deep inelastic scattering $y f\to y f$, where $f$ is a parton inside a nucleon $N$, and $y$ is some particle. The cross-section is then $$\sigma_{\text{DIS}} = \int dx f_{N/f}(x,Q^{2})\sigma_{yf \to yf}(x,Q^{2}),$$ where $Q$ is called factorization scale.

My very basic question is:

• what is the factorization scale? How to determine it for the given process? Is it related to $N+y$ energy at CM frame?

In this sense, the factorisation scale $Q^2$ defines the point at which we make a separation of soft and hard dynamics. All low, non-perturbative scales $q^2< Q^2$ are encoded in the PDF while all high scales $q^2> Q^2$ are present in the hard scattering matrix element, susceptible to description via perturbation theory.