Theory
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We define, the parton distribution function $f(x)$, as the probability for finding a parton carrying a momentum fraction $x$ of the proton. Usually we use subscripts to denote which parton we are considering, for example with $f_q(x)$ we denote the probability for finding a quark with momentum fraction $x$. To specify the flavor of the quark we use the subscripts u,d etc. The parton model predicts that these distribution functions depend only on the variable $x$. This behavior is known as scaling, which is also why $x$ is called the Bjorken scaling variable. If a parton has a certain $x$ it could either have this momentum fraction from the beginning, or it could initially have a larger momentum fraction and reduce it to $x$ through emission of gluons . The avaliable phase space for radiating gluons is larger when $Q^2$ is large. Therefore the distribution functions will show a greater probability to have smaller $x$, and smaller probability for carrying large $x$ for larger $Q^2$. This implies that the distribution functions are not only functions of $x$, but they are functions of $x$ and $Q^2$, $f(x)=f(x,Q^2)$. This is a central feature of QCD, and it is called scaling 