The Parton Distribution Functions in the Limit $x_{Bj}\to 1$

Abstract

We review both the counting rule and the influence of the evolution in $Q^2$ for the large $x_{Bj}$ behaviour of the valance quark distribution functions. Based on a factorization procedure we present a more general perturbative treatment to compute this behaviour. A complete analysis is performed in the scalar $\phi^3_{[6]}$-theory for the parton distribution function of the ``meson'', which shows that logarithmical corrections arise from the distribution amplitude and that the reference momentum square $Q_0^2$ is fixed by $x_{Bj}$.