Small $x$ Contributions to the Structure Function $F_L(x,Q^2)$

Abstract

The gluon contributions to $F_L(x,Q^2)$ in ${\cal O}(\alpha_s)$ are calculated taking into account the transverse momentum of the initial state parton. In comparison with collinear factorization $F_L(x,Q^2)$, is not affected at large $x$ but takes smaller values in the small $x$ range. The onset of the $k_{\perp}$ effect is a function of $Q^2$.