A Direct Test of Perturbative QCD at Small x

We show that recent data from HERA on the proton structure function $F_2$ at small $x$ and large $Q^2$ provide a direct confirmation of the double asymptotic scaling prediction of perturbative QCD. A linear rise of $\ln F_2$ with the scaling variable $\sigma$ is observed throughout the kinematic region probed at HERA, and the measured slope is in excellent agreement with the QCD prediction. This provides a direct determination of the leading coefficient of the beta function. At large values of the scaling variable $\rho$ the data display a small but statistically significant scaling violation.