Quantum Corrections to the Weizsäcker--Williams Distribution Function as Small x

Abstract

We compute the quantum corrections to the gluon distribution function in the background of a non--Abelian Weizsäcker--Williams field. These corrections are valid to all orders in the effective coupling ${\alpha }_s\mu$, where ${\mu }^2$ denotes the average valence quark color charge squared per unit area. We find $\ln (1/x)$ logarithmic corrections to the classical gluon distribution function. The one loop corrections to the classical Weizsäcker-Williams field do not contribute to these singular terms in the distribution function. Their effect is to cause the running of ${\alpha }_s$.

Comments: Latex, 40 pages, 4 figures available upon request to the authors as postscript files