On the Behaviour of Non--Singlet Structure Functions at Small $x$

Abstract

The resummation of $O({\alpha }_s^{l+1}{\ln }^{2l}x)$ terms in the evolution kernels of non--singlet combinations of unpolarized and polarized structure functions is investigated. The agreement with complete calculations up to order ${\alpha }_s^2$ is demonstrated, and the leading small-$x$ contributions to the three--loop non--singlet splitting functions $P^{\pm }$ are derived. The additional contributions due to the resummed terms are studied numerically for the most important non--singlet structure functions. They are found to be about $1\%$ or smaller in the kinematical regions accessible at present and in the foreseeable future.

Comments: 10 pages, encoded ps file using uufiles