Borel singularities at small x

Abstract

D.I.S. at small Bjorken $x$ is considered within the dipole cascade formalism. The running coupling in impact parameter space is introduced in order to parametrize effects that arise from emission of large size dipoles. This results in a new evolution equation for the dipole cascade. Strong coupling effects are analyzed after transforming the evolution equation in Borel ($b$) space. The Borel singularities of the solution are discussed first for the universal part of the dipole cascade and then for the specific process of D.I.S. at small $x$. In the latter case the leading infrared renormalon is at $b=1/\beta_0$ indicating the presence of $1/Q^2$ power corrections for the small-$x$ structure functions.