The resummation approach to evolution equations

Abstract

We derive the evolution equations of parton distribution functions appropriate in different kinematic regions in a unified and simple way using the resummation technique. They include the Gribov-Lipatov-Altarelli-Parisi equation for large momentum transfer $Q$, the Balitskii-Fadin-Kuraev-Lipatov equation for a small Bjorken variable $x$, and the Ciafaloni-Catani-Fiorani-Marchesini equation which unifies the above two equations. We propose a modified Balitskii-Fadin-Kuraev-Lipatov equation from the view point of the resummation. This modified version possesses an intrinsic $Q$ dependence and its predictions for the structure function $F_2(x,Q^2)$ are consistent with the HERA data.

25 pages in Latex