New unified evolution equation

Abstract

We propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken variables x, which is an improved version of the Ciafaloni-Catani-Fiorani-Marchesini equation. In this new equation the cancellation of soft divergences between virtual and real gluon emissions is explicit without introducing infrared cutoffs and next-to-leading contributions to the Sudakov resummation can be included systematically. It is shown that the new equation reduces to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation at large x, to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation at small x, and to the modified BFKL equation with a dependence on momentum transfer Q, if hard virtual gluon contributions are retained.