Abstract

We propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken variables xx, 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, 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 xx, to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation at small xx, and to the modified BFKL equations with a dependence on momentum transfer QQ and with unitarity, if hard virtual gluon contributions and correction to strong rapidity ordering are retained, respectively.

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