CHINESE JOURNAL OF PHYSICS VOL. 38, NO. 4 AUGUST 2000

New Unified Evolution Equation

Jyh-Liong Lim¹ and Hsiang-nan Li<sup>2

1</sup>Department of Electrophysics, National Chiao-Tung University,

Hsinchu, Taiwan 300, R.O.C.

²Department of Physics, National Cheng-Kung University,
Tainan, Taiwan 701, R.O.C.
(Received December 28, 2000)

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.

PACS. 12.38.Cy - Summation of perturbation theory.
PACS. 11.10.Hi $\;$- Renormalization group evolution of parameters.

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