Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1999-03-05
Eur.Phys.J. C10 (1999) 319-325
Physics
High Energy Physics
High Energy Physics - Phenomenology
14 pages in Latex, 1 figure in postscript file
Scientific paper
We demonstrate that all the known single- and double-logarithm summations for a parton distribution function can be unified in the Collins-Soper resummation technique by applying soft approximations appropriate in different kinematic regions to real gluon emissions. Neglecting the gluon longitudinal momentum, we obtain the $k_T$ (double-logarithm) resummation for two-scale QCD processes, and the Balitsky-Fadin-Kuraev-Lipatov (single-logarithm) equation for one-scale processes. Neglecting the transverse momentum, we obtain the threshold (double-logarithm) resummation for two-scale processes, and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (single-logarithm) equation for one-scale processes. If keeping the longitudinal and transverse momenta simultaneously, we derive a unified resummation for large Bjorken variable $x$, and a unified evolution equation appropriate for both intermediate and small $x$.
Li Hsiang-nan
Lim Jyh-Liong
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