Soft gluons in logarithmic summations
H.-N. Li1 - J.-L. Lim2
1 Department of Physics, National Cheng-Kung University,
Tainan 701, Taiwan, P.R. China
2 Department of ElectroPhysics, National Chiao-Tung University, Hsinchu 300, Taiwan, P.R. China
Received: 9 March 1999 / Revised version: 12 April 1999 / Published online: 3 August 1999
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 (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 we keep the longitudinal and transverse momenta simultaneously, we derive a unified resummation for a large Bjorken variable x, and a unified evolution equation appropriate for both intermediate and small x.