DOI 10.1007/s100529900118
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
Abstract
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.
Copyright Springer-Verlag
