Soft Gluons in Logarithmic Summations
نویسنده
چکیده
We demonstrate that all the known singleand 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 kT (double-logarithm) resummation for two-scale QCD processes, and the Balitsky-Fadin-Kuraev-Lipatov (singlelogarithm) equation for one-scale processes. Neglecting the transverse momentum, we obtain the threshold (double-logarithm) resummation for twoscale processes, and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (singlelogarithm) 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.
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