kT and threshold resummations

We demonstrate that both the kT and threshold resummations can be performed in the Collins-Soper resummation formalism by evaluating soft gluon emissions with infrared cutoffs for the longitudinal and transverse loop momenta, respectively. The reason the kT resummation for a parton distribution function leads to suppression in the large b region, b being the conjugate variable of parton transverse momentum kT , and the threshold resummation leads to enhancement in the large N limit, N being the moment of a distribution function, is a consequence of opposite directions of double-logarithm evolutions. The kT and threshold resummations for an energetic final-state jet give suppression. The switch of the threshold resummation from enhancement to suppression is attributed to a nonvanishing jet invariant mass. In the same framework we derive a unification of the kT and threshold resummations for a parton distribution function by requiring infrared cutoffs for both longitudinal and transverse loop momenta. This unified resummation exhibits suppression at large b, similar to the kT resummation, and exhibits enhancement at small b, similar to the threshold resummation.