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Three-body decay functions in space-like parton branches are implemented toevaluate transverse-momentum-dependent (TMD) parton distribution functions inthe next-to-leading logarithmic (NLL) order of quantum chromodynamics (QCD).Interference contributions due to the next-to-leading order contribution aretaken into account for the evaluation of the transverse momenta in initialstate parton radiations. Some properties of the decay functions are alsoexamined. As an example, we compare our results with an algorithm proposed inRef.1), in which a transverse momentum distributions are evaluated at the laststep of parton evolutions.

TMD Parton Distributions based on Three-Body Decay Functions in NLL Order of QCD