QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution, order-by-order in the strong coupling $alpha_s$, as a function of the soft-gluon resolution scale parameter. We examine the cases of transverse-momentum ordering and angular ordering. We illustrate that this approach can be used to treat distributions which depend both on longitudinal and on transverse momenta.
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