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We compute the next-to-leading order corrections to soft-gluon radiationdifferentially in the one-emission phase space. We show that their contributionto the evolution of color dipoles can be obtained in a modified subtractionscheme, such that both one- and two-emission terms are amenable to Monte-Carlointegration. The two-loop cusp anomalous dimension is recovered naturally uponintegration over the full phase space. We present two independentimplementations of the new algorithm in the two event generators Pythia andSherpa, and we compare the resulting fully differential simulation to the CMWscheme.

Leading-color fully differential two-loop soft corrections to QCD dipole showers