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We consider extensions of the soft-gluon effective coupling that generalizethe Catani--Marchesini--Webber (CMW) coupling in the context of soft-gluonresummation beyond the next-to-leading logarithmic accuracy. Starting from theprobability density of correlated soft emission in d dimensions we introduce aclass of soft couplings relevant for resummed QCD calculations ofhard-scattering observables. We show that at the conformal point, where thed-dimensional QCD $\beta$ function vanishes, all these effective couplings areequal and they are also equal to the cusp anomalous dimension. We presentexplicit results in d dimensions for the soft-emission probability density andthe soft couplings at the second-order in the QCD coupling $\alpha_s$. In d=4dimensions we obtain the explicit relation between the soft couplings at ${\calO}(\alpha_s^3).$ Finally, we study the structure of the soft coupling in thelarge-$n_F$ limit and we present explicit expressions to all orders inperturbation theory. We also check that, at the conformal point, ourlarge-$n_F$ results agree with the known result of the cusp anomalousdimension.

Soft-gluon effective coupling: perturbative results and the large-nF limit to all orders