| Summary: | Abstract We consider extensions of the soft-gluon effective coupling that generalize the Catani-Marchesini-Webber (CMW) coupling in the context of soft-gluon resummation beyond the next-to-leading logarithmic accuracy. Starting from the probability density of correlated soft emission in d dimensions we introduce a class of soft couplings relevant for resummed QCD calculations of hard-scattering observables. We show that at the conformal point, where the d-dimensional QCD β function vanishes, all these effective couplings are equal and they are also equal to the cusp anomalous dimension. We present explicit results in d dimensions for the soft-emission probability density and the soft couplings at the second-order in the QCD coupling α S. In d = 4 dimensions we obtain the explicit relation between the soft couplings at O $$ \mathcal{O} $$ ( α S 3 $$ {\alpha}_{\textrm{S}}^3 $$ ). Finally, we study the structure of the soft coupling in the large-n F limit and we present explicit expressions to all orders in perturbation theory. We also check that, at the conformal point, our large-n F results agree with the known result of the cusp anomalous dimension.
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