Search

We consider the extension of the CMW soft-gluon effective coupling [1] in the context of soft-gluon resummation for QCD hard-scattering observables beyond the next-to-leading logarithmic accuracy. We present two proposals of a soft-gluon effective coupling that extend the CMW coupling to all perturbative orders in the MS ¯ coupling α S . Although both effective couplings are well-defined in the physical four-dimensional space time, we examine their behaviour in d = 4 - 2 ϵ space time dimensions. We uncover an all-order perturbative relation with the cusp anomalous dimension: the (four dimensional) cusp anomalous dimension is equal to the d -dimensional soft-gluon effective coupling at the conformal point ϵ = β ( α S ) , where the d -dimensional QCD β -function, β ( α S ) - ϵ , vanishes. We present the explicit expressions of the two soft-gluon couplings up to O ( α S 2 ) in d dimensions. In the four-dimensional case we compute the two soft couplings up to O ( α S 3 ) . For one of the two couplings, we confirm the O ( α S 3 ) result previously presented by other authors. For the other coupling, we obtain the explicit relation with the cusp anomalous dimension up to O ( α S 4 ) . We comment on Casimir scaling at O ( α S 4 ) ., (© The Author(s) 2019.)