https://doi.org/10.1140/epjc/s10052-019-7174-9
Letter
Soft-gluon effective coupling and cusp anomalous dimension
1
INFN, Sezione di Firenze and Dipartimento di Fisica e Astronomia, Università di Firenze, Sesto Fiorentino, 50019, Florence, Italy
2
International Center for Advanced Studies (ICAS), ECyT-UNSAM, Campus Miguelete, 25 de Mayo y Francia, 1650, Buenos Aires, Argentina
3
Physik Institut, Universität Zürich, 8057, Zurich, Switzerland
* e-mail: grazzini@physik.uzh.ch
Received:
6
May
2019
Accepted:
29
July
2019
Published online:
14
August
2019
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 
coupling 
. Although both effective couplings are well-defined in the physical four-dimensional space time, we examine their behaviour in 
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 
, where the d-dimensional QCD 
-function, 
, vanishes. We present the explicit expressions of the two soft-gluon couplings up to 
in d dimensions. In the four-dimensional case we compute the two soft couplings up to 
. For one of the two couplings, we confirm the result previously presented by other authors. For the other coupling, we obtain the explicit relation with the cusp anomalous dimension up to 
. We comment on Casimir scaling at .
© The Author(s), 2019
