  We perform a comparison of soft-gluon resummation in SCET vs. direct QCD
(dQCD), using Higgs boson production in gluon fusion as a case study, with the
goal of tracing the quantitative impact of each source of difference between
the two approaches. We show that saddle-point methods enable a direct
quantitative comparison despite the fact that the scale which is resummed in
the two approaches is not the same. As a byproduct, we put in one-to-one
analytic correspondence various features of either approach: specifically, we
show how the SCET method for treating the Landau pole can be implemented in
dQCD, and how the resummation of the optimal partonic scale of dQCD can be
implemented in SCET. We conclude that the main quantitative difference comes
from power-suppressed subleading contributions, which could in fact be freely
tuned in either approach, and not really characteristic of either. This
conclusion holds for Higgs production in gluon fusion, but it is in fact
generic for processes with similar kinematics. For Higgs production, everything
else being equal, SCET resummation at NNLL in the Becher-Neubert implementation
leads to essentially no enhancement of the NNLO cross-section, unlike dQCD in
the standard implementation of Catani et al..
