Resummation prescriptions and ambiguities in SCET vs. direct QCD: Higgs production as a case study

TL;DR

This paper compares soft-gluon resummation in SCET and direct QCD for Higgs production, revealing that differences mainly stem from power-suppressed contributions, with implications for theoretical predictions in high-energy physics.

Contribution

It establishes a direct analytic correspondence between SCET and dQCD resummation methods, clarifies how to implement each other's features, and assesses the impact of subleading terms on predictions.

Findings

Main difference arises from power-suppressed subleading contributions.

SCET NNLL resummation yields no significant enhancement over NNLO.

Quantitative differences are not intrinsic but tunable in either approach.

Abstract

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..