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

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..

21 pages, 4 figures; final version, to be published in JHEP. Eq. 2.39 and subsequent discussion added, fig.1 and corresponding discussion added, discussion on sqrt{z} prefactor added on pag.17

References in corpus (6)

• Dynamical Threshold Enhancement and Resummation in Drell-Yan Production
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• Threshold Resummation in Momentum Space from Effective Field Theory
• Resummed Higgs cross section at N${}^3$LL
• Updated Higgs cross section at approximate N${}^3$LO
• Updated Predictions for Higgs Production at the Tevatron and the LHC

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• Heavy neutrinos from gluon fusion
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• Threshold resummation of new partonic channels at next-to-leading power
• NNLL soft and Coulomb resummation for squark and gluino production at the LHC
• Resummed next-to-soft corrections to rapidity distribution of Higgs Boson to $\text{NNLO}+\overline{\text{NNLL}}$
• On the approaches to threshold resummation of rapidity distributions for the Drell-Yan process
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• The role of the threshold variable in soft-gluon resummation of the $t\bar{t}h$ production process