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.
Highlights
The full machinery which is necessary for a detailed quantitative comparison is available: the comparison will be the subject of the present paper
In particular, in refs. [10, 11] it was shown that dQCD and SCET resummed expressions differ by subleading logarithms of the hadronic scale, under suitable assumptions on the parton luminosity
Because in the SCET approach considered here it is a hadronic scale which is being resummed, and not a partonic scale as in the dQCD approach, it may seem that a comparison can only be made at the hadronic level, and this was the point of view taken in refs. [10,11,12,13], where the dependence of results on the parton luminosity was discussed
Summary
We present a step-by-step argument which takes from the dQCD to the SCET form of the resummed cross-section. The z-space form of the expression eq (2.30) is obtained by inverse Mellin transformation, and it is given by It follows that eq (2.37) differs from the starting SCET expression of the soft function eq (2.13) by terms which are suppressed by positive powers of 1 − z. If ln m2H μ2sN 2 is not a large log, this leads to the intermediate result eq (2.30), which only differs from the starting dQCD expression by a factor Cr(1)(N, m2H , μ2s), that only contains subleading logarithmic terms, generated by the interference of the neglected O(αS3) terms with the logs which are being resummed. This is the result of ref. [11] (where Cr(0)(N, m2H , μ2s) was called Cr), which corresponds to the very first step of the derivation presented here
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
