The scale of soft resummation in SCET vs perturbative QCD

TL;DR

This paper compares soft resummation in SCET and perturbative QCD, showing how their results can be aligned through scale choices and analyzing the implications of different scale choices on factorization and Landau pole removal.

Contribution

It extends the logarithmic accuracy of SCET resummation to match standard QCD results and provides a master formula relating different scale choices in the two approaches.

Findings

SCET results can be extended to full agreement with QCD with proper scale choice.

Landau pole removal mechanisms differ between SCET and QCD approaches.

Certain subleading terms in SCET can dominate for generic parton distributions.

Abstract

We summarize and extend previous results on the comparison of threshold resummation, performed, using soft-collinear effective theory (SCET), in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross sections. We show that the logarithmic accuracy of this SCET result can be extended by half a logarithmic order, thereby bringing it in full agreement with the standard QCD result if a suitable choice is made for the soft scale mu_s which characterizes the SCET result. We provide a master formula relating the two approaches for other scale choices. We then show that with the Becher-Neubert scale choice the Landau pole, which in the perturbative QCD approach is usually removed through power- or exponentially suppressed terms, in the SCET approach is removed by logarithmically subleading terms which break factorization. Such terms may become leading for generic choices of parton distributions, and are always leading when resummation is used far enough from the hadronic threshold.