Factorization and resummation of s-channel single top quark production

TL;DR

This work applies Soft-Collinear Effective Theory to s-channel single top quark production, showing that in the hadronic threshold limit the cross section factorizes as $\sigma = f \otimes f \otimes H \otimes S \otimes J$, enabling momentum-space resummation via RG evolution to NNLL accuracy. It derives the full set of RG equations for the hard, soft, and jet functions and provides an NNLO expansion of the resummed cross section in terms of threshold distributions $D_n$, including the required 1-loop matching coefficients. Numerically, the resummation increases the NLO cross section by about $3\%-5\%$ at both the Tevatron and LHC and significantly reduces the Tevatron’s factorization-scale uncertainty, while the LHC shows no comparable improvement in scale dependence. The results offer a precise, RG-consistent framework for total s-channel single-top predictions and inform future refinements across collider energies and related production channels.

Abstract

In this paper we study the factorization and resummation of s-channel single top quark production in the Standard Model at both the Tevatron and the LHC. We show that the production cross section in the threshold limit can be factorized into a convolution of hard function, soft function and jet function via soft-collinear-effective-theory (SCET), and resummation can be performed using renormalization group equation in the momentum space resummation formalism. We find that in general, the resummation effects enhance the Next-to-Leading-Order (NLO) cross sections by about $3%-5%$ at both the Tevatron and the LHC, and significantly reduce the factorization scale dependence of the total cross section at the Tevatron, while at the LHC we find that the factorization scale dependence has not been improved, compared with the NLO results.