Next-to-next-to-next-to-leading-order soft-gluon corrections in hard-scattering processes near threshold

TL;DR

This work develops a unified threshold-resummation framework to derive master formulas for soft-gluon corrections up to NNNLO across hadron-hadron and lepton-hadron processes in the $ar{MS}$ scheme and in both 1PI and PIM kinematics. The approach expresses high-order corrections through hard and soft functions, color-space matrices, and soft anomalous dimensions, enabling fixed-order expansions that bypass infrared prescription issues. The author validates the method with applications to charged Higgs production at the LHC (NLL) and top-quark pair production at the Tevatron (NNLL), demonstrating substantial improvements in cross-section predictions and reduced scale dependence. These results underscore the importance of higher-order soft-gluon corrections for precise SM predictions and for backgrounds in searches for Higgs bosons and supersymmetric particles.

Abstract

I present a unified calculation of soft-gluon corrections to hard-scattering cross sections through next-to-next-to-next-to-leading order (NNNLO). Master formulas are derived, from a threshold resummation formalism, that can be applied to total and differential cross sections for hard-scattering processes in hadron colliders. I also present numerical results for charged Higgs production at the LHC where these corrections are large, and for top quark production at the Tevatron where these corrections greatly reduce the scale dependence of the cross section.

Figures (3)

• Figure 1: The total cross section for charged Higgs production at the LHC.
• Figure 2: The $K$-factors for charged Higgs production at the LHC.
• Figure 3: The scale dependence of top production in the $q {\bar{q}}$ channel at the Tevatron.