A unified approach to NNLO soft and virtual corrections in electroweak, Higgs, QCD, and SUSY processes

TL;DR

The paper introduces a unified NNLO framework for soft and virtual QCD corrections across electroweak, Higgs, QCD, and SUSY processes by developing threshold-resummation-based master formulas applicable to hadron-hadron and lepton-hadron collisions in both MS and DIS schemes and in 1PI or PIM kinematics. It derives explicit NLO and NNLO expressions for simple color flows and extends to complex color flows, validating the approach by reproducing known NNLO results for Drell-Yan, Higgs production, DIS, and W+gamma, and providing new NNLO predictions for charged Higgs, vector bosons with jets, direct photons, heavy-quark production, jets, and squark/gluino production. The framework yields explicit color-space structures (H,S,ΓS) and universal two-loop anomalous-dimension components, enabling NNLL resummations and scale cancellation checks across processes. The unified method reduces duplicated effort, clarifies universality in soft-gluon corrections, and paves the way for higher-order extensions in precision collider phenomenology.

Abstract

I present a unified approach to calculating the next-to-next-to-leading order (NNLO) soft and virtual QCD corrections to cross sections for electroweak, Higgs, QCD, and SUSY processes. I derive master formulas that can be used for any of these processes in hadron-hadron and lepton-hadron collisions. The formulas are based on a unified threshold resummation formalism and can be applied to both total and differential cross sections for processes with either simple or complex color flows and for various factorization schemes and kinematics. As a test of the formalism, I rederive known NNLO results for Drell-Yan and Higgs production, deep inelastic scattering, and W+ gamma production, and I obtain expressions for several two-loop anomalous dimensions and other quantities needed in next-to-next-to-leading-logarithm (NNLL) resummations. I also present new results for the production of supersymmetric charged Higgs bosons; massive electroweak vector bosons; photons; heavy quarks in lepton-hadron and hadron-hadron collisions and in flavor-changing neutral current processes; jets; and squarks and gluinos. The NNLO soft and virtual corrections are often dominant, especially near threshold. Thus, a unified approach to these corrections is important in the search for new physics at present and future colliders.