Regularization Schemes and Higher Order Corrections

Abstract

I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional reduction, but I find that the four dimensional helicity scheme produces incorrect results at next-to-next-to-leading order and singular results at next-to-next-to-next-to-leading order. It is not, therefore, a unitary regularization scheme.

References added and typographical errors corrected

References in corpus (3)

• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• Using Dimensional Reduction for Hadronic Collisions
• Dimensional Reduction applied to QCD at three loops

Cited by in corpus (30)

• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• A subtraction scheme for NNLO computations
• Interaction corrections to the minimal conductivity of graphene via dimensional regularization
• Multi-loop techniques for massless Feynman diagram calculations
• A prescription for projectors to compute helicity amplitudes in D dimensions
• Dimensional Regularization and Breitenlohner-Maison / 't Hooft-Veltman Scheme for ${\gamma }_5$ applied to Chiral YM Theories: Full One-Loop Counterterm and RGE Structure
• SCET approach to regularization-scheme dependence of QCD amplitudes
• Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order
• The one loop gluon emission light cone wave function
• Employing Helicity Amplitudes for Resummation
• Two-loop off-shell QCD amplitudes in FDR
• Three-loop MSSM Higgs-Boson Mass Predictions and Regularization by Dimensional Reduction
• The Four Dimensional Helicity Scheme Beyond One Loop
• The Infrared Structure of QCD Amplitudes and $H\to gg$ in FDH and DRED
• The four-dimensional helicity scheme and dimensional reconstruction
• Computation of $H\to gg$ in FDH and DRED: renormalization, operator mixing, and explicit two-loop results
• Regularization-scheme dependence of QCD amplitudes in the massive case
• Two-loop renormalisation of gauge theories in $4D$ Implicit Regularisation and connections to dimensional methods
• A step towards a consistent treatment of chiral theories at higher loop order: the abelian case
• FeynArts model file for MSSM transition counterterms from DREG to DRED
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Renormalisation Group Equations for BRST-Restored Chiral Theory in Dimensional Renormalisation: Application to Two-Loop Chiral-QED
• Three-loop anomalous dimensions for squarks in supersymmetric QCD
• Dimensional schemes for cross sections at NNLO
• Three-Loop Calculation of the Higgs Boson Mass in Supersymmetry
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Integrated Unitarity for Scattering Amplitudes
• Effective Field Theories for the LHC
• Signature of the $\gamma$+jet and dijet production mediated by an excited quark with QCD next-to-leading order accuracy at the LHC