Two-Loop Renormalization in the Standard Model Part III: Renormalization Equations and their Solutions

Abstract

In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics.

52 pages, LaTeX, 24 figures, uses axodraw.sty

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• Path integral quantization for massive vector bosons
• Complex-mass scheme and perturbative unitarity
• Bounding the Higgs Width Using Effective Field Theory
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• Vector form factor of the pion in chiral effective field theory
• Nucleon-to-Delta transition form factors in chiral effective field theory using the complex-mass scheme
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• Anomalous Threshold as the Pivot of Feynman Amplitudes
• Mass and width of the $\Delta (1232)$ resonance using complex-mass renormalization
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• Chiral effective field theories of the strong interactions
• Impact of New Physics on Momentum-Dependent Particle Widths and Propagators
• SMEFT deviations
• Axial-vector nucleon-to-delta transition form factors using the complex-mass renormalization scheme
• Infrared structure of $SU(N)\times U(1)$ gauge theory to three loops