2001/09/30 by Pietro Antonio Grassi, Pietro A. Grassi, Bernd A. Kniehl +2
Mathematics · Physics and Astronomy · #Amplitude #Combinatorics #Electron #Gauge (firearms) #Gauge theory #Graph #High-Energy Particle Collisions Research #Materials science #Mathematical physics #Mathematics #Order (exchange) #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Self-energy #Vertex (graph theory) #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.65.085001
published as Phys.Rev. D65 (2002) 085001 · 20 pages (Latex); minor changes included, accepted for publication in Phys. Rev. D
arxiv created 2002/01/18 · openalex publication_date 2002/03/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Fundamental properties of unstable particles, including mass, width, and partial widths, are examined on the basis of the Nielsen identities (NI) that describe the gauge dependence of Green functions. In particular, we prove that the pole residues and associated definitions of branching ratios and partial widths are gauge independent to all orders. A simpler, previously discussed definition of branching ratios and partial widths is found to be gauge independent through next-to-next-to-leading order. It is then explained how it may be modified in order to extend the gauge independence to all orders. We also show that the physical scattering amplitude is the most general combination of self-energy, vertex, and box contributions that is gauge independent for arbitrary s, discuss the analytical properties of the NI functions, and exhibit explicitly their one-loop expressions in the Z\ensuremath-\ensuremathγ sector of the standard model.