Complete 2-Loop Quantum Electrodynamic Contributions to the Muon Lifetime in the Fermi Model

1998/08/31 by Timo van Ritbergen, Robin G. Stuart · 9 citations
Engineering · Physics and Astronomy · #Muon and positron interactions and applications #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1103/physrevlett.82.488

published as Phys.Rev.Lett.82:488-491,1999 · 5 pages REVTeX. 2 figures. Uses axodraw.sty. References added, minor changes in text. To be published in Phys. Rev. Lett

arxiv created 1998/12/07 · openalex publication_date 1999/01/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The complete 2-loop quantum electrodynamic corrections to the muon lifetime are calculated in the Fermi theory. The exact result for the effects of virtual and real photons, virtual electrons, muons as well as e⁺e^\ensuremath- pair creation, is \ensuremathΔ\ensuremathΓ_QED⁽²⁾\phantom\rule0ex0ex=\phantom\rule0ex0ex\ensuremathΓ₀(\frac\ensuremathα\ensuremathπ)²[(156815)/(5184)\ensuremath-(1036)/(27)\ensuremathζ(2)\ensuremath-(895)/(36)\ensuremathζ(3)+(67)/(8)\ensuremathζ(4)+53\ensuremathζ(2)ln(2)]\phantom\rule0ex0ex=\phantom\rule0ex0ex\ensuremathΓ₀(\frac\ensuremathα\ensuremathπ)²6.743, where \ensuremathΓ₀ is the tree-level width. The theoretical error in the value of the Fermi coupling constant G_F is now rendered negligible compared to the experimental uncertainty coming from the measurement of the muon lifetime. The overall error in G_F is then roughly halved, giving G_F\phantom\rule0ex0ex=\phantom\rule0ex0ex(1.16637\ifmmode±\else\textpm\fi0.00001)\ifmmode×\else\texttimes\fi10^\ensuremath-5GeV^\ensuremath-2.

Citations

• Current algebra formulation of radiative corrections in gauge theories and the universality of the weak interactions
• Degenerate Systems and Mass Singularities
• Radiative corrections in theSU(2)L×U(1)theory: A simple renormalization framework

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