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On the Precise Determination of the Fermi Coupling Constant from the Muon Lifetime

Timo van Ritbergen, Robin G. Stuart

Abstract

The determination of the Fermi coupling constant, G_F, is examined in the light of recently calculated 2-loop QED corrections and planned experiments to measure the muon lifetime to a level below 1ppm. The methods used in the calculation of the QED corrections are described in detail. Sources of the dominant theoretical and experimental uncertainties are identified. Finally the incorporation of G_F into analyses using the full electroweak Standard Model is discussed.

On the Precise Determination of the Fermi Coupling Constant from the Muon Lifetime

Abstract

The determination of the Fermi coupling constant, G_F, is examined in the light of recently calculated 2-loop QED corrections and planned experiments to measure the muon lifetime to a level below 1ppm. The methods used in the calculation of the QED corrections are described in detail. Sources of the dominant theoretical and experimental uncertainties are identified. Finally the incorporation of G_F into analyses using the full electroweak Standard Model is discussed.

Paper Structure

This paper contains 19 sections, 115 equations, 11 figures.

Table of Contents

  1. Introduction
  2. The Muon Lifetime and The Fermi Coupling Constant
  3. The Definition of the Fermi Coupling Constant
  4. Renormalization of the Electromagnetic Coupling Constant
  5. The Calculation of the 2-loop QED Contributions
  6. The evaluation of primitive integrals
  7. Example 2
  8. Example 3
  9. Example 4
  10. The Theoretical Uncertainty
  11. Experimental Uncertainties
  12. Weak Corrections to the Muon lifetime
  13. 1-loop Electroweak Corrections to $\Delta r$
  14. 2-loop Electroweak Corrections to $\Delta r$
  15. $G_F$ in the Analysis of Electroweak Data
  16. ...and 4 more sections

Figures (11)

  • Figure 1: 4-loop diagrams whose cuts give contributions to the muon decay rate. The diagrams are grouped according to the main integration topologies A--G (see Figs. \ref{['TopoAFigs']}--\ref{['TopoDEFGFigs']}). The results for the individual diagrams are given in Appendix \ref{['sec:diagresults']}
  • Figure 2: Examples of triangle diagrams with different mass configurations for which the triangle relation Eq. (\ref{['defTriangleRel']}) holds. The lines are numbered according to Eq. (\ref{['defTriangle']}).
  • Figure 3: Integration topologies A$^{(3)}$ and A. The lines are numbered according to Eq.(\ref{['defTopoA3']}) and Eq. (\ref{['defTopoA']}) respectively
  • Figure 4: Integration topologies B and C. The lines are numbered according to Eqs. (\ref{['defTopoB']},\ref{['defTopoC']})
  • Figure 5: Integration topologies D -- G. The lines are numbered according to Eqs. (\ref{['defTopoE']}) and (\ref{['defTopoF']})
  • ...and 6 more figures