Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1999-05-21
Nucl.Phys. B560 (1999) 23-32
Physics
High Energy Physics
High Energy Physics - Phenomenology
11 pages, latex, no figures To be published in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(99)00475-7
The FAC, PMS, and BLM optimization methods are applied to the QED corrections to the muon lifetime in the Fermi V-A theory. The FAC and PMS scales are close to m_e, while the BLM scale nearly concides with the geometric average \sqrt{m_e m_\mu}. The optimized expressions are employed to estimate the third order coefficient in the \alpha(m_\mu) expansion and the theoretical error of the perturbative series. Using arguments based on effective field theory and a simple examination of Feynman diagrams, it is shown that, if contributions of O(\alpha m_\mu^2/M_W^2) are neglected, the corrections to muon decay in the SM factorize into the QED correction of the Fermi V-A theory and the electroweak amplitude g^2/(1-\Delta r), both of which are strictly scale-independent. We use the results to clarify how the QED corrections to muon decay and the Fermi constant G_F should be used in the SM, and what is the natural choice of scales if running couplings are employed.
Ferroglia Andrea
Ossola Giovanni
Sirlin Alberto
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