Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-03-26
Phys.Rev.D59:054008,1999
Physics
High Energy Physics
High Energy Physics - Phenomenology
7 pages, 1 figure; added: discussion of non-perturbative effects; discussion of charm and bottom quark mass averages; referenc
Scientific paper
10.1103/PhysRevD.59.054008
I calculate the QED coupling, alpha, directly in the MS-bar scheme using an unsubtracted dispersion relation for the three light quarks, and perturbative QCD for charm and bottom quarks. Compact analytical expressions are presented, making this approach particularly suitable for electroweak fits. After alpha^(-1) (m_tau) = 133.513 +- 0.025 is obtained in a first step, I perform a 4-loop renormalization group evolution with 3-loop matching conditions to arrive at alpha^(-1) (M_Z) = 127.934 +- 0.026 for alpha_s (M_Z) = 0.120. The corresponding hadronic contribution to the on-shell coupling is Delta alpha_had^(5) (M_Z) = 0.02779 +- 0.00019. The error is mainly from m_c, and from experimental uncertainties in e^+ e^- annihilation into unflavored and strange hadrons and tau decay data.
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