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Three-Loop Polarization Function and ${\cal O}(α_s^2)$ Corrections to the Production of Heavy Quarks

K. G. Chetyrkin·J. H. Kuehn·M. Steinhauser
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Abstract

The three-loop vacuum polarization function $Π(q^2)$ induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the ${\cal O}(α_s^2)$ result for the production of heavy quarks $R(s)=σ(e^+e^-\to \mbox{hadrons})/σ(e^+e^-\to μ^+μ^-)$ can be extracted. Explicit formulae separated into the different colour factors are given.

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K. G. Chetyrkin, J. H. Kuehn, M. Steinhauser. 1996-06-05. Three-Loop Polarization Function and ${\cal O}(α_s^2)$ Corrections to the Production of Heavy Quarks. https://doi.org/10.1016/s0550-3213(96)00534-2

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