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Optimization of R(e+e-) and "Freezing" of the QCD Couplant at Low Energies

A. C. Mattingly·P. M. Stevenson
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Abstract

The new result for the third-order QCD corrections to R_{e^+e^-}, unlike the old, incorrect result, is nicely compatible with the principle-of-minimal-sensitivity optimization method. Moreover, it leads to infrared fixed-point behaviour: the optimized couplant, alpha_s/pi, for R(e+e-) does not diverge at low energies, but "freezes" to a value 0.26 below about 300 MeV. This provides some direct theoretical evidence, purely from perturbation theory, for the "freezing" of the couplant -- an idea that has long been a popular and successful phenomenological hypothesis. We use the "smearing" method of Poggio, Quinn, and Weinberg to compare the resulting theoretical prediction for R(e+e-) with experimental data down to the lowest energies, and find excellent agreement.

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A. C. Mattingly, P. M. Stevenson. 1993-07-13. Optimization of R(e+e-) and "Freezing" of the QCD Couplant at Low Energies. https://doi.org/10.1103/physrevd.49.437

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