Fourier Transformation of the Renormalization-Invariant Coupling |
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Authors: | Shirkov D V |
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Institution: | (1) Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia |
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Abstract: | We discuss integral transformations of the QCD renormalization-invariant coupling (running coupling constant). Special attention is paid to the Fourier transformation, i.e., to the transition from the space–time to the energy–momentum representation. Our first conclusion is that the condition for the possibility of such a transition provides one more argument against the real existence of unphysical singularities observed in the perturbative QCD. The second conclusion relates to a way to translate some singular long-wave asymptotic behaviors to the infrared region of transferred momenta. Such a transition must be performed with the Tauberian theorem taken into account. This comment relates to the recent ALPHA collaboration results on the asymptotic behavior of the QCD effective coupling obtained by numerical lattice simulation. |
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Keywords: | Tauberian theorem IR behavior in QCD Fourier transformation |
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