Abstract
Heavy fermion pair production in $e^+e^-$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the Principle of Maximum Conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass $m_f$, which enters the hard virtual corrections, and the other scale is of order $ v\,m_f$, where $v$ is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated.
Highlights
Heavy fermion pair production in eþe− annihilation is a fundamental process in the Standard Model (SM)
The conventional procedure of setting the renormalization scale as μr 1⁄4 mf violates the physical behavior of the reaction and leads to the unreliable predictions near the threshold region
(i) It is remarkable that two distinctly different scales are determined for the heavy fermion pair production near the threshold region using the principle of maximum conformality (PMC)
Summary
Heavy fermion pair production in eþe− annihilation is a fundamental process in the Standard Model (SM). An essential feature of heavy quark pair production in the threshold region of eþe− annihilation is the presence of singular terms from the QCD Coulomb corrections. It is conventional to set the renormalization scale to the mass of the heavy fermion μr 1⁄4 mf This conventional procedure obviously violates the physical behavior of the QCD corrections and will lead inevitably to unreliable predictions for the production cross sections in the threshold region. We shall apply the PMC to make comprehensive analyses for the heavy fermion pair production in eþe− annihilation near the threshold region.
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