Year: 2020
Type: article
Abstract: In this article, based on the approach of McKeon et al., we show that the renormalization group equation related to the radiative mass scale $\ensuremath{\mu}$ operates as a summation over QCD perturbative terms. Employing the full QCD $\ensuremath{\beta}$ function within this summation, all logarithmic corrections can be presented as log-independent contributions. In another step of this approach, the renormalization scheme dependence for QCD observables characterized by Stevenson can be examined by specifying the renormalization scheme, in which the $\ensuremath{\beta}$ function beyond two-loop order is utilized. In this regard, there are two choices of renormalization scheme. In the first scheme, the QCD observable involves two powers of the running coupling constant, such that the perturbative series contains just two terms. In the second scheme, the perturbative series expansion is written as an infinite series in terms of the two-loop running coupling, which can be represented by the Lambert $W$ function. In both cases, the QCD observable involves parameters that are renormalization scheme invariant and the coupling constant, which is independent of the renormalization scale. We then consider another approach, which is called complete renormalization group improvement (CORGI). In this approach, by using the self-consistency principle it is possible to reconstruct the conventional perturbative series in terms of scheme-invariant quantities and the coupling constant as a function of the Lambert $W$ function. It should be noted that while in the renormalization group summation method of McKeon et al. the scheme dependence of observables is investigated separately from their scale dependence, in the CORGI approach, through the principle of self-consistency, both scale and scheme parameters are utilized. Then, we numerically examine these two approaches, considering two QCD observables. The first is the ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ ratio, investigated at three different colliding energies, and the second is the Higgs decay width to a gluon pair. We compare our results for ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ with the available experimental data. The results based on the McKeon et al. approach are in better agreement with the experimental data.
Authors: M. Akrami, A. Mirjalili
Institution: Yazd University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Funder: Yazd University
OpenAlex ID: W2995692821