Renormalization scale setting for some QCD observable, based on the PMC and CORGI approaches

Abstract

In this paper we present the principle of Maximum conformality (PMC) and Complete Renormalization Group Improvement (CORGI) approaches of scale setting which are based essentially on Refs. [S.J. Brodsky, M. Mojaza, X.G. Wu, Phys. Rev. D 89 (2014) 014027; X.G. Wu,Y. Ma, S.Q. Wang, S.J. Brodsky and M. Mojaza, Rep. Prog. Phys. 78 (2015) 126201; C.J. Maxwell, Nucl. Phys. Proc. Suppl. 86 (2000) 74; C.J. Maxell, A. Mirjalili, Nucl. Phys. B 299 (2000) 289]. The PMC establishes a systematic method to eliminate the renormalization scheme and renormalization scale dependencies of conventional perterbative QCD predictions. This approach, using the renormalization group equation, exposes a pattern of βi−terms in the perterbative series. Then by absorbing all βi−terms into the running coupling constant, one can obtain a result that is independent of renormalization scale and scheme. On the other hand the CORGI approach improves the precision of calculations. In this approach the standard perturbative series of QCD observable reconstructed in terms of scheme-invariant quantities. Here, we will examine the PMC and CORGI approaches by comparing its predictions for the electron-positron annihilation to hadrons and the Higgs decay width to gluon. The two results are compared with each other and with the available experimental data. At the end we may conclude which approach has more advantage in considering the perturbative series.